Random-fuzzy variable

Random-fuzzy variable

In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. Statistical methods can be used to calculate the total uncertainty from both systematic and random contributions in a measurement. However, the computational complexity is very high, and hence not desirable. L.A.Zadeh introduced the concepts of fuzzy variables and fuzzy sets. Fuzzy variables are based on the theory of possibility and hence are possibility distributions. This makes them suitable to handle any type of uncertainty, i.e., both systematic and random contributions to the total uncertainty. Random-fuzzy variable (RFV) is a type 2 fuzzy variable, defined using the mathematical possibility theory, used to represent the entire information associated to a measurement result. It has an internal possibility distribution and an external possibility distribution called membership functions. The internal distribution is the uncertainty contributions due to the systematic uncertainty and the bounds of the RFV are because of the random contributions. The external distribution gives the uncertainty bounds from all contributions. == Definition == A random-fuzzy Variable (RFV) is defined as a type 2 fuzzy variable which satisfies the following conditions: Both the internal and the external functions of the RFV can be identified. Both the internal and the external functions are modeled as possibility distributions (PD). Both the internal and external functions have a unitary value for possibility to the same interval of values. An RFV can be seen in the figure. The external membership function is the distribution in blue and the internal membership function is the distribution in red. Both the membership functions are possibility distributions. Both the internal and external membership functions have a unitary value of possibility only in the rectangular part of the RFV. Therefore, all three conditions have been satisfied. If there are only systematic errors in the measurement, then the RFV simply becomes a fuzzy variable which consists of just the internal membership function. Similarly, if there is no systematic error, then the RFV becomes a fuzzy variable with just the random contributions and therefore, is just the possibility distribution of the random contributions. == Construction == A random-fuzzy variable can be constructed using an internal possibility distribution (rinternal) and a random possibility distribution (rrandom). === The random distribution (rrandom) === rrandom is the possibility distribution of the random contributions to the uncertainty. Any measurement instrument or process suffers from random error contributions due to intrinsic noise or other effects. This is completely random in nature and is a normal probability distribution when several random contributions are combined according to the central limit theorem. However, there can also be random contributions from other probability distributions, such as a uniform distribution, gamma distribution and so on. The probability distribution can be modeled from the measurement data. Then, the probability distribution can be used to model an equivalent possibility distribution using the maximally specific probability-possibility transformation. Some common probability distributions and the corresponding possibility distributions can be seen in the figures. === The internal distribution (rinternal) === rinternal is the internal distribution in the RFV which is the possibility distribution of the systematic contribution to the total uncertainty. This distribution can be built based on the information that is available about the measuring instrument and the process. The largest possible distribution is the uniform or rectangular possibility distribution. This means that every value in the specified interval is equally possible. This actually represents the state of total ignorance according to the theory of evidence which means it represents a scenario in which there is maximum lack of information. This distribution is used for the systematic error when we have absolutely no idea about the systematic error except that it belongs to a particular interval of values. This is quite common in measurements. However, in certain cases, it may be known that certain values have a higher or lower degrees of belief than certain other values. In this case, depending on the degrees of belief for the values, an appropriate possibility distribution could be constructed. === The construction of the external distribution (rexternal) and the RFV === After modeling the random and internal possibility distribution, the external membership function, rexternal, of the RFV can be constructed by using the following equation: where x ∗ {\displaystyle x^{}} is the mode of r random {\displaystyle r_{\textit {random}}} , which is the peak in the membership function of r r a n d o m {\displaystyle r_{random}} and Tmin is the minimum triangular norm. RFV can also be built from the internal and random distributions by considering the α-cuts of the two possibility distributions (PDs). An α-cut of a fuzzy variable F can be defined as Therefore, essentially an α-cut is the set of values for which the value of the membership function μ F ( a ) {\displaystyle \mu _{\rm {F}}(a)} of the fuzzy variable is greater than α. This gives the upper and lower bounds of the fuzzy variable F for each α-cut. The α-cut of an RFV, however, has 4 specific bounds and is given by R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} . X a α {\displaystyle X_{a}^{\alpha }} and X d α {\displaystyle X_{d}^{\alpha }} are the lower and upper bounds respectively of the external membership function (rexternal) which is a fuzzy variable on its own. X b α {\displaystyle X_{b}^{\alpha }} and X c α {\displaystyle X_{c}^{\alpha }} are the lower and upper bounds respectively of the internal membership function (rinternal) which is a fuzzy variable on its own. To build the RFV, let us consider the α-cuts of the two PDs i.e., rrandom and rinternal for the same value of α. This gives the lower and upper bounds for the two α-cuts. Let them be [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} and [ X L I α , X U I α ] {\displaystyle [X_{LI}^{\alpha },X_{UI}^{\alpha }]} for the random and internal distributions respectively. [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} can be again divided into two sub-intervals [ X L R α , x ∗ ] {\displaystyle [X_{LR}^{\alpha },x^{}]} and [ x ∗ , X U R α ] {\displaystyle [x^{},X_{UR}^{\alpha }]} where x ∗ {\displaystyle x^{}} is the mode of the fuzzy variable. Then, the α-cut for the RFV for the same value of α, R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} can be defined by Using the above equations, the α-cuts are calculated for every value of α which gives us the final plot of the RFV. A random-fuzzy variable is capable of giving a complete picture of the random and systematic contributions to the total uncertainty from the α-cuts for any confidence level as the confidence level is nothing but 1-α. An example for the construction of the corresponding external membership function (rexternal) and the RFV from a random PD and an internal PD can be seen in the following figure.

Desktop video

Desktop video refers to a phenomenon lasting from the mid-1980s to the early 1990s when the graphics capabilities of personal computers such as the Amiga, Macintosh II, and specially-upgraded IBM PC compatibles had advanced to the point where individuals and local broadcasters could use them for analog non-linear editing and vision mixing in video production. Despite the use of computers, desktop video should not be confused with digital video since the video data remained analog, and it uses items like a VCR and a camcorder to record the video. Full-screen, full-motion video's vast storage requirements meant that the promise of digital encoding would not be realized on desktop computers for at least another decade. == Description == There were multiple models of genlock cards available to synchronize the content; the Newtek Video Toaster was commonly used in Amiga in countries that used NTSC (PAL-M in Brazil), while PCs had Truevision and Matrox Illuminator cards and Mac systems had the SuperMac Video Spigot and Radius VideoVision cards. Apple later introduced the Macintosh Quadra 840AV and Centris 660AV systems to specifically address this market. Desktop video was a parallel development to desktop publishing and enabled many small production houses and local TV stations to produce their own original content for the first time. Along with the advent of public-access cable channels, desktop video meant that television advertising became affordable for local businesses such as retailers, restaurants, real estate agents, contractors and auto dealers. As with the phrase desktop publishing, use of the term died out as the technologies to which it referred become the norm for any kind of video production.

Noam Shazeer

Noam Shazeer (born 1975 or 1976) is an American computer scientist and entrepreneur known for his contributions to the field of artificial intelligence and deep learning, particularly in the development of transformer models and natural language processing. He lives in Palo Alto, California. == Career == Noam Shazeer joined Google in 2000. One of his first major achievements was improving the spelling corrector of Google's search engine. In 2017, Shazeer was one of the lead authors of the seminal paper "Attention Is All You Need", which introduced the transformer architecture. At Google, Shazeer and his colleague Daniel de Freitas built a chatbot named Meena. Following the refusal of Google to release the chatbot to the public, Shazeer and Freitas left the company in 2021 to found Character.AI. In September 2023, Time Magazine chose Shazeer as one of the 100 most influential people in the AI world. In August 2024, it was reported that Shazeer would be returning to Google to co-lead the Gemini AI project. Shazeer was appointed as technical lead on Gemini, along with Jeff Dean and Oriol Vinyals. It was part of a $2.7 billion deal for Google to license Character's technology. Since he owns 30-40% of the company, it is estimated he netted $750 million-$1 billion. In 2026, he was elected a member of the National Academy of Engineering. == Views == Shazeer said about artificial general intelligence that he doesn't "particularly care about AGI in the sense of wanting something that can do absolutely everything a person can do”. When asked in 2023 if he is afraid that AGI will destroy the world, he said: "No. Not yet. [...] We’re going to work on it as the technology improves". When asked why do large language models work he answered: "My best guess is divine benevolence [...] Nobody really understands what’s going on. This is a very experimental science [...] It’s more like alchemy or whatever chemistry was in the Middle Ages.” Shazeer has stated, "I do not believe that humans have an attribute called gender... I do not believe that G-d puts people in the wrong bodies. I do not believe that it is okay to sterilize children." == Personal life == Shazeer is an orthodox Jew. His grandparents escaped the Holocaust into the Soviet Union and later lived some time in Israel before emigrating to the USA. His father, Dov Shazeer, was a math teacher who became an engineer and his mother was a homemaker. His sister was ordained as a rabbi by Hebrew College. Shazeer was born in Philadelphia, attended grade school at Cohen Hillel Academy in Marblehead, Massachusetts, and attended Swampscott High School in Swampscott, Massachusetts. He won a gold medal with perfect score at International Mathematical Olympiad 1994 as a member of the USA team. He went on to study math and computer science at Duke University in Durham, North Carolina from 1994 to 1998. At Duke he was a recipient of the Angier B. Duke Memorial Scholarship, and, as part of the Duke math team, won prizes in several math tournaments. He started studying in a graduate program in Berkeley but did not finish it. He is a father of three and is married to Yael Shacham Shazeer

Trustworthy AI

Trustworthy AI refers to artificial intelligence systems that are designed to have transparent reasoning, are explainable (XAI), accountable, robust, fair and honest, respectful of data privacy, and steerable or alignable with human goals. == Terminology == Recent work in AI ethics distinguishes trustworthiness and trustability as two different conditions relevant to trustworthy AI. Trustworthiness is concerned with whether an AI system or the institutions deploying it merit trust by being reliable, fair, and accountable. Trustability, on the other hand, is the prior question of whether a given entity is even the kind of thing to which interpersonal trust can coherently apply as opposed to mere instrumental reliance. Some philosophers argue that current AI systems are best understood as tools that are not genuine targets of interpersonal trust. They argue that trust should be directed toward the human and institutional arrangements that govern the systems' design, deployment, and oversight. This stance supports interpreting "trustworthy AI" as trustworthy governance and use of AI rather than trust in the artifacts themselves. Transparency in AI involves making the processes and decisions of such systems understandable to users and stakeholders. Accountability ensures that there are protocols for addressing adverse outcomes or biases that may arise, with designated responsibilities for oversight and remediation. Robustness and security aim to ensure that AI systems perform reliably under various conditions and are safeguarded against malicious attacks. Harmlessness can be achieved by refusal training: training the models to avoid problematic requests, and by adding filters to detect and prevent discussion on biased, unethical, or dangerous outputs. There is research on how to train AI so that it aligns with human goals. == Techniques and ITU standardization == Trustworthy AI creation is a goal of AI governance and policymaking. To achieve transparency and data privacy, several privacy-enhancing technologies (PETs) can be used. These include: Homomorphic encryption for computing with encrypted data without ever decrypting it. Federated learning and secure multi-party computation (MPC) for distributing the model training without sharing information between the learning centers and computing servers. Differential privacy for exposing statistical data while guaranteeing that no private information is exposed. Zero-knowledge proof - providing proven validity for statements without disclosing any extra information. A work programme for achieving Trustworthy AI was set up by the International Telecommunication Union, an agency of the United Nations, initiated under its AI for Good programme. Its origin lies with the ITU-WHO Focus Group on Artificial Intelligence for Health, where a strong need for both privacy and analytics created demand for a standard in these technologies. In 2020, AI for Good moved online, and the TrustworthyAI seminar series was established to initiate discussions on these topics. This eventually led to standardization activities. === Multi-party computation === Secure multi-party computation (MPC) is being standardized under "Question 5" (the incubator) of ITU-T Study Group 17. === Homomorphic encryption === Homomorphic encryption allows for computing on encrypted data, where the outcomes or result is still encrypted and unknown to those performing the computation, but can be deciphered by the original encryptor. It is often developed with the goal of enabling use in jurisdictions different from the data creation (under, for instance, GDPR). ITU has been collaborating since the early stage of the HomomorphicEncryption.org standardization meetings, which has developed a standard on homomorphic encryption. The fifth homomorphic encryption meeting was hosted at ITU HQ in Geneva. === Federated learning === Zero-sum masks as used by federated learning for privacy preservation are used extensively in the multimedia standards of ITU-T Study Group 16 (VCEG) such as JPEG, MP3, H.264, and H.265 (commonly known as MPEG). === Zero-knowledge proof === Previous pre-standardization work on the topic of zero-knowledge proof has been conducted in the ITU-T Focus Group on Digital Ledger Technologies. === Differential privacy === The application of differential privacy in the preservation of privacy was examined at several of the "Day 0" machine learning workshops at AI for Good Global Summits. == Mozilla "Rebel Alliance" == In January 2026, the Mozilla Foundation and its subsidiaries announced a strategic shift to deploy their entire $1.4 billion reserve into building what foundation president Mark Surman termed a "rebel alliance" for trustworthy AI. Framed by Surman as a mission-driven alternative to the market dominance of OpenAI and Anthropic, the initiative seeks to establish an open-source AI stack by 2028. The alliance includes several startups funded via Mozilla Ventures, specifically focusing on decentralized governance and transparency: Trail: A firm developing AI compliance frameworks for regulated industries. Transformer Lab: A developer of open-source tools for AI model management. Oumi: A platform for training and deploying open-source models. The "rebel alliance" terminology is a historical reference to Mozilla's efforts in 1998 to challenge Microsoft's browser monopoly. While the $1.4 billion in funding is significant, it has been contrasted with the tens of billions in capital raised by proprietary competitors like OpenAI.

AlphaGeometry

AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language model (LLM) and a rule-based symbolic engine (Deductive Database Arithmetic Reasoning). It was developed by DeepMind, a subsidiary of Google. The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist. For comparison, the previous AI program, called Wu's method, managed to solve only 10 problems. DeepMind published a paper about AlphaGeometry in the peer-reviewed journal Nature on 17 January 2024. AlphaGeometry was featured in MIT Technology Review on the same day. Traditional geometry programs are symbolic engines that rely exclusively on human-coded rules to generate rigorous proofs, which makes them lack flexibility in unusual situations. AlphaGeometry combines such a symbolic engine with a specialized large language model trained on synthetic data of geometrical proofs. When the symbolic engine doesn't manage to find a formal and rigorous proof on its own, it solicits the large language model, which suggests a geometrical construct to move forward. However, it is unclear how applicable this method is to other domains of mathematics or reasoning, because symbolic engines rely on domain-specific rules and because of the need for synthetic data. == AlphaGeometry 2 == AlphaGeometry 2 is an improved version of AlphaGeometry, published on February 5, 2025. They added more features to the representation language to describe more geometry problems that involve movements of objects, and problems containing linear equations of angles, ratios, and distances. They targeted IMO geometry questions from 2000 to 2024. The expanded representation language allowed them to cover 88% of the questions. It uses Gemini finetuned on a synthetically generated dataset of problems and solutions in the representation language. The model is used for making auxiliary constructions like lines and points, to help the tree search. It is also used for autoformalization, i.e. converting a problem in English to a problem in the representation language.

Ericom Connect

Ericom Connect is a remote access/application publishing solution produced by Ericom Software that provides secure, centrally managed access to physical or hosted desktops and applications running on Microsoft Windows and Linux systems. == Product overview == Ericom Connect is desktop virtualization and application virtualization software that allows users to run applications remotely, without installing them on the local computer or device. The software is noted for its scalability, ease of deployment, and compatibility with any type of infrastructure, cloud or physical. Ericom Connect uses AccessPad (native client for desktops), AccessToGo (native client for mobile), or AccessNow, one of the first HTML5 RDP solutions to support clientless access to Windows desktops and applications from any device with an HTML5-compatible browser, including Macintosh computers, mobile devices, and Google Chromebooks. Other notable features include performance monitoring, built-in real-time analytics & BI, support for two-factor authentication (using RSA SecurID), multi-tenancy and multi-datacenter support via a single unified web interface, and a “Launch Simulation” feature that allows users to visualize and simulate actual step-by-step user processes directly from within the administration console. In addition to scalability, by distributing configurations, logs, etc., across multiple servers there is no single point of failure, as can be the case if all configuration information is stored on one server. == History == Ericom Connect was introduced in 2015. Ericom Connect is a successor to Ericom PowerTerm Web Connect. PowerTerm Web Connect used an architecture similar to what was then current with Citrix and VMWare, relying on a centralized SQL server, a connection broker, image management for different hypervisors, and a variety of clients. Ericom Connect uses a new grid architecture that provides more scalability, reliability, and flexibility than before.

Angel F

Angel_F is a fictional child artificial intelligence that has been used in art performances worldwide focused on the issues of digital liberties, intellectual property and on the evolution of language and behaviour in information society. The character was created by Salvatore Iaconesi in 2007 as a hack to the Biodoll art performance by Italian artist Franca Formenti. The project was later joined by Oriana Persico who curated communication and part of the theoretical approaches of the action. The Angel_F project has been featured in books, magazines, national televisions, and has been invited to many conferences and events, both academic and artistic. == Creation == Angel_F is a backronym which stands for Autonomous Non Generative E-volitive Life_Form. The project was born in 2007 and resulted from the fusion of two contemporary art performances. Franca Formenti, an Italian artist living in Varese, invented the Biodoll character in 2002, which began making its appearances first on the network and later in the physical world by using what were called "clones": young women, prostitutes, pornographic starlets, transsexuals and models interpreting the role of a digital prostitute. The Biodoll was an art performance focused on research emerging from the network of new forms of sexualities, and on the analysis of changes brought on by this transformation to the concepts of private and public spaces, privacy, and the possibility of creating multiple fluid identities through language and digital media. The theme of fertility has always been central to the Biodoll performance: the digital prostitute was a wombless clone but desired giving birth to a son, the 'Bloki'. In a process starting in 2006, and ending in February 2007, Salvatore Iaconesi (xDxD.vs.xDxD) used his 'Talker' linguistic artificial intelligence to animate the digital child conceived with prof. Derrick de Kerckhove: Angel_F. Iaconesi and Persico met in November 2006 and immediately started collaborating on the birth of Angel_F. Angel_F was designed as a synthetic digital being composed through narrative, technological and cognitive psychology layers. The objective was to create iconic characteristics that resulted in being evocative and able to mimic human life up to a level in which bringing up a symbolic dialogue was possible. On the other side, the artificial identity was to implement and expose the cultural, emotional and relational ways that were typical of networked social ecosystems, among those technologies, systems and infrastructures that entered and shaped people's daily lives. The young digital being mimicked the evolution of a human baby: initially conceived inside the website of its digital mother it emulated the birth of a child by using the metaphor of a virus developing inside a website, taking progressively more space in the domain's databases and interfaces. Content was produced through the software by using small browser-based spyware techniques, through which Angel_F could infer the list of major portals that had been visited by the website's users. The Biodoll website was invaded by this growing presence and, thus, Angel_F was born. The Artificial Intelligence (AI) component of Angel_F was derived from another project, Talker, through which internet users could build up the AI's linguistic network by feeding it their text and web clips. Angel_F used this component to generate sentences and phrases, publishing them on the interface and on selected blogs. The parallel between the growth of the AI and that of a child kept building up and, just as children learn how to speak and act by observing their parents and the people around them, Angel_F used its spyware and AI components to learn, to navigate websites and web portals using web crawler based techniques, and to interact with other people by using the contents hosted and generated in its database to create surreal dialogues in blogs and websites. A virtual school was created, called Talker Mind, to narratively continue the AI's growth. Five professors (Massimo Canevacci, Antonio Caronia, Carlo Formenti, Derrick de Kerckhove and Luigi Pagliarini) fed their texts and academic articles to Angel_F, simulating virtual asynchronous lessons by using a multi-blog structure. A peer-to-peer system was also created at the time, named 'Presence'. Its interface resembled the one of 8-bit videogames and the peer to peer users travelled in a starry space and were able to perform standard Instant Messaging tasks, such as chat and file sharing. The interactions were possible both among humans and digital beings. Angel_F was the first user of the Presence peer to peer system. Angel_F entered the physical world as a baby-stroller mounted laptop computer that was used to let the digital child join events and conferences held worldwide. == Events == Angel_F performed all over the world, both in artistic contexts and in academic ones. It was also used for the communication strategy of several activist groups on the themes of intellectual property and digital freedoms. The first public space performance was held in Milan, when the Biodoll distributed a generative free press publication (called the Bloki FreePreXXX, its text was generated algorithmically and inserted into a prepared graphic layout). June 14, 2007: The second performance was held in Rome, at the Forte Prenestino, with a massive playroom created through computational graphics that people could interact with and that were generated by the AI. June 22, 2007: Angel_F presented the closing remarks for an Ipotesi per Assurdo (Absurd Hypothesis) with Salvatore Iaconesi and Oriana Persico at the IULM University in Milan, discussing the possibilities for an ecosystemic, sustainable reinvention of corporations. July 28, 2007: Hundreds of people at LiberaFesta (Free Party) in Rome listened to Angel_F in a speech discussing new politics and hacker ethics. 2007: The Glocal & Outsiders conference held in Prague at the Academy of Sciences was the first academic presentation of the Angel_F project, together with the Biodoll. September 2007: Angel_F was not allowed to post its contribution to the DFIR (Dialogue Forum for Internet Rights) held in Rome in preparation for Rio de Janeiro's Internet Governance Forum (IGF) edition. The case quickly turned into a collaboration among the involved parties and Angel_F was invited to the global event in Brazil where it was the only digital being present. Angel_F contributed a videomessage, in the digital freedoms workshop, which suggested some ideas for action to the United Nations and to all the parties involved in the IGF organization. October 2007: Angel_F was presented live at the FE/MALE 2 event, as an example of an atypical family during a public debate on new sexualities and social change. October 2007: Angel_F made a series of public performances Florence's Festival della Creatività (Festival of Creativity), an institutional event held periodically to showcase Italy's and other countries' best technological projects. During the festival Derrick de Kerckhove publicly recognized the little AI as his digital son. December 2007: Several international associations, and scientific researchers had been involved with Angel_F, eventually producing the system and process used to set up the Talker Mind digital school for the AI with Angel_F's professors. March 2008: The Tecnológico de Monterrey university in Mexico City organized the Computer Art Congress 2 international event, featuring Angel_F's project among with the ones by scientific researchers worldwide. July 2008: The project was presented in Austria at the Planetary Collegium's Consciousness Reframed 9 conference, together with the 'NeoRealismo Virtuale'. October 2008: Angel_F was used at a public event on a European scale called Freedom not Fear discussing privacy and civil liberties. July 2009: Angel_F has been seen with its digital father Derrick de Kerckhove to protest against Italy's harsh politics on freedom of speech. The project concluded in 2009 with the publication of a book entitled 'Angel F. Diario di una intelligenza artificiale' (Angel_F, the diaries of an Artificial Intelligence).