AI Grammar Summarizer

AI Grammar Summarizer — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Vatican News App

    Vatican News App

    The Vatican News App is an official mobile application software issued by the Vatican's Dicastery for Communication. Formerly titled The Pope App, the app was launched on January 23, 2013, under the auspices of the Pontifical Council for Social Communications, a now-defunct dicastery that was merged into the Secretariat (now Dicastery) for Communication in March 2016. Initially, The Pope App was available only on iOS devices, but became available for Android phones at the end of February 2013. The app is available for download on iOS and Android in five languages: English, French, Italian, Portuguese and Spanish. It was originally promoted as an application with focus on the figure of the Pope which made it possible to follow the Pope's events while they are taking place. Alerts notified the followers by informing and offering access to "official papal-related content in a variety of formats". The app also enabled its users to see areas of the Vatican through webcams allocated throughout St. Peter's Square in Rome that broadcast images. In early 2018, The Pope App was relaunched as the Vatican News App, accompanied by a redesign that eliminated many of the previous version's features, reducing the app to a more conventional news service, with increased emphasis on news from the Vatican and the worldwide Catholic Church and less focus on the day-to-day activities of the Pope.

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  • Galatea (video game)

    Galatea (video game)

    Galatea is an interactive fiction video game by Emily Short featuring a modern rendition of the Greek myth of Galatea, the sculpture of a woman that gained life. It took "Best of Show" in the 2000 IF Art Show and won a XYZZY Award for Best non-player character. The game displays an unusually rich approach to non-player character dialogue and diverts from the typical puzzle-solving in interactive fiction: gameplay consists entirely of interacting with a single character in a single room. Galatea is licensed under the Creative Commons BY-NC-ND 3.0 US license. == Gameplay == Galatea alters the typical interactive fiction game mechanics by concentrating instead on the player's interactions with a single non-player character (NPC), the eponymous Galatea. Much of the interest of the piece derives from the ambiguous nature of the player–NPC dialogue: the form of the conversation and, indeed, the nature of Galatea herself shift depending on the focus the player places on certain aspects of the character's personality. Numerous endings are possible. Gameplay centers around the developing dialogue between Galatea and the player when asking about topics in the previous conversation. Two commands, "think about" and "recap", are provided to keep track of what has already been said; the former is also used to advance the storyline, as the player character draws conclusions about the story as it has unfolded to that point. The game also encourages using sensory commands ("touch", "listen to", "look at"), adding immersion to the experience. == Plot == Galatea is loosely based on the myth of Pygmalion, who carved the sculpture of a woman. In the myth, he falls in love with the statue, named Galatea or Elise in different versions, and the goddess Venus brings her to life. The story begins at the opening of an exhibition of artificial intelligences. The player, alone, discovers Galatea displayed on a pedestal with a small information placard. She is illuminated by a spotlight and wears an emerald dress. Seeing the player about to turn away, Galatea says, "They told me you were coming." From this point, the story may proceed in a number of ways depending on the player's words and actions. === Multilinear interactive fiction === Short describes this as "multilinear interactive fiction": while interactive fiction in general allows the player to find their own way through the story, this leads in most cases to a single ending (or at least a single desired 'correct' ending). With Galatea, Short presents a story with around 70 different endings and hundreds of possible ways of reaching them. The plot is thus designed to appear open-ended with the development of the story entirely dependent on what the player decides to talk or ask about or what actions they choose to perform. Thus the original author and the player share in the creation of a work of fiction. == Development == In interviews, Emily Short has explained that Galatea arose out of her efforts to develop advanced dialog coding for interactive fiction engines. Although code for simple conversational programs like ELIZA have existed since the 1960s, and limited dialog options have existed in interactive fiction since the 1970s, Short's efforts to develop chatterbot-like dialog required her to produce a simple test case scenario to test NPC interaction. Thus the single-room, single-occupant Galatea was a natural result. Development of the game progressed organically with Short engaging in test runs and drafting new dialog options for every conversational dead-end that arose. The game's multiple endings also arose in a similar fashion although Short had intended that there be multiple endings from the start. Although the nature of the game's development as well as its minimalist final form has led to questions regarding whether it is really a game and not just an experimental conversational program, Short has suggested that to her the definition of interactive fiction requires nothing more than a world model and a parser, and "anything you can cook up with those features counts as IF." Short has acknowledged the helpful influence of the close-knit IF community and the "atmosphere in which experimentation is valued" as leading to the success of her works like Galatea. == Reception == Galatea was well received, achieving critical acclaim from interactive fiction reviewers and literary scholars. The game is considered to aspire to a new level of art in interactive fiction, and thereby to have revolutionized the genre, establishing its author, Emily Short, as one of the key figures in the modern interactive fiction scene. Fellow award-winning IF author, Adam Cadre has called Galatea "the best NPC ever"—a view that was echoed by Joystiq's John Bardinelli. Cadre also describes the game as an example of an alternative kind of puzzle where "interactivity comes in deciding where to go, what to see, what to say. Rather than having to open gates along a path, you discover that they're all open at first, but stepping through one causes others to close." Galatea was described in 2007 by Indiegames.com as a "fascinating journey." In a 2009 article, Rock, Paper, Shotgun praised the depth and detail of the game, the complexities of the character design and its "masterful balance between intricacy and simplicity", and "Galatea's emotional turmoil" that is "encoded sweetly into the subtext of what's going on. By simply interacting in a logical manner, you learn more about this character than any cut-scene or info-dump could ever hope to convey." This was reiterated in a 2010 1UP.com article that listed Galatea as #2 in its "Top 5 Introductory Interactive Fiction Games" feature, describing it as intriguingly replayable, and as a "surprisingly rich game for its apparent minimalism". In 2011, PC Gamer highlighted Galatea as an example of the artistic and literary aspects of the interactive fiction genre. The titular character, Galatea, has been compared to the 2007 Portal character GLaDOS due to similarities in the personalities of the characters.

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  • Artificial Intelligence Cold War

    Artificial Intelligence Cold War

    The Artificial Intelligence Cold War (AI Cold War) is a narrative in which geopolitical tensions between the United States of America (USA) and the People's Republic of China (PRC) could lead to a Second Cold War waged in the area of artificial intelligence technology rather than in the areas of nuclear capabilities or ideology. The context of the AI Cold War narrative is the AI arms race, which involves a build-up of military capabilities using AI technology by the US and China and the usage of increasingly advanced semiconductors which power those capabilities. According to a February 2019 publication by the Center for a New American Security, General Secretary of the Chinese Communist Party Xi Jinping – believes that being at the forefront of AI technology will be critical to the future of China's global military and economic power competition. == Origins of the term == The term AI Cold War first appeared in 2018 in an article in Wired magazine by Nicholas Thompson and Ian Bremmer. The two authors trace the emergence of the AI Cold War narrative to 2017, when China published its AI Development Plan, which included a strategy aimed at becoming the global leader in AI by 2030. While the authors acknowledge the use of AI by China to strengthen its authoritarian (totalitarian) rule, they warn against the perils for the US of engaging in an AI Cold War strategy. Thompson and Bremmer rather advocate for a technological cooperation between the US and China to encourage global standards in privacy and ethical use of AI. Shortly after the publication of the article in Wired magazine, the former U.S. Treasury Secretary Hank Paulson referred to the emergence of an ‘Economic Iron Curtain’ between the US and China, reinforcing the new AI Cold War narrative. == Proponents of the AI Cold War narrative == Politico contributed to reinforcing the AI Cold War narrative. In 2020, the paper argued that because of the increasing AI capabilities of China, the US and other democratic countries have to create an alliance to stay ahead of China. Former Google chief executive Eric Schmidt, together with Graham T. Allison alleged in an article in Project Syndicate that, in the context of the COVID-19 pandemic, the AI capabilities of China are ahead of the US in most critical areas. Scientists who have immigrated to the U.S. play an outsize role in the country's development of AI technology. Many of them were educated in China, prompting debates about national security concerns amid worsening relations between the two countries. Policy and technology experts have pointed to concerns about unethical use of AI which would be primarily associated with China. Ethics would therefore constitute a major ideological divide in the upcoming AI Cold War. Fears around disrupting supply chains and a global semiconductor shortage are linked to Taiwan's critical role in the production of semiconductors. 70% of semiconductors are either produced in Taiwan or transfer through Taiwan, where TSMC, world's largest chipmaker is headquartered. The PRC does not recognize the sovereignty of Taiwan and trade restrictions by the US on companies selling semiconductors to the PRC have disrupted in the past the commercial relationships between TSMC and Huawei. == Reactions to the AI Cold War == === Review of the validity of the AI Cold War narrative === Academics and observers expressed concerns about the validity and soundness of the AI Cold War narrative. Denise Garzia expressed concern in Nature that the AI Cold War narrative will undermine the efforts by the US to establish global rules for AI ethics. Researchers have warned in MIT Technology Review that the breakdown in international collaboration in the area of science because of the threat of the alleged AI Cold War would be detrimental to progress. Additionally, the AI Cold War narrative impacts on many more areas including the planning of supply chains and the proliferation of AI. The dissemination of the AI Cold War narrative could therefore be costly and destructive and exacerbate existing tensions. Joanna Bryson and Helena Malikova have pointed to Big Tech's potential interest in promoting the AI Cold War narrative, as technology companies lobby for less onerous regulation of AI in the US and the EU. A factual assessment of the existing AI capabilities of different countries shows a less binary reality than portrayed by the AI Cold War narrative. The AI Cold War started as a narrative but it could turn into a self-fulfilling prophecy and fuel an arms race, not only because of corporate interests but also because of the existing interests at different national security departments. Regarding cyber power, the International Institute for Strategic Studies published a study in June 2021, which argued that the online capabilities of China have been exaggerated and that Chinese cyber power is at least a decade behind the US, largely due to lingering security issues. === Restrictions to trading with China === US politicians and European industry players have invoked the looming AI Cold War as a reason to ban procurement by public authorities in Europe of Huawei 5G technology due to concerns over the Chinese state-sponsored surveillance industry. In 2019, the Trump administration successfully lobbied the Dutch government into stopping the Netherlands-based company ASML from exporting equipment to China. ASML manufactures a machine called an extreme ultraviolet lithography system used by semiconductor producers, including TSMC and Intel to produce state-of the-art microchips. The Biden administration adopted the same course of action as the Trump administration and requested the Netherlands to restrict sales by ASML to China, invoking national-security concerns. The trade restrictions imposed by the Trump administration affected semiconductors imports from China to the US and raised concerns by the US industry that supply chains will be disrupted in case of an AI Cold War. This prompted US technology companies to develop mitigation strategies including hoarding semiconductors and trying to set up local semiconductor production facilities, with the support of government subsidies. === Industrial policy initiatives === ==== United States ==== In June 2021, the US Senate approved the U.S. Innovation and Competition Act providing around 250 billion US dollars public money support to the US technological and manufacturing industry. The alleged Chinese threat in the area of technology helped secure a strong bipartisan support for the new legislation, amounting to the largest industrial policy move by the US in decades. Chinese authorities reproached to the US that the bill was “full of cold war zero-sum thinking”. The legislative bill is aimed at strengthening capabilities in the area of technology, such as quantum computing and AI specifically to face the competitive threat from China perceived as urgent. Senator Chuck Schumer, the leader of the Senate majority and one of the sponsors of the industrial policy bill invoked the threat of authoritarian regimes that want “grab the mantle of global economic leadership and own the innovations”. In 2022, U.S. Innovation and Competition Act was amended and turned into the Chips and Science Act with planned spending of 280 billion US dollars, 53 billion thereof are allocated directly to subsidies for semiconductors manufacturing. Commentators identified possible positive effects on innovation from the US attempts to compete with China in a perceived rivalry. Among the main beneficiaries of the US CHIPS Act are the semiconductor producers Intel, TSMC and Micron Technology. ==== European Chips Act ==== In February 2022, the European Union introduced its own European Chips Act initiative. The background of the initiative would be the objective of European strategic autonomy. The EU's initiative puts forward subsidies of 30 billion euros to encourage manufacturing of semiconductors in the EU. The US company Intel is one beneficiary of the initiative. The US and European chips acts raise concerns of protectionism and a risk of a subsidies "race to the bottom." === New world order === The AI Cold War heralds a new world order in geopolitics, according to Hemant Taneja and Fareed Zakaria. This new world order is a departure from the unipolar system dominated by the US. It is characterized by existence of two parallel digital ecosystems, ran by China and the US. In order to succeed countries that consider themselves as democracies are to align their technological ecosystems to that of the US, in a process labelled re-globalization.

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  • Fuzzy pay-off method for real option valuation

    Fuzzy pay-off method for real option valuation

    The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real option). The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem. == Method == The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the three cash-flow scenarios a corresponding definition with regards to a fuzzy number (triangular fuzzy number for three scenarios and a trapezoidal fuzzy number for four scenarios). This means that the pay-off distribution is created without any simulation whatsoever. This makes the procedure easy and transparent. The scenarios used are a minimum possible scenario (the lowest possible outcome), the maximum possible scenario (the highest possible outcome) and a best estimate (most likely to happen scenario) that is mapped as a fully possible scenario with a full degree of membership in the set of possible outcomes, or in the case of four scenarios used - two best estimate scenarios that are the upper and lower limit of the interval that is assigned a full degree of membership in the set of possible outcomes. The main observations that lie behind the model for deriving the real option value are the following: The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers. The mean value of the positive values of the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values. Real option value, ROV, calculated from the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The real option formula can then be written simply as: R O V = A ( P o s ) A ( P o s ) + A ( N e g ) × E [ A + ] {\displaystyle \mathrm {ROV} ={\frac {A(\mathrm {Pos} )}{A(\mathrm {Pos} )+A(\mathrm {Neg} )}}\times E[A_{+}]} where A(Pos) is the area of the positive part of the fuzzy distribution, A(Neg) is the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+]. As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. At the same time, simulation is not an absolutely necessary step in the Datar–Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar–Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different. == Use of the method == The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options). The method has been taken into use in some large international industrial companies for the valuation of research and development projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments. The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology and at the Tampere University of Technology in Finland.

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  • Nextcloud

    Nextcloud

    Nextcloud is a modular workspace platform designed to provide teams and businesses with a comprehensive environment for digital collaboration. Beyond central data management, it integrates office suites like Collabora Online and EuroOffice office suites. for seamless, cooperative workflows. The platform features built-in tools for chat, videoconferencing, and a privacy-focused AI assistant capable of running entirely on local LLMs. Supported by a rich ecosystem of apps, it can be hosted in the cloud or on premises and can scale up to millions of users. It has been translated into over 100 languages. == Features == Nextcloud files are stored in conventional directory structures, accessible via WebDAV if necessary. A SQLite, MySQL/MariaDB or PostgreSQL database is required to provide additional functionality like permissions, shares, and comments. Nextcloud can synchronize with local clients running Windows (Windows 8.1 and above), macOS (10.14 or later), Linux and FreeBSD. Nextcloud permits user and group administration locally or via different backends like OpenID or LDAP. Content can be shared inside the system by defining granular read/write permissions between users and groups. Nextcloud users can create public URLs when sharing files. Logging of file-related actions, as well as disallowing access based on file access rules is also available. Security options like brute-force protection and multi-factor authentication using TOTP, WebAuthn, Oauth2, and OpenID Connect are available. Nextcloud has planned new features such as monitoring capabilities, full-text search and Kerberos authentication, as well as audio/video conferencing, expanded federation and smaller user interface improvements. == History == In April 2016 Frank Karlitschek and most core contributors left ownCloud Inc. These included some of ownCloud's staff according to sources near to the ownCloud community. Karlitschek and many of these contributors went on to fork ownCloud, creating Nextcloud. The fork was preceded by a blog post of Karlitschek announcing his departure and raising questions about the management of the ownCloud, its community, and priorities between growth, money, and sustainability. There have been no official statements about the reason for the fork. However, Karlitschek mentioned the fork several times in a talk at the 2018 FOSDEM conference and in two appearances on the FLOSS Weekly podcast, emphasizing cultural mismatch between open source developers and business oriented people not used to the open source community. On June 2, within 12 hours of the announcement of the fork, the American entity "ownCloud Inc." announced that it is shutting down with immediate effect, stating that "[...] main lenders in the US have cancelled our credit. Following American law, we are forced to close the doors of ownCloud, Inc. with immediate effect and terminate the contracts of 8 employees." ownCloud Inc. accused Karlitschek of poaching developers, while Nextcloud developers such as Arthur Schiwon stated that he "decided to quit because not everything in the ownCloud Inc. company world evolved as I imagined". ownCloud GmbH continued operations, secured financing from new investors and took over the business of ownCloud Inc. In April 2018 Informationstechnikzentrum Bund (ITZBund) reported Nextcloud won the tender for "Bundescloud" (Germany government cloud) project. In August 2019 it was announced that the governments of France, Sweden and the Netherlands would use Nextcloud for file transfer. In January 2020 Nextcloud 18 "Nextcloud Hub" was released. The major change was direct integration with an Office suite (OnlyOffice) and Nextcloud announced that their goal was to compete with Office 365 and Google Docs. A partnership with Ionos was revealed – its hosting location in Germany and compliance with GDPR should support the goal of data sovereignty. In spring 2020 remote work and web conferencing usage increased due to the COVID-19 pandemic and Nextcloud released version 19 with chat and videoconferencing Talk app integrated into the application core. Communication with an optional "high performance back-end" allows self-hosting of web conferences with more than 10 participants. Collabora Online was introduced as another integrated office suite. In August 2021 Nextcloud was chosen as a collaboration platform for European cloud software GAIA-X. In a September 2021 European Commission report it was mentioned as "the most widely deployed Open Source content collaboration platform" Following the 2025 United States tariffs against the European Union, fear of overreliance on US cloud providers such as Microsoft 365 and Google Workspace increased, with Nextcloud being one of the foremost contenders to replace them. Some governmental organisations including the European Data Protection Supervisor and the German state of Schleswig-Holstein have since switched from Microsoft's Sharepoint to Nextcloud. According to Nextcloud, during the first 5 months of 2025, customer interest in the software had tripled.

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  • Fuzzy classification

    Fuzzy classification

    Fuzzy classification is the process of grouping elements into fuzzy sets whose membership functions are defined by the truth value of a fuzzy propositional function. A fuzzy propositional function is analogous to an expression containing one or more variables, such that when values are assigned to these variables, the expression becomes a fuzzy proposition. Accordingly, fuzzy classification is the process of grouping individuals having the same characteristics into a fuzzy set. A fuzzy classification corresponds to a membership function μ C ~ : P F ~ × U → T ~ {\textstyle \mu _{\tilde {C}}:{\tilde {PF}}\times U\to {\tilde {T}}} that indicates the degree to which an individual i ∈ U {\textstyle i\in U} is a member of the fuzzy class C ~ {\textstyle {\tilde {C}}} , given its fuzzy classification predicate Π ~ C ~ ∈ P F ~ {\textstyle {\tilde {\Pi }}_{\tilde {C}}\in {\tilde {PF}}} . Here, T ~ {\textstyle {\tilde {T}}} is the set of fuzzy truth values, i.e., the unit interval [ 0 , 1 ] {\textstyle [0,1]} . The fuzzy classification predicate Π ~ C ~ ( i ) {\textstyle {\tilde {\Pi }}_{\tilde {C}}(i)} corresponds to the fuzzy restriction " i {\textstyle i} is a member of C ~ {\textstyle {\tilde {C}}} ". == Classification == Intuitively, a class is a set that is defined by a certain property, and all objects having that property are elements of that class. The process of classification evaluates for a given set of objects whether they fulfill the classification property, and consequentially are a member of the corresponding class. However, this intuitive concept has some logical subtleties that need clarification. A class logic is a logical system which supports set construction using logical predicates with the class operator { ⋅ | ⋅ } {\textstyle \{\cdot |\cdot \}} . A class C = { i | Π ( i ) } {\displaystyle C=\{i|\Pi (i)\}} is defined as a set C of individuals i satisfying a classification predicate Π which is a propositional function. The domain of the class operator { .| .} is the set of variables V and the set of propositional functions PF, and the range is the powerset of this universe P(U) that is, the set of possible subsets: { ⋅ | ⋅ } : V × P F → P ( U ) {\displaystyle \{\cdot |\cdot \}:V\times PF\rightarrow P(U)} Here is an explanation of the logical elements that constitute this definition: An individual is a real object of reference. A universe of discourse is the set of all possible individuals considered. A variable V :→ R {\textstyle V:\rightarrow R} is a function which maps into a predefined range R without any given function arguments: a zero-place function. A propositional function is "an expression containing one or more undetermined constituents, such that, when values are assigned to these constituents, the expression becomes a proposition". In contrast, classification is the process of grouping individuals having the same characteristics into a set. A classification corresponds to a membership function μ that indicates whether an individual is a member of a class, given its classification predicate Π. μ : P F × U → T {\displaystyle \mu :PF\times U\rightarrow T} The membership function maps from the set of propositional functions PF and the universe of discourse U into the set of truth values T. The membership μ of individual i in Class C is defined by the truth value τ of the classification predicate Π. μ C ( i ) := τ ( Π ( i ) ) {\displaystyle \mu C(i):=\tau (\Pi (i))} In classical logic the truth values are certain. Therefore a classification is crisp, since the truth values are either exactly true or exactly false.

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  • AI-assisted targeting in the Gaza Strip

    AI-assisted targeting in the Gaza Strip

    As part of the Gaza war, the Israel Defense Forces (IDF) have used artificial intelligence to rapidly and automatically perform much of the process of determining what to bomb. Israel has greatly expanded the bombing of the Gaza Strip, which in previous wars had been limited by the Israeli Air Force running out of targets. These tools include the Gospel, an AI which automatically reviews surveillance data looking for buildings, equipment and people thought to belong to the enemy, and upon finding them, recommends bombing targets to a human analyst who may then decide whether to pass it along to the field. Another is Lavender, an "AI-powered database" which lists tens of thousands of Palestinian men linked by AI to Hamas or Palestinian Islamic Jihad, and which is also used for target recommendation. Critics have argued the use of these AI tools puts civilians at risk, blurs accountability, and results in militarily disproportionate violence in violation of international humanitarian law. == The Gospel == Israel uses an AI system dubbed "Habsora", "the Gospel", to determine which targets the Israeli Air Force would bomb. It automatically provides a targeting recommendation to a human analyst, who decides whether to pass it along to soldiers in the field. The recommendations can be anything from individual fighters, rocket launchers, Hamas command posts, to private homes of suspected Hamas or Islamic Jihad members. AI can process military intelligence far faster than humans. Retired Lt Gen. Aviv Kohavi, head of the IDF until 2023, stated that the system could produce 100 bombing targets in Gaza a day, with real-time recommendations which ones to attack, where human analysts might produce 50 a year. A lecturer interviewed by NPR estimated these figures as 50–100 targets in 300 days for 20 intelligence officers, and 200 targets within 10–12 days for the Gospel. === Technological background === The Gospel uses machine learning, where an AI is tasked with identifying commonalities in vast amounts of data (e.g. scans of cancerous tissue, photos of a facial expression, surveillance of Hamas members identified by human analysts), then looking for those commonalities in new material. What information the Gospel uses is not known, but it is thought to combine surveillance data from diverse sources in enormous amounts. Recommendations are based on pattern-matching. A person with enough similarities to other people labeled as enemy combatants may be labelled a combatant themselves. Regarding the suitability of AIs for the task, NPR cited Heidy Khlaaf, engineering director of AI Assurance at the technology security firm Trail of Bits, as saying "AI algorithms are notoriously flawed with high error rates observed across applications that require precision, accuracy, and safety." Bianca Baggiarini, lecturer at the Australian National University's Strategic and Defence Studies Centre wrote AIs are "more effective in predictable environments where concepts are objective, reasonably stable, and internally consistent." She contrasted this with telling the difference between a combatant and non-combatant, which even humans frequently can't do. Khlaaf went on to point out that such a system's decisions depend entirely on the data it's trained on, and are not based on reasoning, factual evidence or causation, but solely on statistical probability. === Operation === The IAF ran out of targets to strike in the 2014 war and 2021 crisis. In an interview on France 24, investigative journalist Yuval Abraham of +972 Magazine stated that to maintain military pressure, and due to political pressure to continue the war, the military would bomb the same places twice. Since then, the integration of AI tools has significantly sped up the selection of targets. In early November, the IDF stated more than 12,000 targets in Gaza had been identified by the target administration division that uses the Gospel. NPR wrote on December 14 that it was unclear how many targets from the Gospel had been acted upon, but that the Israeli military said it was currently striking as many as 250 targets a day. The bombing, too, has intensified to what the December 14 article called an astonishing pace: the Israeli military stated at the time it had struck more than 22,000 targets inside Gaza, at a daily rate more than double that of the 2021 conflict, more than 3,500 of them since the collapse of the truce on December 1. Early in the offensive the head of the Air Force stated his forces only struck military targets, but added: "We are not being surgical." Once a recommendation is accepted, another AI, Fire Factory, cuts assembling the attack down from hours to minutes by calculating munition loads, prioritizing and assigning targets to aircraft and drones, and proposing a schedule, according to a pre-war Bloomberg article that described such AI tools as tailored for a military confrontation and proxy war with Iran. One change that The Guardian noted is that since senior Hamas leaders disappear into tunnels at the start of an offensive, systems such as the Gospel have allowed the IDF to locate and attack a much larger pool of more junior Hamas operatives. It cited an official who worked on targeting decisions in previous Gaza operations as saying that while the homes of junior Hamas members had previously not been targeted for bombing, the official believes the houses of suspected Hamas operatives were now targeted regardless of rank. In the France 24 interview, Abraham, of +972 Magazine, characterized this as enabling the systematization of dropping a 2000 lb bomb into a home to kill one person and everybody around them, something that had previously been done to a very small group of senior Hamas leaders. NPR cited a report by +972 Magazine and its sister publication Local Call as asserting the system is being used to manufacture targets so that Israeli military forces can continue to bombard Gaza at an enormous rate, punishing the general Palestinian population. NPR noted it had not verified this; it was unclear how many targets are being generated by AI alone, but there had been a substantial increase in targeting, with an enormous civilian toll. In principle, the combination of a computer's speed to identify opportunities and a human's judgment to evaluate them can enable more precise attacks and fewer civilian casualties. Israeli military and media have emphasized this capacity to minimize harm to non-combatants. Richard Moyes, researcher and head of the NGO Article 36, pointed to "the widespread flattening of an urban area with heavy explosive weapons" to question these claims, while Lucy Suchman, professor emeritus at Lancaster University, described the bombing as "aimed at maximum devastation of the Gaza Strip". The Guardian wrote that when a strike was authorized on private homes of those identified as Hamas or Islamic Jihad operatives, target researchers knew in advance the expected number of civilians killed, each target had a file containing a collateral damage score stipulating how many civilians were likely to be killed in a strike, and according to a senior Israeli military source, operatives use a "very accurate" measurement of the rate of civilians evacuating a building shortly before a strike. "We use an algorithm to evaluate how many civilians are remaining. It gives us a green, yellow, red, like a traffic signal." ==== 2021 use ==== Kohavi compared the target division using the Gospel to a machine and stated that once the machine was activated in the war of May 2021, it generated 100 targets a day, with half of them being attacked, in contrast with 50 targets in Gaza per year beforehand. Approximately 200 targets came from the Gospel out of the 1,500 targets Israel struck in Gaza in the war, including both static and moving targets according to the military. The Jewish Institute for National Security of America's after action report identified an issue, stating the system had data on what was a target, but lacked data on what wasn't. The system depends entirely on training data, and intel that human analysts had examined and deemed didn't constitute a target had been discarded, risking bias. The vice president expressed his hopes this had since been rectified. === Organization === The Gospel is used by the military's target administration division (or Directorate of Targets or Targeting Directorate), which was formed in 2019 in the IDF's intelligence directorate to address the air force running out of targets to bomb, and which Kohavi described as "powered by AI capabilities" and including hundreds of officers of soldiers. In addition to its wartime role, The Guardian wrote it'd helped the IDF build a database of between 30,000 and 40,000 suspected militants in recent years, and that systems such as the Gospel had played a critical role in building lists of individuals authorized to be assassinated. The Gospel was developed by Unit 8200 of the Israeli Intelligence C

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  • Fuzzy control system

    Fuzzy control system

    A fuzzy control system is a control system based on fuzzy logic – a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively). Fuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, such that that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans. == History and applications == Fuzzy logic was proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas in a 1973 paper that introduced the concept of "linguistic variables", which in this article equates to a variable defined as a fuzzy set. Other research followed, with the first industrial application, a cement kiln built in Denmark, coming on line in 1976. Fuzzy systems were initially implemented in Japan. Interest in fuzzy systems was sparked by Seiji Yasunobu and Soji Miyamoto of Hitachi, who in 1985 provided simulations that demonstrated the feasibility of fuzzy control systems for the Sendai Subway. Their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the Namboku Line opened in 1987. In 1987, Takeshi Yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an "inverted pendulum" experiment. This is a classic control problem, in which a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth. Yamakawa subsequently made the demonstration more sophisticated by mounting a wine glass containing water and even a live mouse to the top of the pendulum: the system maintained stability in both cases. Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field. Japanese engineers subsequently developed a wide range of fuzzy systems for both industrial and consumer applications. In 1988 Japan established the Laboratory for International Fuzzy Engineering (LIFE), a cooperative arrangement between 48 companies to pursue fuzzy research. The automotive company Volkswagen was the only foreign corporate member of LIFE, dispatching a researcher for a duration of three years. Japanese consumer goods often incorporate fuzzy systems. Matsushita vacuum cleaners use microcontrollers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly. Hitachi washing machines use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergent. Canon developed an autofocusing camera that uses a charge-coupled device (CCD) to measure the clarity of the image in six regions of its field of view and use the information provided to determine if the image is in focus. It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot. The camera's fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the CCD and 6 to measure the rate of change of lens movement. The output is the position of the lens. The fuzzy control system uses 13 rules and requires 1.1 kilobytes of memory. An industrial air conditioner designed by Mitsubishi uses 25 heating rules and 25 cooling rules. A temperature sensor provides input, with control outputs fed to an inverter, a compressor valve, and a fan motor. Compared to the previous design, the fuzzy controller heats and cools five times faster, reduces power consumption by 24%, increases temperature stability by a factor of two, and uses fewer sensors. Other applications investigated or implemented include: character and handwriting recognition; optical fuzzy systems; robots, including one for making Japanese flower arrangements; voice-controlled robot helicopters (hovering is a "balancing act" rather similar to the inverted pendulum problem); rehabilitation robotics to provide patient-specific solutions (e.g. to control heart rate and blood pressure ); control of flow of powders in film manufacture; elevator systems; and so on. Work on fuzzy systems is also proceeding in North America and Europe, although on a less extensive scale than in Japan. The US Environmental Protection Agency has investigated fuzzy control for energy-efficient motors, and NASA has studied fuzzy control for automated space docking: simulations show that a fuzzy control system can greatly reduce fuel consumption. Firms such as Boeing, General Motors, Allen-Bradley, Chrysler, Eaton, and Whirlpool have worked on fuzzy logic for use in low-power refrigerators, improved automotive transmissions, and energy-efficient electric motors. In 1995 Maytag introduced an "intelligent" dishwasher based on a fuzzy controller and a "one-stop sensing module" that combines a thermistor, for temperature measurement; a conductivity sensor, to measure detergent level from the ions present in the wash; a turbidity sensor that measures scattered and transmitted light to measure the soiling of the wash; and a magnetostrictive sensor to read spin rate. The system determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water. It even adjusts for dried-on foods by tracking the last time the door was opened, and estimates the number of dishes by the number of times the door was opened. Xiera Technologies Inc. has developed the first auto-tuner for the fuzzy logic controller's knowledge base known as edeX. This technology was tested by Mohawk College and was able to solve non-linear 2x2 and 3x3 multi-input multi-output problems. Research and development is also continuing on fuzzy applications in software, as opposed to firmware, design, including fuzzy expert systems and integration of fuzzy logic with neural-network and so-called adaptive "genetic" software systems, with the ultimate goal of building "self-learning" fuzzy-control systems. These systems can be employed to control complex, nonlinear dynamic plants, for example, human body. == Fuzzy sets == The input variables in a fuzzy control system are in general mapped by sets of membership functions similar to this, known as "fuzzy sets". The process of converting a crisp input value to a fuzzy value is called "fuzzification". The fuzzy logic based approach had been considered by designing two fuzzy systems, one for error heading angle and the other for velocity control. A control system may also have various types of switch, or "ON-OFF", inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or another. Given "mappings" of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form: IF brake temperature IS warm AND speed IS not very fast THEN brake pressure IS slightly decreased. In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets. The output variable, "brake pressure" is also defined by a fuzzy set that can have values like "static" or "slightly increased" or "slightly decreased" etc. === Fuzzy control in detail === Fuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement. From three to seven curves are generally appropriate to cover the required range of an input value, or the "universe of discourse" in fuzzy jargon. As discussed earlier, the processing stage is based on a collection of logic rules in the form of IF-THEN statements, where the IF part is called the "antecedent" and the THEN part is called the "consequent". Typical fuzzy

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  • Cybersecurity in space

    Cybersecurity in space

    Cybersecurity in space involves the defense of all space assets (e.g. navigation systems, satellites, ground antennas, networks, etc.). The security of space can be affected by attacks such as disruption, corruption as well as the destruction of depended-upon assets/collected data. Government (e.g. militaries) and non-government sectors (e.g. financial industries) have started to become more reliant on numerous space-based services. Due to the criticality of these services, space security experts have identified these assets as high-value targets (HVT) that can cause detrimental consequences to all of Earth. == Scope and definitions == Space assets are broken down by three sub-sectors: the space component, the ground component, and the individual user component. The architecture of space assets is extremely complex and allows for a frequent attack vector utilized, the disruption by radio frequency (RF) cyber-attacks. In 2020, a memorandum was published by President Donald Trump, Space Policy Directive‑5 (SPD‑5). It established principles to ensure the safeguarding of all space assets. In 2023, the National Institute of Standards and Technology’s (NIST) published IR 8270, Introduction to Cybersecurity for Commercial Satellite Operations. This report established a baseline risk-management framework (RMF) to be implemented into space operations. == History == During the Cold War in the 1950s-1960s, the United States and Russia entered what was called the “Space Race”. By 1957, the Soviet Union successfully launched the first satellite into space named Sputnik. By 1961, the first key milestone was accomplished when the Soviet Union’s Yuri Gagarin became the first human to orbit Earth. This was later followed by the first American, Alan Shepard, to be launched into space; this was followed by John Glenn becoming the first American to orbit Earth in 1962. In 1969, a pinnacle milestone was reached when Apollo 11 launched into space and Neil Armstrong became the first man to walk on the moon. As space operations furthered, Commercial off-the-shelf products became increasingly popular but resulted in a rapid increase to the cyber-attack surface. Public awareness of space security did not increase until 2022, when the Viasat KA-SAT incident occurred, resulting in the disruption of a large number of modems across Europe. The attack was later accredited to Russia by the U.S. and the U.K. Policy and standards started to rapidly increase by 2020. The establishment of SPD-5 was released in 2020 followed by asset hardening instructions in 2022, and NIST’s IR 8270 in 2023. It was not until 2025 that Europe published their own findings in the Space Threat Landscape 2025 Report. This document led to the EU’s security proposals and standards. == Threats == === Radio-frequency Interference and Global Navigation Satellite Systems (GNSS) Spoofing === Space services are highly dependent on RF links for systems such as GNSS, however, a consequence of this dependency on RF is denial of service and deception. In 2017, the Black Sea maritime event occurred when numerous ships were subject to spoofing. Space services depend on RF links susceptible to jamming (denial) and spoofing (deception), including for GNSS/Positioning, Navigation, and Timing (PNT). Annotated incidents include the 2017 Black Sea maritime spoofing event affecting numerous ships, and extensive aviation GNSS spoofing patterns surveyed in various regions during 2024–2025. === Network intrusion and malware === Cyber threats can intrude and infect assets with malware. They do this by finding misconfiguration vulnerabilities, remote-management interfaces, and/or supply-chain vulnerabilities mainly in ground networks and user terminals. When KA-SAT occurred, it resulted from bulk modem disturbances. Forensic analysts later suggested malicious management controls and wiper malware as the root cause. === Supply-chain and lifecycle risks === The outsource of COTS components, external vendors, and software defined payloads allowed for vulnerabilities to emerge in the System/Product Lifecycle. In response, EU recommended the implementation of lifecycle-wide controls as mitigating factors. === Espionage, disruption, and influence === As Advanced Persistent Threats (APTs), Global Positioning System (GPS) intervention, and information warfare increased, assets like transponders became more frequent targets of attack. == Noteworthy incidents == The Viasat KA‑SAT incident of 2022, where a large number of modems in Europe were disrupted, resulted in the loss of telemetry access to a significant amount of wind turbines in Germany. The mass GNSS deception of the Black Sea in 2017 affected numerous ships when they started to convey fake central locations in Russia. Between 2024 and 2025, there was a mass, repetitive aviation GNSS spoofing that affected the aircraft of various regions. == Standards, guidelines, and best practices == SPD‑5 (U.S.) – This established risk-based engineering, verifying and ensuring positive control, and the implementation of risk mitigation controls. NIST IR 8270 – This created a RMF for COTS satellites. CISA/FBI SATCOM Advisory (AA22‑076) – Provided guidance on hardening techniques such as least-privileged, access control, encryption, etc.). ENISA Space Threat Landscape 2025 – It established the categorization of assets to organize threats, ensuring the observation of system/product lifecycle, and an RMF for COTS satellites. ECSS‑E‑ST‑80C (2024) – This established a standard for securing lifecycles in space, covering all segments (e.g. ground, launch, etc.). == Regulation and governance == As of 2025, there is no international regulations established for space assets, but the U.S., EU, and ESA institutional initiatives have published standards to address security concerns. The U.S. implemented SPD-5 and the Federal Communications Commission (FCC); the FCC addressed orbital debris. While the EU created standards to address technological mandates and support the implementation of NIS2. Lastly, the ESA created a special operations center to safeguard their satellites. International governance is still evolving, but forums have been held by the United Nations Committee on the Peaceful Uses of Outer Space. International conversations under forums such as the UN Committee on the Peaceful Uses of Outer Space (COPUOS) progressively note the cyber–space safety relationship, though formal global norms specific to space cybersecurity continue evolving. == Risk management approaches == Through RMF, mitigation controls have been implemented to reduce the risk of exploitation while increasing the security of space. Controls addressing mitigation include proper configuration, system hardening, zero-trust architectures, encryption, etc. Both the government and industries have placed an emphasis on incident response procedures to identify, contain, and remediate breaches.

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  • Fuzzy measure theory

    Fuzzy measure theory

    In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures, possibility/necessity measures, and probability measures, which are a subset of classical measures. == Definitions == Let X {\displaystyle \mathbf {X} } be a universe of discourse, C {\displaystyle {\mathcal {C}}} be a class of subsets of X {\displaystyle \mathbf {X} } , and E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} . A function g : C → R {\displaystyle g:{\mathcal {C}}\to \mathbb {R} } where ∅ ∈ C ⇒ g ( ∅ ) = 0 {\displaystyle \emptyset \in {\mathcal {C}}\Rightarrow g(\emptyset )=0} E ⊆ F ⇒ g ( E ) ≤ g ( F ) {\displaystyle E\subseteq F\Rightarrow g(E)\leq g(F)} is called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . == Properties of fuzzy measures == A fuzzy measure is: additive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\geq g(E)+g(F)} ; submodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\geq g(E)+g(F)} ; subadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\leq g(E)+g(F)} ; symmetric if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have | E | = | F | {\displaystyle |E|=|F|} implies g ( E ) = g ( F ) {\displaystyle g(E)=g(F)} ; Boolean if for any E ∈ C {\displaystyle E\in {\mathcal {C}}} , we have g ( E ) = 0 {\displaystyle g(E)=0} or g ( E ) = 1 {\displaystyle g(E)=1} . Understanding the properties of fuzzy measures is useful in application. When a fuzzy measure is used to define a function such as the Sugeno integral or Choquet integral, these properties will be crucial in understanding the function's behavior. For instance, the Choquet integral with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted averaging (OWA) operator. Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral. == Möbius representation == Let g be a fuzzy measure. The Möbius representation of g is given by the set function M, where for every E , F ⊆ X {\displaystyle E,F\subseteq X} , M ( E ) = ∑ F ⊆ E ( − 1 ) | E ∖ F | g ( F ) . {\displaystyle M(E)=\sum _{F\subseteq E}(-1)^{|E\backslash F|}g(F).} The equivalent axioms in Möbius representation are: M ( ∅ ) = 0 {\displaystyle M(\emptyset )=0} . ∑ F ⊆ E | i ∈ F M ( F ) ≥ 0 {\displaystyle \sum _{F\subseteq E|i\in F}M(F)\geq 0} , for all E ⊆ X {\displaystyle E\subseteq \mathbf {X} } and all i ∈ E {\displaystyle i\in E} A fuzzy measure in Möbius representation M is called normalized if ∑ E ⊆ X M ( E ) = 1. {\displaystyle \sum _{E\subseteq \mathbf {X} }M(E)=1.} Möbius representation can be used to give an indication of which subsets of X interact with one another. For instance, an additive fuzzy measure has Möbius values all equal to zero except for singletons. The fuzzy measure g in standard representation can be recovered from the Möbius form using the Zeta transform: g ( E ) = ∑ F ⊆ E M ( F ) , ∀ E ⊆ X . {\displaystyle g(E)=\sum _{F\subseteq E}M(F),\forall E\subseteq \mathbf {X} .} == Simplification assumptions for fuzzy measures == Fuzzy measures are defined on a semiring of sets or monotone class, which may be as granular as the power set of X, and even in discrete cases the number of variables can be as large as 2|X|. For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that g ( E ) = ∑ i ∈ E g ( { i } ) {\displaystyle g(E)=\sum _{i\in E}g(\{i\})} and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or λ {\displaystyle \lambda } -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively. === Sugeno λ-measure === The Sugeno λ {\displaystyle \lambda } -measure is a special case of fuzzy measures defined iteratively. It has the following definition: ==== Definition ==== Let X = { x 1 , … , x n } {\displaystyle \mathbf {X} =\left\lbrace x_{1},\dots ,x_{n}\right\rbrace } be a finite set and let λ ∈ ( − 1 , + ∞ ) {\displaystyle \lambda \in (-1,+\infty )} . A Sugeno λ {\displaystyle \lambda } -measure is a function g : 2 X → [ 0 , 1 ] {\displaystyle g:2^{X}\to [0,1]} such that g ( X ) = 1 {\displaystyle g(X)=1} . if A , B ⊆ X {\displaystyle A,B\subseteq \mathbf {X} } (alternatively A , B ∈ 2 X {\displaystyle A,B\in 2^{\mathbf {X} }} ) with A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } then g ( A ∪ B ) = g ( A ) + g ( B ) + λ g ( A ) g ( B ) {\displaystyle g(A\cup B)=g(A)+g(B)+\lambda g(A)g(B)} . As a convention, the value of g at a singleton set { x i } {\displaystyle \left\lbrace x_{i}\right\rbrace } is called a density and is denoted by g i = g ( { x i } ) {\displaystyle g_{i}=g(\left\lbrace x_{i}\right\rbrace )} . In addition, we have that λ {\displaystyle \lambda } satisfies the property λ + 1 = ∏ i = 1 n ( 1 + λ g i ) {\displaystyle \lambda +1=\prod _{i=1}^{n}(1+\lambda g_{i})} . Tahani and Keller as well as Wang and Klir have shown that once the densities are known, it is possible to use the previous polynomial to obtain the values of λ {\displaystyle \lambda } uniquely. === k-additive fuzzy measure === The k-additive fuzzy measure limits the interaction between the subsets E ⊆ X {\displaystyle E\subseteq X} to size | E | = k {\displaystyle |E|=k} . This drastically reduces the number of variables needed to define the fuzzy measure, and as k can be anything from 1 (in which case the fuzzy measure is additive) to X, it allows for a compromise between modelling ability and simplicity. ==== Definition ==== A discrete fuzzy measure g on a set X is called k-additive ( 1 ≤ k ≤ | X | {\displaystyle 1\leq k\leq |\mathbf {X} |} ) if its Möbius representation verifies M ( E ) = 0 {\displaystyle M(E)=0} , whenever | E | > k {\displaystyle |E|>k} for any E ⊆ X {\displaystyle E\subseteq \mathbf {X} } , and there exists a subset F with k elements such that M ( F ) ≠ 0 {\displaystyle M(F)\neq 0} . == Shapley and interaction indices == In game theory, the Shapley value or Shapley index is used to indicate the weight of a game. Shapley values can be calculated for fuzzy measures in order to give some indication of the importance of each singleton. In the case of additive fuzzy measures, the Shapley value will be the same as each singleton. For a given fuzzy measure g, and | X | = n {\displaystyle |\mathbf {X} |=n} , the Shapley index for every i , … , n ∈ X {\displaystyle i,\dots ,n\in X} is: ϕ ( i ) = ∑ E ⊆ X ∖ { i } ( n − | E | − 1 ) ! | E | ! n ! [ g ( E ∪ { i } ) − g ( E ) ] . {\displaystyle \phi (i)=\sum _{E\subseteq \mathbf {X} \backslash \{i\}}{\frac {(n-|E|-1)!|E|!}{n!}}[g(E\cup \{i\})-g(E)].} The Shapley value is the vector ϕ ( g ) = ( ψ ( 1 ) , … , ψ ( n ) ) . {\displaystyle \mathbf {\phi } (g)=(\psi (1),\dots ,\psi (n)).}

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  • Fuzzy pay-off method for real option valuation

    Fuzzy pay-off method for real option valuation

    The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real option). The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem. == Method == The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the three cash-flow scenarios a corresponding definition with regards to a fuzzy number (triangular fuzzy number for three scenarios and a trapezoidal fuzzy number for four scenarios). This means that the pay-off distribution is created without any simulation whatsoever. This makes the procedure easy and transparent. The scenarios used are a minimum possible scenario (the lowest possible outcome), the maximum possible scenario (the highest possible outcome) and a best estimate (most likely to happen scenario) that is mapped as a fully possible scenario with a full degree of membership in the set of possible outcomes, or in the case of four scenarios used - two best estimate scenarios that are the upper and lower limit of the interval that is assigned a full degree of membership in the set of possible outcomes. The main observations that lie behind the model for deriving the real option value are the following: The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers. The mean value of the positive values of the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values. Real option value, ROV, calculated from the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The real option formula can then be written simply as: R O V = A ( P o s ) A ( P o s ) + A ( N e g ) × E [ A + ] {\displaystyle \mathrm {ROV} ={\frac {A(\mathrm {Pos} )}{A(\mathrm {Pos} )+A(\mathrm {Neg} )}}\times E[A_{+}]} where A(Pos) is the area of the positive part of the fuzzy distribution, A(Neg) is the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+]. As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. At the same time, simulation is not an absolutely necessary step in the Datar–Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar–Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different. == Use of the method == The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options). The method has been taken into use in some large international industrial companies for the valuation of research and development projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments. The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology and at the Tampere University of Technology in Finland.

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  • Human-based evolutionary computation

    Human-based evolutionary computation

    Human-based evolutionary computation (HBEC) is a set of evolutionary computation techniques that rely on human innovation. == Classes and examples == Human-based evolutionary computation techniques can be classified into three more specific classes analogous to ones in evolutionary computation. There are three basic types of innovation: initialization, mutation, and recombination. Here is a table illustrating which type of human innovation are supported in different classes of HBEC: All these three classes also have to implement selection, performed either by humans or by computers. === Human-based selection strategy === Human-based selection strategy is a simplest human-based evolutionary computation procedure. It is used heavily today by websites outsourcing collection and selection of the content to humans (user-contributed content). Viewed as evolutionary computation, their mechanism supports two operations: initialization (when a user adds a new item) and selection (when a user expresses preference among items). The website software aggregates the preferences to compute the fitness of items so that it can promote the fittest items and discard the worst ones. Several methods of human-based selection were analytically compared in studies by Kosorukoff and Gentry. Because the concept seems too simple, most of the websites implementing the idea can't avoid the common pitfall: informational cascade in soliciting human preference. For example, digg-style implementations, pervasive on the web, heavily bias subsequent human evaluations by prior ones by showing how many votes the items already have. This makes the aggregated evaluation depend on a very small initial sample of rarely independent evaluations. This encourages many people to game the system that might add to digg's popularity but detract from the quality of the featured results. It is too easy to submit evaluation in digg-style system based only on the content title, without reading the actual content supposed to be evaluated. A better example of a human-based selection system is Stumbleupon. In Stumbleupon, users first experience the content (stumble upon it), and can then submit their preference by pressing a thumb-up or thumb-down button. Because the user doesn't see the number of votes given to the site by previous users, Stumbleupon can collect a relatively unbiased set of user preferences, and thus evaluate content much more precisely. === Human-based evolution strategy === In this context and maybe generally, the Wikipedia software is the best illustration of a working human-based evolution strategy wherein the (targeted) evolution of any given page comprises the fine tuning of the knowledge base of such information that relates to that page. Traditional evolution strategy has three operators: initialization, mutation, and selection. In the case of Wikipedia, the initialization operator is page creation, the mutation operator is incremental page editing. The selection operator is less salient. It is provided by the revision history and the ability to select among all previous revisions via a revert operation. If the page is vandalised and no longer a good fit to its title, a reader can easily go to the revision history and select one of the previous revisions that fits best (hopefully, the previous one). This selection feature is crucial to the success of the Wikipedia. An interesting fact is that the original wiki software was created in 1995, but it took at least another six years for large wiki-based collaborative projects to appear. Why did it take so long? One explanation is that the original wiki software lacked a selection operation and hence couldn't effectively support content evolution. The addition of revision history and the rise of large wiki-supported communities coincide in time. From an evolutionary computation point of view, this is not surprising: without a selection operation the content would undergo an aimless genetic drift and would unlikely to be useful to anyone. That is what many people expected from Wikipedia at its inception. However, with a selection operation, the utility of content has a tendency to improve over time as beneficial changes accumulate. This is what actually happens on a large scale in Wikipedia. === Human-based genetic algorithm === Human-based genetic algorithm (HBGA) provides means for human-based recombination operation (a distinctive feature of genetic algorithms). Recombination operator brings together highly fit parts of different solutions that evolved independently. This makes the evolutionary process more efficient.

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  • Actifsource

    Actifsource

    Actifsource is a domain-specific modeling workbench. It is realized as plug-in for the software development environment Eclipse. Actifsource supports the creation of multiple domain models which can be linked together. It comes with a UML-like graphical editor to create domain-specific languages and a general graphical editor to edit structures in the created languages. It supports code generation using user-defined generic code templates which are directly linked to the domain models. Code generation is integrated into Eclipse's incremental build process. == Interoperability == Actifsource can use models from other modelling tools by importing and exporting the ecore format which is defined by the Eclipse Modeling Framework. == Licensing policy == There are two versions of actifsource available: The free community edition which can be used freely for non-commercial projects and the enterprise edition which contains additional features. The enterprise edition comes with customer support and maintenance for a limited period of time. This package allows the customers to upgrade to new versions and maintenance releases during their support period.

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  • Uncertain inference

    Uncertain inference

    Uncertain inference was first described by C. J. van Rijsbergen as a way to formally define a query and document relationship in Information retrieval. This formalization is a logical implication with an attached measure of uncertainty. == Definitions == Rijsbergen proposes that the measure of uncertainty of a document d to a query q be the probability of its logical implication, i.e.: P ( d → q ) {\displaystyle P(d\to q)} A user's query can be interpreted as a set of assertions about the desired document. It is the system's task to infer, given a particular document, if the query assertions are true. If they are, the document is retrieved. In many cases the contents of documents are not sufficient to assert the queries. A knowledge base of facts and rules is needed, but some of them may be uncertain because there may be a probability associated to using them for inference. Therefore, we can also refer to this as plausible inference. The plausibility of an inference d → q {\displaystyle d\to q} is a function of the plausibility of each query assertion. Rather than retrieving a document that exactly matches the query we should rank the documents based on their plausibility in regards to that query. Since d and q are both generated by users, they are error prone; thus d → q {\displaystyle d\to q} is uncertain. This will affect the plausibility of a given query. By doing this it accomplishes two things: Separate the processes of revising probabilities from the logic Separate the treatment of relevance from the treatment of requests Multimedia documents, like images or videos, have different inference properties for each datatype. They are also different from text document properties. The framework of plausible inference allows us to measure and combine the probabilities coming from these different properties. Uncertain inference generalizes the notions of autoepistemic logic, where truth values are either known or unknown, and when known, they are true or false. == Example == If we have a query of the form: q = A ∧ B ∧ C {\displaystyle q=A\wedge B\wedge C} where A, B and C are query assertions, then for a document D we want the probability: P ( D → ( A ∧ B ∧ C ) ) {\displaystyle P(D\to (A\wedge B\wedge C))} If we transform this into the conditional probability P ( ( A ∧ B ∧ C ) | D ) {\displaystyle P((A\wedge B\wedge C)|D)} and if the query assertions are independent we can calculate the overall probability of the implication as the product of the individual assertions probabilities. == Further work == Croft and Krovetz applied uncertain inference to an information retrieval system for office documents they called OFFICER. In office documents the independence assumption is valid since the query will focus on their individual attributes. Besides analysing the content of documents one can also query about the author, size, topic or collection for example. They devised methods to compare document and query attributes, infer their plausibility and combine it into an overall rating for each document. Besides that uncertainty of document and query contents also had to be addressed. Probabilistic logic networks is a system for performing uncertain inference; crisp true/false truth values are replaced not only by a probability, but also by a confidence level, indicating the certitude of the probability. Markov logic networks allow uncertain inference to be performed; uncertainties are computed using the maximum entropy principle, in analogy to the way that Markov chains describe the uncertainty of finite-state machines.

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  • Shy Girl

    Shy Girl

    Shy Girl is a horror novel initially self-published in February 2025 by Mia Ballard. Publishing rights for the book were acquired by Hachette Book Group, which released the book in the United Kingdom in November 2025 and planned to publish it in the United States in 2026. Its US release was cancelled and its UK release was discontinued after it faced accusations of being created with generative AI. Ballard denied having personally used AI in the book's writing, claiming that a freelance editor had introduced AI-generated changes. She also stated that she would take legal action against the editor. == Premise == The novel follows Gia, a depressed woman with obsessive–compulsive disorder, who encounters a mysterious man named Nathan while looking for a sugar daddy to ease her financial troubles. Nathan offers to erase all of Gia's debts in exchange for her agreeing to live as his pet. Living like an animal convinces her that she is becoming an animal, making her behave like one. == Publication and cancellation == Shy Girl was first self-published online by Mia Ballard in February 2025. Marketing material described the book as a "buzzy BookTok sensation" and "bloody and unforgiving". The self-published edition of the book was highly successful and had over 4,900 ratings on Goodreads and an average score of 3.52 stars. In an interview, Ballard described her writing style as lyrical, feverish, and introspective, and stated she was more interested in "what it feels like to live inside a body" than in plot-driven storylines. Publishing rights were acquired by Hachette Book Group and it was published by its Wildfire imprint in the United Kingdom in November 2025. By March 2026, the book had sold 1,800 copies in the United Kingdom. A US release was planned for 2026 by the imprint Orbit Books. After the British publication, critics and readers began to make claims that the book appeared to have been written by generative AI. A January 2026 post on Reddit claimed that the book had many of the hallmarks of having been written with a large language model, and stated that it was "repulsive" that the book was accepted by Hachette. A two-and-a-half-hour video essay covering the book, titled "i'm pretty sure this book is ai slop", received 1.2 million views on YouTube by March 2026. In response, Hachette Book Group announced in March 2026 that it would cancel the book's US publication and discontinue its UK publication. It told The Wall Street Journal that it had made "a lengthy investigation" before deciding to cancel the book. Ballard told The New York Times that she had not used AI when writing the book, but that AI-generated elements were added by a freelance editor without her knowledge. She also stated that she could not elaborate on her claim because she was pursuing legal action against the editor. Writer Andrea Bartz opined that the situation "raises many concerns about trust, authenticity and publishing's readiness for a new, A.I.-assisted world", but that "readers made it abundantly clear they want books by humans, not machines".

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