Comparing the best AI voice assistant? An AI voice assistant is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI voice assistant slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Stride (software)
Stride was a cloud-based team business communication and collaboration tool, launched by Atlassian on 7 September 2017 to replace the cloud-based version of HipChat. Stride software was available to download onto computers running Windows, Mac or Linux, as well as Android, iOS smartphones, and tablets. Stride was bought by Atlassian's competitor Slack Technologies and was discontinued on February 15, 2019. The features of Stride include chat rooms, one-on-one messaging, file sharing, 5 GB of file storage, group voice and video calling, built-in collaboration tools, and up to 25,000 of searchable message history. Premium features include unlimited file storage, users, group chat rooms, file sharing and storage, apps, and history retention. The premium version, priced at $3/user/month, also includes advanced meeting functionality like group screen sharing, remote desktop control, and dial-in/dial-out capabilities. Stride offered integrations with Atlassian's other products as well as other third-party applications listed in the Atlassian Marketplace, such as GitHub, Giphy, Stand-Bot and Google Calendar. Stride offered additional features beyond messaging to improve efficiency and productivity. It aimed to reduce collaboration noise by introducing a "focus" mode, and eliminates the divisions between text chat, voice meetings, and videoconferencing, by simplifying transitioning between these modes in the same channel. On July 26, 2018, Atlassian announced that HipChat and Stride would be discontinued February 15, 2019, and that it had reached a deal to sell their intellectual property to Slack. Slack paid an undisclosed amount over three years to assume the user bases of the services, while Atlassian took a minority investment in Slack. The companies also announced a commitment to work on integration of Slack with Atlassian services.
Deepfake
Deepfakes (a portmanteau of 'deep learning' and 'fake') are images, videos, or audio that have been edited or generated using artificial intelligence, AI-based tools or audio-video editing software. They may depict real or fictional people and are considered a form of synthetic media, that is media that is usually created by artificial intelligence systems by combining various media elements into a new media artifact. While the act of creating fake content is not new, deepfakes uniquely leverage machine learning and artificial intelligence techniques, including facial recognition algorithms and artificial neural networks such as variational autoencoders and generative adversarial networks (GANs). In turn, the field of image forensics has worked to develop techniques to detect manipulated images. Deepfakes have garnered widespread attention for their potential use in creating child sexual abuse material, celebrity pornographic videos, revenge porn, fake news, hoaxes, bullying, and financial fraud. Academics have raised concerns about the potential for deepfakes to promote disinformation and hate speech, as well as interfere with elections. In response, the information technology industry and governments have proposed recommendations and methods to detect and mitigate their use. Academic research has also delved deeper into the factors driving deepfake engagement online as well as potential countermeasures to malicious application of deepfakes. From traditional entertainment to gaming, deepfake technology has evolved to be increasingly convincing and available to the public, allowing for the disruption of the entertainment and media industries. == History == Photo manipulation was developed in the 19th century and soon applied to motion pictures. Technology steadily improved during the 20th century, and more quickly with the advent of digital video. Deepfake technology has been developed by researchers at academic institutions beginning in the 1990s, and later by amateurs in online communities. More recently, the methods have been adopted by industry. The development of generative adversarial networks (GANs) in the mid-2010s represented a key technical turning point in the evolution of deepfakes. GANs allowed for the creation of highly realistic fake images and videos by training competing neural networks, achieving a much improved visual fidelity over previous methods of creating the content using rules or by using autoencoders, and formed the basis for modern deepfake methods. === Academic research === Academic research related to deepfakes is split between the field of computer vision, a sub-field of computer science, which develops techniques for creating and identifying deepfakes, and humanities and social science approaches that study the social, ethical, aesthetic implications as well as journalistic and informational implications of deepfakes. As deepfakes have risen in prominence in popularity with innovations provided by AI tools, significant research has gone into detection methods and defining the factors driving engagement with deepfakes on the internet. Deepfakes have been shown to appear on social media platforms and other parts of the internet for purposes ranging from entertainment and education related to deepfakes to misinformation to elicit strong reactions. There are gaps in research related to the propagation of deepfakes on social media. Negativity and emotional response are the primary driving factors for users sharing deepfakes. === Social science and humanities approaches to deepfakes === In cinema studies, deepfakes illustrate how "the human face is emerging as a central object of ambivalence in the digital age". Video artists have used deepfakes to "playfully rewrite film history by retrofitting canonical cinema with new star performers". Film scholar Christopher Holliday analyses how altering the gender and race of performers in familiar movie scenes destabilizes gender classifications and categories. The concept of "queering" deepfakes is also discussed in Oliver M. Gingrich's discussion of media artworks that use deepfakes to reframe gender, including British artist Jake Elwes' Zizi: Queering the Dataset, an artwork that uses deepfakes of drag queens to intentionally play with gender. The aesthetic potentials of deepfakes are also beginning to be explored. Theatre historian John Fletcher notes that early demonstrations of deepfakes are presented as performances, and situates these in the context of theater, discussing "some of the more troubling paradigm shifts" that deepfakes represent as a performance genre. While most English-language academic studies of deepfakes focus on the Western anxieties about disinformation and pornography, digital anthropologist Gabriele de Seta has analyzed the Chinese reception of deepfakes, which are known as huanlian, which translates to "changing faces". The Chinese term does not contain the "fake" of the English deepfake, and de Seta argues that this cultural context may explain why the Chinese response has centered on practical regulatory measures to "fraud risks, image rights, economic profit, and ethical imbalances". === Computer science research on deepfakes === A landmark early project was the "Video Rewrite" program, published in 1997. The program modified existing video footage of a person speaking to depict that person mouthing the words from a different audio track. It was the first system to fully automate this kind of facial reanimation, and it did so using machine learning techniques to make connections between the sounds produced by a video's subject and the shape of the subject's face. Contemporary academic projects have focused on creating more realistic videos and improving deepfake techniques. The "Synthesizing Obama" program, published in 2017, modifies video footage of former president Barack Obama to depict him mouthing the words contained in a separate audio track. The project lists as a main research contribution to its photorealistic technique for synthesizing mouth shapes from audio. The "Face2Face" program, published in 2016, modifies video footage of a person's face to depict them mimicking another person's facial expressions. The project highlights its primary research contribution as the development of the first method for re-enacting facial expressions in real time using a camera that does not capture depth, enabling the technique to work with common consumer cameras. Researchers have also shown that deepfakes are expanding into other domains such as medical imagery. In this work, it was shown how an attacker can automatically inject or remove lung cancer in a patient's 3D CT scan. The result was so convincing that it fooled three radiologists and a state-of-the-art lung cancer detection AI. To demonstrate the threat, the authors successfully performed the attack on a hospital in a White hat penetration test. A survey of deepfakes, published in May 2020, provides a timeline of how the creation and detection of deepfakes have advanced over the last few years. The survey identifies that researchers have been focusing on resolving the following challenges of deepfake creation: Generalization. High-quality deepfakes are often achieved by training on hours of footage of the target. This challenge is to minimize the amount of training data and the time to train the model required to produce quality images and to enable the execution of trained models on new identities (unseen during training). Paired Training. Training a supervised model can produce high-quality results, but requires data pairing. This is the process of finding examples of inputs and their desired outputs for the model to learn from. Data pairing is laborious and impractical when training on multiple identities and facial behaviors. Some solutions include self-supervised training (using frames from the same video), the use of unpaired networks such as Cycle-GAN, or the manipulation of network embeddings. Identity leakage. This is where the identity of the driver (i.e., the actor controlling the face in a reenactment) is partially transferred to the generated face. Some solutions proposed include attention mechanisms, few-shot learning, disentanglement, boundary conversions, and skip connections. Occlusions. When part of the face is obstructed with a hand, hair, glasses, or any other item then artifacts can occur. A common occlusion is a closed mouth which hides the inside of the mouth and the teeth. Some solutions include image segmentation during training and in-painting. Temporal coherence. In videos containing deepfakes, artifacts such as flickering and jitter can occur because the network has no context of the preceding frames. Some researchers provide this context or use novel temporal coherence losses to help improve realism. As the technology improves, the interference is diminishing. Overall, deepfakes are expected to have several implications in media and society, med
The Last Question
"The Last Question" is a science fiction short story by American writer Isaac Asimov. It first appeared in the November 1956 issue of Science Fiction Quarterly; and in the anthologies in the collections Nine Tomorrows (1959), The Best of Isaac Asimov (1973), Robot Dreams (1986), The Best Science Fiction of Isaac Asimov (1986), the retrospective Opus 100 (1969), and Isaac Asimov: The Complete Stories, Vol. 1 (1990). While he also considered it one of his best works, "The Last Question" was Asimov's favorite short story of his own authorship, and is one of a loosely connected series of stories concerning a fictional computer called Multivac. Through successive generations, humanity questions Multivac on the subject of entropy. The story blends science fiction, theology, and philosophy. It has been recognized as a counterpoint to Fredric Brown's short short story "Answer", published two years earlier. == History == In conceiving Multivac, Asimov was extrapolating the trend towards centralization that characterized computation technology planning in the 1950s to an ultimate centrally managed global computer. After seeing a planetarium adaptation of his work, Asimov "privately" concluded that the story was his best science fiction yet written. He placed it just higher than "The Ugly Little Boy" (September 1958) and "The Bicentennial Man" (1976). The story asks the question of humanity's fate, and human existence as a whole, highlighting Asimov's focus on important aspects of our future like population growth and environmental issues. "The Last Question" ranks with "Nightfall" (1941) as one of Asimov's best-known and most acclaimed short stories. He wrote in 1973 that he appreciated how easy the story was to write after he had the idea. He was so often approached by fans who remembered the story but not the title, that in one instance he gave the answer, correctly, before the fan had even described the story. == Plot summary == By the year 2061, Multivac, a self-adjusting and self-correcting computer, has allowed mankind to reach beyond the planetary confines of Earth and harness solar energy. Two technicians, Adell and Lupov, celebrate Multivac's role in this development. Over drinks, they discuss that the sun will expire due to the second law of thermodynamics, which states that entropy inevitably increases. When Adell asks Multivac whether this can be reversed, the computer responds that it has insufficient data to answer. In several episodes over ten trillion years, increasingly advanced humans pose the same question to the computers of their time. Each time the computer gives the same response. At the heat death of the universe, the last disembodied consciousness of Man asks the question a final time of a computer that resides in hyperspace before merging with it. After collecting the last data from the dead universe, the computer continues to process it alone and finds an answer to the last question. Having no one to tell it to, it proceeds to demonstrate by saying "LET THERE BE LIGHT!" == Themes == === Philosophy === Although science and religion are frequently presented as having an oppositional relationship, "The Last Question" explores some biblical contexts ("Let there be light"). In Asimov's story, aspects like the great meaning of existence are culminated through both technology and human knowledge. The evolution from Multivac to AC also emulates a sort of cycle of existence. === Dystopian happy ending === Multivac's purpose was conceptualized with a desire for knowledge, promoting the idea that more knowledge will lead to a better and more fruitful future for humanity. However, the computer's answers regarding the future suggest an inevitable exhaustion of the Sun, and this thirst for knowledge becomes an obsession with the future. The story's end displays a dichotomy between annihilation and peace. == Dramatic adaptations == === Planetarium shows === "The Last Question" was first adapted for the Abrams Planetarium at Michigan State University (in 1966), featuring the voice of Leonard Nimoy, as Asimov wrote in his autobiography In Joy Still Felt (1980). It was adapted for the Strasenburgh Planetarium in Rochester, New York (in 1969), under the direction of Ian C. McLennan. It was adapted for the Edmonton Space Sciences Centre in Edmonton, Alberta (early 1970s), under the direction of John Hault. It was adapted for the Gates Planetarium at the Denver Museum of Natural History in 1973 under the direction of Mark B. Peterson It subsequently played at the: Fels Planetarium of the Franklin Institute in Philadelphia in 1973 Planetarium of the Reading School District in Reading, Pennsylvania in 1974 Buhl Planetarium, Pittsburgh in 1974 The Space Transit Planetarium of the Museum of Science in Miami during 1977 Vanderbilt Planetarium in Centerport New York, in 1978, read by singer-songwriter and Long Island resident Harry Chapin. Hansen Planetarium in Salt Lake City, Utah (in 1980 and 1989) A reading of the story was played on BBC Radio 7 in 2008 and 2009. Gates Planetarium in Denver, Colorado (in early 2020) In 1989 Asimov updated the star show adaptation to add in quasars and black holes. The story was adapted as a comic book by Don Thompson and drawn by John Estes in the third issue of ORBiT.
Herbrand Award
The Herbrand Award for Distinguished Contributions to Automated Reasoning is an award given by the Conference on Automated Deduction (CADE), Inc., (although it predates the formal incorporation of CADE) to honour persons or groups for important contributions to the field of automated deduction. The award is named after the French scientist Jacques Herbrand and given at most once per CADE or International Joint Conference on Automated Reasoning (IJCAR). It comes with a prize of US$1,000. Anyone can be nominated, the award is awarded after a vote among CADE trustees and former recipients, usually with input from the CADE/IJCAR programme committee. == Recipients == Past award recipients are: === 1990s === Larry Wos (1992) Woody Bledsoe (1994) John Alan Robinson (1996) Wu Wenjun (1997) Gérard Huet (1998) Robert S. Boyer and J Strother Moore (1999) === 2000s === William W. McCune (2000) Donald W. Loveland (2001) Mark E. Stickel (2002). Peter B. Andrews (2003) Harald Ganzinger (2004) Martin Davis (2005) Wolfgang Bibel (2006) Alan Bundy (2007) Edmund M. Clarke (2008) Deepak Kapur (2009) === 2010s === David Plaisted (2010) Nachum Dershowitz (2011) Melvin Fitting (2012) C. Greg Nelson (2013) Robert L. Constable (2014) Andrei Voronkov (2015) Zohar Manna and Richard Waldinger (2016) Lawrence C. Paulson (2017) Bruno Buchberger (2018) Nikolaj Bjørner and Leonardo de Moura (2019) === 2020s === Franz Baader (2020) Tobias Nipkow (2021) Natarajan Shankar (2022) Moshe Vardi (2023) Armin Biere (2024) Aart Middeldorp (2025)
The Master Algorithm
The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from people outside the field. == Overview == The book outlines five approaches of machine learning: inductive reasoning, connectionism, evolutionary computation, Bayes' theorem and analogical modelling. The author explains these tribes to the reader by referring to more understandable processes of logic, connections made in the brain, natural selection, probability and similarity judgments. Throughout the book, it is suggested that each different tribe has the potential to contribute to a unifying "master algorithm". Towards the end of the book the author pictures a "master algorithm" in the near future, where machine learning algorithms asymptotically grow to a perfect understanding of how the world and people in it work. Although the algorithm doesn't yet exist, he briefly reviews his own invention of the Markov logic network. == In the media == In 2016 Bill Gates recommended the book, alongside Nick Bostrom's Superintelligence, as one of two books everyone should read to understand AI. In 2018 the book was noted to be on Chinese Communist Party general secretary Xi Jinping's bookshelf. === Reception === A computer science educator stated in Times Higher Education that the examples are clear and accessible. In contrast, The Economist agreed Domingos "does a good job" but complained that he "constantly invents metaphors that grate or confuse". Kirkus Reviews praised the book, stating that "Readers unfamiliar with logic and computer theory will have a difficult time, but those who persist will discover fascinating insights." A New Scientist review called it "compelling but rather unquestioning".
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