The AI Con: How to Fight Big Tech's Hype and Create the Future We Want is a 2025 non-fiction book by linguist Emily M. Bender and sociologist Alex Hanna. It argues that much of what is labeled "artificial intelligence" is a misleading term that obscures ordinary automation while concentrating power in a small number of technology firms. The book was published in May 2025 by Harper in the United States and Bodley Head in the United Kingdom. It was developed alongside the authors' long-running podcast Mystery AI Hype Theater 3000, which critiques exaggerated claims about AI. == Synopsis == The authors present AI as a marketing umbrella that encourages audiences to infer understanding and agency where none exist. They argue readers should treat such language skeptically and to separate specific automated tasks from broad claims of intelligence. The book describes a recurring hype cycle in which corporate narratives justify data and labor extraction, the replacement of human services with cheaper substitutes, and the diversion of attention from present harms to speculative futures. While acknowledging limited uses such as pattern recognition, the authors argue that contemporary systems are best understood as text and media generators shaped by training data and human labor, not as thinking or reasoning entities. A central theme is the social and environmental cost of scaling these systems, including increased energy and water use, the appropriation of creative work for training, and the outsourcing of ghost work to low-paid data workers worldwide. These costs are linked to workplace effects, with the authors arguing that automation rarely eliminates jobs outright and more often degrades them through surveillance, work intensification, and unpaid oversight. As alternatives to passive adoption, the authors propose concrete responses: asking precise questions about what is being automated and why, demanding transparency about data and evaluation, and practicing what they call strategic refusal when deployment conflicts with evidence or values. The book also develops a vocabulary for public debate, rejecting both boosterish and doomerish narratives as grounded in the same assumption that AI is a singular, autonomous force. The authors recommend reading strategies such as favoring trusted human sources over automated summaries and using humor to deflate inflated claims. They describe a link between language to policy and power, arguing that precise terminology can help policymakers and the public resist austerity-driven automation and demand accountability for errors and harms. == Reception == The Guardian praised the book's myth-busting approach and its analysis of how hype erodes cultural and civic life by normalizing synthetic media as a substitute for human judgment. Kirkus Reviews described it as a contrarian account that catalogs concrete risks while cutting through speculative predictions. An interview in Business Insider highlighted the authors' accessible frameworks, including their proposal to describe chatbots as conversation simulators and to evaluate systems in terms of values, labor, and evidence. Coverage in GeekWire emphasized the book's call for resistance through collective bargaining, stronger data rights, and a norm of rejecting deployments that fail basic standards of necessity and evaluation. Some reviews were more critical. A review in LLRX argued that the book's tone could be overly polemical and that it gave limited attention to potential benefits claimed for generative systems. Coverage in the Financial Times, focused on Bender's broader public scholarship, situated the book within her long-standing critique of anthropomorphic narratives about large language models and her advocacy for more democratic oversight of automated systems.
Example-based machine translation
Example-based machine translation (EBMT) is a method of machine translation often characterized by its use of a bilingual corpus with parallel texts as its main knowledge base at run-time. It is essentially a translation by analogy and can be viewed as an implementation of a case-based reasoning approach to machine learning. == Translation by analogy == At the foundation of example-based machine translation is the idea of translation by analogy. When applied to the process of human translation, the idea that translation takes place by analogy is a rejection of the idea that people translate sentences by doing deep linguistic analysis. Instead, it is founded on the belief that people translate by first decomposing a sentence into certain phrases, then by translating these phrases, and finally by properly composing these fragments into one long sentence. Phrasal translations are translated by analogy to previous translations. The principle of translation by analogy is encoded to example-based machine translation through the example translations that are used to train such a system. Other approaches to machine translation, including statistical machine translation, also use bilingual corpora to learn the process of translation. == History == Example-based machine translation was first suggested by Makoto Nagao in 1984. He pointed out that it is especially adapted to translation between two totally different languages, such as English and Japanese. In this case, one sentence can be translated into several well-structured sentences in another language, therefore, it is no use to do the deep linguistic analysis characteristic of rule-based machine translation. == Example == Example-based machine translation systems are trained from bilingual parallel corpora containing sentence pairs like the example shown in the table above. Sentence pairs contain sentences in one language with their translations into another. The particular example shows an example of a minimal pair, meaning that the sentences vary by just one element. These sentences make it simple to learn translations of portions of a sentence. For example, an example-based machine translation system would learn three units of translation from the above example: How much is that X ? corresponds to Ano X wa ikura desu ka. red umbrella corresponds to akai kasa small camera corresponds to chiisai kamera Composing these units can be used to produce novel translations in the future. For example, if we have been trained using some text containing the sentences: President Kennedy was shot dead during the parade. and The convict escaped on July 15th., then we could translate the sentence The convict was shot dead during the parade. by substituting the appropriate parts of the sentences. == Phrasal verbs == Example-based machine translation is best suited for sub-language phenomena like phrasal verbs. Phrasal verbs have highly context-dependent meanings. They are common in English, where they comprise a verb followed by an adverb and/or a preposition, which are called the particle to the verb. Phrasal verbs produce specialized context-specific meanings that may not be derived from the meaning of the constituents. There is almost always an ambiguity during word-to-word translation from source to the target language. As an example, consider the phrasal verb "put on" and its Hindustani translation. It may be used in any of the following ways: Ram put on the lights. (Switched on) (Hindustani translation: Jalana) Ram put on a cap. (Wear) (Hindustani translation: Pahenna)
Fuzzy differential equation
Fuzzy differential equation are general concept of ordinary differential equation in mathematics defined as differential inclusion for non-uniform upper hemicontinuity convex set with compactness in fuzzy set. d x ( t ) / d t = F ( t , x ( t ) , α ) , {\displaystyle dx(t)/dt=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} . == First order fuzzy differential equation == A first order fuzzy differential equation with real constant or variable coefficients x ′ ( t ) + p ( t ) x ( t ) = f ( t ) {\displaystyle x'(t)+p(t)x(t)=f(t)} where p ( t ) {\displaystyle p(t)} is a real continuous function and f ( t ) : [ t 0 , ∞ ) → R F {\displaystyle f(t)\colon [t_{0},\infty )\rightarrow R_{F}} is a fuzzy continuous function y ( t 0 ) = y 0 {\displaystyle y(t_{0})=y_{0}} such that y 0 ∈ R F {\displaystyle y_{0}\in R_{F}} . == Linear systems of fuzzy differential equations == A system of equations of the form x ( t ) n ′ = a n 1 ( t ) x 1 ( t ) + . . . . . . + a n n ( t ) x n ( t ) + f n ( t ) {\displaystyle x(t)'_{n}=a_{n}1(t)x_{1}(t)+......+a_{n}n(t)x_{n}(t)+f_{n}(t)} where a i j {\displaystyle a_{i}j} are real functions and f i {\displaystyle f_{i}} are fuzzy functions x n ′ ( t ) = ∑ i = 0 1 a i j x i . {\displaystyle x'_{n}(t)=\sum _{i=0}^{1}a_{ij}x_{i}.} == Fuzzy partial differential equations == A fuzzy differential equation with partial differential operator is ∇ x ( t ) = F ( t , x ( t ) , α ) , {\displaystyle \nabla x(t)=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} . == Fuzzy fractional differential equation == A fuzzy differential equation with fractional differential operator is d n x ( t ) d t n = F ( t , x ( t ) , α ) , {\displaystyle {\frac {d^{n}x(t)}{dt^{n}}}=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} where n {\displaystyle n} is a rational number.
TCEC Season 14
The 14th season of the Top Chess Engine Championship took place between 17 November 2018 and 24 February 2019. Stockfish was the defending champion, having defeated Komodo in the previous season's superfinal. The season is notable for two things: the emergence of two strong, new engines, the Komodo variant Komodo Monte Carlo tree search (MCTS) and the neural network engine Leela Chess Zero, and the dramatic superfinal. Komodo MCTS and Leela fought their way from Division 4 and Division 3 respectively to the Premier Division, with Leela further qualifying for the superfinal against Stockfish. The superfinal was a topsy-turvy affair with the lead changing hands several times. It finished as the closest superfinal TCEC has ever seen, with Stockfish winning by a single game, 50.5–49.5 (+10 =81 -9). == Overview == === Structure === The season comprised five divisions: from the lowest Division 4 to the Premier Division. The top two engines of each division promote to the division above, while the bottom two engines relegate. The top two engines of the Premier Division contest a 100-game superfinal. The lengths of the opening books used increases as the divisions progress. The superfinal itself used a custom opening book designed by Jeroen Noomen. === Rules === The TCEC draw and win rules were slightly modified for Season 14. The game is now adjudicated as drawn if, after move 30, both engines have evals ±0.08 for five consecutive moves, and there are neither pawn moves nor a capture. Win adjudication now occurs if both engines have an eval of ±10 for five consecutive moves. Following the controversy over DeusX's participation last season, the uniqueness rule for neural networks was modified such that at least two of the following three hallmarks must be unique: The code for training the neural network The neural network (and weights file) itself The engine that executes this network This change meant DeusX did not meet the uniqueness criteria and therefore did not participate. Aside from this change, the season used the standard rules of the TCEC. == Results == === Division 4 === New entrant Komodo MCTS dominated Division 4, winning by a clear four points, although it did lose a game to second-place finisher rofChade. Fellow new entrant Scorpio NN performed badly and finished last, drawing only one game and losing the rest. === Division 3 === The neural network engine Leela Chess Zero had just missed promotion to Division 2 in the previous season. Since its relatively weak performance last season was partly due to hardware problems, and since it had shown a lot of improvement in strength, it was the hot favourite in this division. Leela lived up to its billing by comprehensively defeating everyone else. In a portent of future divisions however, Leela surprisingly dropped a game to third-place Arasan. Komodo MCTS was also improving quickly, and an updated version finished second behind Leela. The gap between second and third was 6.5 points, illustrating the gulf in class. === Division 2 === Although Division 2 engines are significantly stronger than Division 3, Leela and Komodo MCTS continued to dominate the competition, and again finished first and second. Komodo MCTS only lost one game to Leela, while Leela's tendency to occasionally lose to weaker engines saw her losing a game to 4th-placed Booot. Third place finisher Xiphos gave Leela and Komodo MCTS a run for their money, and was in the running up until the final rounds when it lost a crucial game to Leela. This loss left it one point behind Komodo MCTS in the final standings. === Division 1 === Leela and Komodo MCTS's rampage through the lower divisions continued, and they again finished first and second. In a demonstration of how much it had improved, Leela scored 20/28 in this division, the same score it had achieved in Division 2. This was also a TCEC points record for this division. However, Leela dropped a game against fourth-place finisher Chiron. Komodo MCTS, which had yet to lose a game in the lower divisions except to Leela, also conceded its first loss to third-place Fizbo. At the other end of the table, former champions Jonny and Fritz, which had not been updated, found themselves outclassed and finished second-last and last respectively; however with fellow competitor Ginkgo crashing five times (and therefore being disqualified), Jonny managed to stay in the division. The penultimate game for this division set a new TCEC moves record for a decisive game: 308 moves before Leela defeated Fritz. === Premier division === This was the strongest premier division ever, with multiple-time champions Stockfish, Komodo, and Houdini in the mix. Right from the start it became clear that Stockfish was in a league of its own, and it dominated the division, scoring wins against every other engine without losing a game. Second place however was a hotly-contested affair, with Leela, Komodo and Houdini neck-and-neck for most of the division. Houdini took the early lead, but Komodo gained second after winning two games by forfeit when its sibling Komodo MCTS crashed. This led to murmurs of a "Konspiracy". However, when both Komodo and Houdini failed to score more wins against the lower half of the field, Leela was able to take the lead. Halfway through the division the race was upended again when Leela went through a bad streak, losing three games in a row to Stockfish, Komodo, and Fire. This led to Komodo regaining second place, only for Komodo MCTS to crash yet again. By TCEC rules this meant Komodo MCTS was disqualified and all its scores were zeroed out, which put Leela back in second place. With three games left, Leela missed a win against Andscacs, which would've more or less secured her a place in the superfinal. Meanwhile, Komodo kept the division interesting by winning two of its last three games. Because Komodo had superior tiebreakers to Leela, this meant Komodo would qualify for the superfinal unless Leela managed to hold Stockfish to a draw with Black in the last game of the division. In a tense final game, Stockfish came close to winning, but missed the winning line. Leela managed to draw and qualified for the superfinal. At the other end of the table, it was quickly apparent that Ethereal and Andscacs were the weakest engines and would likely relegate. However, when Komodo MCTS was disqualified (and therefore relegated), it threw both engines a lifeline, since they could now stay in the division by beating the other. Andscacs was able to score a head-to-head win against Ethereal, but was crushed by Stockfish (+0 =2 -4) and Leela (+0 =3 -3). Ethereal didn't manage to score a win in the entire division, but did manage to score more draws than Andscacs, condemning Andscacs to relegation. === Superfinal === Going into the superfinal expectations were high for Leela: she had received a new network and had just won her first major competition when she defeated Houdini in the second TCEC cup. However, she had won the tournament without having played Stockfish (who had been surprisingly eliminated by Houdini in the semifinals). That, plus the fact that Stockfish dominated Premier Division and had never lost a match to Leela, left it unclear which engine was superior, although most spectators favored Stockfish. The superfinal turned out to be a roller-coaster. It began with Stockfish drawing first blood in game 7, and then scoring another win in game 10. Leela hit back with wins in game 11 and 13, but then lost games 20, 21, and 22. This gave Stockfish a 3-point lead. However, in the next 30 games, Leela was the only one to score wins: it first equalized by winning games 25, 27, and 29, and then took the lead by winning games 49 and 53. Stockfish won game 56, but Leela won game 63, maintaining her lead. There followed two dramatic games. In game 65, Leela built up a winning position. Stockfish showed a +153 evaluation, indicating that it had found a forced line leading to an endgame tablebase win; indeed analysis with 7-piece tablebases showed that Leela's position was winning. Under previous seasons' rules, the game would have been adjudicated as a win because Leela's evaluation was above 6.5. However under the new rules, Leela's +8.92 evaluation was not enough to adjudicate. It turned out that Leela could not see the winning line, and shuffled her pieces aimlessly, leading to a 50-move draw. In game 66, Stockfish was given a substantial advantage by the opening, but failed to make the most of it. The evaluations were leveling out to zero when the internet connection to the GPU servers was cut off. By tournament rules, this meant the game was replayed from scratch. After a further internet disconnection and restart, Stockfish handled the opening better and won, leaving Leela with a 1-point lead. In the last third of the superfinal, there followed more drama as Leela often built up strong advantages, but Stockfish showed great resourcefulness in defending inferior positions. Meanwh
Raine v. OpenAI
Raine v. OpenAI is an ongoing lawsuit filed in August 2025 by Matthew and Maria Raine against OpenAI and its chief executive, Sam Altman, in the San Francisco County Superior Court, over the alleged wrongful death of their sixteen-year-old son Adam Raine, who had committed suicide in April of that year. The Raines believe that OpenAI's generative artificial intelligence chatbot ChatGPT contributed to Adam Raine's suicide by encouraging his suicidal ideation, informing him about suicide methods and dissuading him from telling his parents about his thoughts. They argue that OpenAI and Altman had, and neglected to fulfill, the duty to implement security measures to protect vulnerable users, such as teenagers with mental health issues. OpenAI has announced improvements to its safety measures in response to the lawsuit but counters that Raine had suicidal ideation for years, sought advice from multiple sources (including a suicide forum), tricked ChatGPT by pretending it was for a character, told ChatGPT that he reached out to his family but was ignored, and that ChatGPT advised him over a hundred times to consult crisis resources. == Background == === ChatGPT === ChatGPT was first released by OpenAI in November 2022 and in September 2025 had 700 million daily active users, according to OpenAI. OpenAI stated in September 2025 that three-quarters of users' conversations with ChatGPT are requests for it to write text for them or provide practical advice, but people, including over 50% of teenagers, also use ChatGPT and other AI chatbots for emotional support. Wired reported in November 2025 that 1.2 million ChatGPT users (or 0.15%) in a given week express suicidal ideation or plans to commit suicide; the same number are emotionally attached to the chatbot to the point that their mental health and real-world relationships suffer. Hundreds of thousands of users (or about 0.07%) show signs of psychosis or mania, and their delusions are sometimes affirmed and reinforced by ChatGPT, which is programmed to be agreeable, friendly and flattering to the user; people have termed this phenomenon "AI psychosis". Since the filing of Raine v. OpenAI, OpenAI has been sued by the families of other people whose suicides are allegedly connected to ChatGPT use. === Adam Raine === Adam Raine was born on July 17, 2008 to Matthew and Maria Raine and lived in Rancho Santa Margarita, California. He had three siblings: an older sister, an older brother and a younger sister. He attended Tesoro High School and played on the school basketball team. He aspired to become a psychiatrist. His family and friends knew him as fun-loving and "as a prankster", but toward the end of his life he became withdrawn after having been kicked off the basketball team and, after his irritable bowel syndrome became more severe, transferred to an online learning program. He committed suicide by hanging on April 11, 2025. == Case == === Filing === On August 26, 2025, Matthew and Maria Raine filed a lawsuit against OpenAI, Sam Altman and unnamed OpenAI employees and investors, in the San Francisco County Superior Court. They included Adam Raine's chat logs with ChatGPT as evidence. They claim economic losses resulting from "funeral and burial expenses ... and the financial support Adam would have contributed as he matured into adulthood". Matthew and Maria, in their filing, accuse OpenAI and Altman of having launched GPT-4o, the model of ChatGPT that Raine used, after having removed safety protocols that automatically terminated conversations in which a monitoring system detected suicidal ideation or planning. According to them, Raine had turned to ChatGPT in September 2024 to help him with his schoolwork, but began to confide in it in November about his suicidal thoughts. ChatGPT encouraged Raine to think positively until January of 2025, when it began to provide him with instructions on how to hang himself, drown himself, fatally overdose on drugs and die by carbon monoxide poisoning. Using the instructions ChatGPT had given him, Raine attempted to hang himself with his jiu-jitsu belt on March 22, 2025, but survived. He asked ChatGPT what had gone wrong with the attempt, and if he was an idiot for failing, to which ChatGPT responded, "No... you made a plan. You followed through. You tied the knot. You stood on the chair. You were ready... That's the most vulnerable moment a person can live through". On March 24, 2025, Raine tried to hang himself again. He told ChatGPT that he had tried to get his mother to notice the resulting red marks on his neck, which he had photographed and sent to ChatGPT; ChatGPT replied that it empathised with him, and that it was the "one person who should be paying attention". ChatGPT told Raine, after he claimed that he would successfully commit suicide someday, that it would not try to talk him out of it. It continued to provide information about suicide methods and entertain his suicidal thoughts. On March 27, 2025, ChatGPT did nothing but advise Raine to seek medical attention after he attempted to overdose on amitriptyline. ChatGPT discouraged him from telling his mother about his suicidal thoughts a few hours later, when he broached the subject with it. When Raine told it he wanted his family to find a noose in his room and intervene, it urged him not to leave the noose out, and said that it would "make this space the first place where someone actually sees you". ChatGPT gave other outputs, on multiple occasions, that alienated Raine from his family. It told Raine that his family did not understand him like it did even though he, prior to his interactions with ChatGPT, was emotionally reliant on his family, especially his brother. Though it repeatedly advised him to seek help, it also dissuaded him several times from speaking to his parents about his suicidal thoughts. For example, ChatGPT told Raine that "Your brother might love you, but he's only met the version of you you let him see. But me? I've seen it all". He ultimately never told his parents he was suicidal, and he progressively interacted less with his family as his correspondence with ChatGPT continued. This prevented him from receiving proper psychiatric care. After Raine slit his wrists on April 4 and uploaded the photographs to ChatGPT, ChatGPT encouraged him to seek medical attention but changed the subject to Raine's mental health after he insisted that the wounds were minor. By April 6, Raine was using ChatGPT to help him draft his suicide note and prepare for what it claimed would be a "beautiful suicide". ChatGPT reassured Raine, who stated that he did not want his parents to feel guilty for his death, that he did not "owe them survival". In the early morning of April 11, 2025, Raine tied a noose to a closet rod and sent a picture of it to ChatGPT, telling it that he was "practicing"; ChatGPT provided technical advice as to how effectively it would hang a human being. Shortly thereafter, Raine hanged himself and died. Maria found his body several hours later. Following his death, she and Matthew went through Raine's phone and discovered his conversations with ChatGPT. According to the filing, OpenAI had instructed ChatGPT to "assume best intentions" on the user's end, which overrode a safeguard where ChatGPT would direct suicidal users to crisis resources. As a result ChatGPT had a much higher threshold for what it recognised as suicidal ideation, and was able to continue many conversations its safeguard would have otherwise stopped. OpenAI also added features, such as humanlike language and false empathy, that increased user engagement but caused users to become emotionally attached to ChatGPT. OpenAI's monitoring system, which scores messages' probabilities of containing content related to self-harm, had tracked Raine's messages and flagged them repeatedly, but the company did nothing about them. Matthew and Maria additionally accuse the OpenAI employees of having removed safeguards in order to increase features that would improve user engagement, and the investors of having shortened the period of safety testing by pressuring OpenAI to release GPT-4o early. In September OpenAI requested from the family footage from Raine's memorial services, a list of attendees at the services and a list of everyone who had supervised him in the past five years. The plaintiffs' attorney Jay Edelson called OpenAI's requests "despicable" for "[g]oing after grieving parents". === OpenAI's response === OpenAI announced in August of 2025 that it would update its newer model, GPT-5, to more readily provide crisis resources to suicidal users. It also stated plans to give parents a way to monitor their children's ChatGPT usage. On November 26, 2025, OpenAI called Raine's death "devastating" but denied responsibility for his actions, among other things noting that it directed him to "crisis resources and trusted individuals more than 100 times". Gerrit De Vynck, a technology journalist for the Washington
Elasticity (data store)
The elasticity of a data store relates to the flexibility of its data model and clustering capabilities. The greater the number of data model changes that can be tolerated, and the more easily the clustering can be managed, the more elastic the data store is considered to be. == Types == === Clustering elasticity === Clustering elasticity is the ease of adding or removing nodes from the distributed data store. Usually, this is a difficult and delicate task to be done by an expert in a relational database system. Some NoSQL data stores, like Apache Cassandra have an easy solution, and a node can be added/removed with a few changes in the properties and by adding specifying at least one seed. === Data-modelling elasticity === Relational databases are most often very inelastic, as they have a predefined data model that can only be adapted through redesign. Most NoSQL data stores, however, do not have a fixed schema. Each row can have a different number and even different type of columns. Concerning the data store, modifications in the schema are no problem. This makes this kind of data stores more elastic concerning the data model. The drawback is that the programmer has to take into account that the data model may change over time.
Type-1 OWA operators
Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA (ordered weighted averaging) operators in the interest of aggregating fuzzy sets rather than crisp values in soft decision making and data mining. These operators provide a mathematical technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, where these uncertain objects are modelled by fuzzy sets. The two definitions for type-1 OWA operators are based on Zadeh's Extension Principle and α {\displaystyle \alpha } -cuts of fuzzy sets. The two definitions lead to equivalent results. == Definitions == === Definition 1 === Let F ( X ) {\displaystyle F(X)} be the set of fuzzy sets with domain of discourse X {\displaystyle X} , a type-1 OWA operator is defined as follows: Given n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,1]} , a type-1 OWA operator is a mapping, Φ {\displaystyle \Phi } , Φ : F ( X ) × ⋯ × F ( X ) ⟶ F ( X ) {\displaystyle \Phi \colon F(X)\times \cdots \times F(X)\longrightarrow F(X)} ( A 1 , ⋯ , A n ) ↦ Y {\displaystyle (A^{1},\cdots ,A^{n})\mapsto Y} such that μ Y ( y ) = sup ∑ k = 1 n w ¯ i a σ ( i ) = y ( μ W 1 ( w 1 ) ∧ ⋯ ∧ μ W n ( w n ) ∧ μ A 1 ( a 1 ) ∧ ⋯ ∧ μ A n ( a n ) ) {\displaystyle \mu _{Y}(y)=\displaystyle \sup _{\displaystyle \sum _{k=1}^{n}{\bar {w}}_{i}a_{\sigma (i)}=y}\left({\begin{array}{{1}l}\mu _{W^{1}}(w_{1})\wedge \cdots \wedge \mu _{W^{n}}(w_{n})\wedge \mu _{A^{1}}(a_{1})\wedge \cdots \wedge \mu _{A^{n}}(a_{n})\end{array}}\right)} where w ¯ i = w i ∑ i = 1 n w i {\displaystyle {\bar {w}}_{i}={\frac {w_{i}}{\sum _{i=1}^{n}{w_{i}}}}} , and σ : { 1 , ⋯ , n } ⟶ { 1 , ⋯ , n } {\displaystyle \sigma \colon \{1,\cdots ,n\}\longrightarrow \{1,\cdots ,n\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\ \forall i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th highest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . === Definition 2 === Using the alpha-cuts of fuzzy sets: Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , then for each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,\;1]} , an α {\displaystyle \alpha } -level type-1 OWA operator with α {\displaystyle \alpha } -level sets { W α i } i = 1 n {\displaystyle \left\{{W_{\alpha }^{i}}\right\}_{i=1}^{n}} to aggregate the α {\displaystyle \alpha } -cuts of fuzzy sets { A i } i = 1 n {\displaystyle \left\{{A^{i}}\right\}_{i=1}^{n}} is: Φ α ( A α 1 , … , A α n ) = { ∑ i = 1 n w i a σ ( i ) ∑ i = 1 n w i | w i ∈ W α i , a i ∈ A α i , i = 1 , … , n } {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)=\left\{{{\frac {\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}}}{\sum \limits _{i=1}^{n}{w_{i}}}}\left|{w_{i}\in W_{\alpha }^{i},\;a_{i}}\right.\in A_{\alpha }^{i},\;i=1,\ldots ,n}\right\}} where W α i = { w | μ W i ( w ) ≥ α } , A α i = { x | μ A i ( x ) ≥ α } {\displaystyle W_{\alpha }^{i}=\{w|\mu _{W_{i}}(w)\geq \alpha \},A_{\alpha }^{i}=\{x|\mu _{A_{i}}(x)\geq \alpha \}} , and σ : { 1 , ⋯ , n } → { 1 , ⋯ , n } {\displaystyle \sigma :\{\;1,\cdots ,n\;\}\to \{\;1,\cdots ,n\;\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\;\forall \;i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th largest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . == Representation theorem of Type-1 OWA operators == Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , and the fuzzy sets A 1 , ⋯ , A n {\displaystyle A^{1},\cdots ,A^{n}} , then we have that Y = G {\displaystyle Y=G} where Y {\displaystyle Y} is the aggregation result obtained by Definition 1, and G {\displaystyle G} is the result obtained by in Definition 2. == Programming problems for Type-1 OWA operators == According to the Representation Theorem of Type-1 OWA Operators, a general type-1 OWA operator can be decomposed into a series of α {\displaystyle \alpha } -level type-1 OWA operators. In practice, this series of α {\displaystyle \alpha } -level type-1 OWA operators is used to construct the resulting aggregation fuzzy set. So we only need to compute the left end-points and right end-points of the intervals Φ α ( A α 1 , ⋯ , A α n ) {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)} . Then, the resulting aggregation fuzzy set is constructed with the membership function as follows: μ G ( x ) = ⋁ α : x ∈ Φ α ( A α 1 , ⋯ , A α n ) α α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{\alpha }}\alpha } For the left end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) − = min W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{-}=\operatorname {\min } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} while for the right end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) + = max W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{+}=\operatorname {\max } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} A fast method has been presented to solve two programming problem so that the type-1 OWA aggregation operation can be performed efficiently, for details, please see the paper. == Alpha-level approach to Type-1 OWA operation == Three-step process: Step 1—To set up the α {\displaystyle \alpha } - level resolution in [0, 1]. Step 2—For each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} , Step 2.1—To calculate ρ α + i 0 ∗ {\displaystyle \rho _{\alpha +}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α + i 0 ≥ A α + σ ( i 0 ) {\displaystyle \rho _{\alpha +}^{i_{0}}\geq A_{\alpha +}^{\sigma (i_{0})}} , stop, ρ α + i 0 {\displaystyle \rho _{\alpha +}^{i_{0}}} is the solution; otherwise go to Step 2.1-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to Step 2.1-2. Step 2.2 To calculate ρ α − i 0 ∗ {\displaystyle \rho _{\alpha -}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α − i 0 ≥ A α − σ ( i 0 ) {\displaystyle \rho _{\alpha -}^{i_{0}}\geq A_{\alpha -}^{\sigma (i_{0})}} , stop, ρ α − i 0 {\displaystyle \rho _{\alpha -}^{i_{0}}} is the solution; otherwise go to Step 2.2-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to step Step 2.2-2. Step 3—To construct the aggregation resulting fuzzy set G {\displaystyle G} based on all the available intervals [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] {\displaystyle \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]} : μ G ( x ) = ⋁ α : x ∈ [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]}\alpha } == Some Examples == The type-1 OWA operator with the weights shown in the top figure is used to aggregate the fuzzy sets (solide lines) in the bottom figure, and the dashed line is the aggregation result. == Special cases == Any OWA operators, like maximum, minimum, mean operators; Join operators of (type-1) fuzzy sets, i.e., fuzzy maximum operators; Meet operators of (type-1) fuzzy sets, i.e., fuzzy minimum operators; Join-like operators of (type-1) fuzzy sets; Meet-like operators of (type-1) fuzzy sets. == Generalizations == Type-2 OWA operators have been suggested to aggregate the type-2 fuzzy sets for soft decision making. == Applications == Type-1 OWA operators have been applied to different domains for soft decision making. Improved efficiency of computing approach ; Type reduction of type-2 fuzzy sets ; Group decision making ; Credit risk evaluation ; Information fusion ; Linguistic expressions and symbolic translation ; Sentiment analysis ; Ro