Virtual collective consciousness (VCC) is a term rebooted and promoted by two behavioral scientists, Yousri Marzouki and Olivier Oullier in their 2012 Huffington Post article titled: "Revolutionizing Revolutions: Virtual Collective Consciousness and the Arab Spring", after its first appearance in 1999-2000. VCC is now defined as an internal knowledge catalyzed by social media platforms and shared by a plurality of individuals driven by the spontaneity, the homogeneity, and the synchronicity of their online actions. VCC occurs when a large group of persons, brought together by a social media platform think and act with one mind and share collective emotions. Thus, they are able to coordinate their efforts efficiently, and could rapidly spread their word to a worldwide audience. When interviewed about the concept of VCC that appeared in the book - Hyperconnectivity and the Future of Internet Communication - he edited, Professor of Pervasive Computing, Adrian David Cheok mentioned the following: "The idea of a global (collective) virtual consciousness is a bottom-up process and a rather emergent property resulting from a momentum of complex interactions taking place in social networks. This kind of collective behaviour (or intelligence) results from a collision between a physical world and a virtual world and can have a real impact in our life by driving collective action." == Etymology == In 1999-2000, Richard Glen Boire provided a cursory mention and the only occurrence of the term "Virtual collective consciousness" in his text as follows: The trend of technology is to overcome the limitations of the human body. And, the Web has been characterized as a virtual collective consciousness and unconsciousness The recent definition of VCC evolved from the first empirical study that provided a cyberpsychological insight into the contribution of Facebook to the 2011 Tunisian revolution. In this study, the concept was originally called "collective cyberconsciousness". The latter is an extension of the idea of "collective consciousness" coupled with "citizen media" usage. The authors of this study also made a parallel between this original definition of VCC and other comparable concepts such as Durkheim's collective representation, Žižek's "collective mind" or Boguta's "new collective consciousness" that he used to describe the computational history of the Internet shutdown during the Egyptian revolution. Since VCC is the byproduct of the network's successful actions, then these actions must be timely, acute, rapid, domain-specific, and purpose-oriented to successfully achieve their goal. Before reaching a momentum of complexity, each collective behavior starts by a spark that triggers a chain of events leading to a crystallized stance of a tremendous amount of interactions. Thus, VCC is an emergent global pattern from these individual actions. In 2012, the term virtual collective consciousness resurfaced and was brought to light after extending its applications to the Egyptian case and the whole social networking major impact on the success of the so-called Arab Spring. Moreover, the acronym VCC was suggested to identify the theoretical framework covering on-line behaviors leading to a virtual collective consciousness. Hence, online social networks have provided a new and faster way of establishing or modifying "collective consciousness" that was paramount to the 2011 uprisings in the Arab world. == Theoretical underpinnings of VCC == Various theoretical references in fields ranging from sociology to computer science were mentioned in order to account for the key features that render the framework for a virtual collective consciousness. The following list is not exhaustive, but the references it contains are often highlighted: Émile Durkheim's collective representations are at the heart of VCC since collectivity taken decisions according to Durkheim's assumptions will approve or disapprove individuals' actions and help them eventually reach their final goal. Marshall McLuhan's global village: The shrinking of our big world to a small place called cyberspace is made possible by technological extensions of human consciousness. Carl Jung's collective unconscious: When a society witnesses significant changes, the anchoring of archetypal images (e.g., political leaders) seems to be deeply rooted in individuals' collective unconscious that is likely to bias their political choices. Individual memories of public events were also supposed to convey a "collective awareness" that can be subconsciously altered by the instantaneous spread of information through social networking around the world. Daniel Wegner's transactive memory (TM): social-networking platforms such as Facebook during the Tunisian revolution or Twitter during the Egyptian revolution served as placeholders of a VCC where information can be harnessed and steered to the highly specific revolutionary purpose. Although research on TM was originally limited to couples, small groups, and organizations, recent studies strongly suggest that an effective TM can operate on a very large scale too. James Surowiecki's wisdom of crowds Collective influence algorithm: The CI (Collective influence) algorithm is effective in finding influential nodes in a variety of networks, including social networks, communication networks, and biological networks. It has been used to identify influencers on social-media platforms, to identify key nodes in transportation networks, and to identify potential drug-targets in biological networks. == Some illustrations of VCC == Besides the studied effect of social networking on the Tunisian and Egyptian revolutions, the former via Facebook and the latter via Twitter other applications were studied under the prism of VCC framework: The Whitacre's virtual choir: A compelling example of the degree of autonomy and self-identity members of a spontaneously created network through a VCC is Eric Whitacre's unique musical project that involved a collection of singers performing remotely to create a virtual Choir. The effect of all the voices illustrated a genuine virtual collective empathy merging the artist's mind with all the singers through his silent conducting gestures. The Harlem Shake dance: The Bitcoin protocol: It was questioned whether or not the Bitcoin protocol can morph into virtual collective consciousness. The Byzantine generals problem was used as an analogy to understand the behavioral complexity of the community of Bitcoin's users. Artificial Social Networking Intelligence (ASNI): refers to the application of artificial intelligence within social networking services and social media platforms. It encompasses various technologies and techniques used to automate, personalize, enhance, improve, and synchronize users' interactions and experiences within social networks. ASNI is expected to evolve rapidly, influencing how we interact online and shaping our digital experiences. Transparency, ethical considerations, media influence bias, and user control over data will be crucial to ensure responsible development and positive impact.
Lexical choice
Lexical choice is the subtask of Natural language generation that involves choosing the content words (nouns, non-auxiliary verbs, adjectives, and adverbs) in a generated text. Function words (determiners, for example) are usually chosen during realisation. == Examples == The simplest type of lexical choice involves mapping a domain concept (perhaps represented in an ontology) to a word. For example, the concept Finger might be mapped to the word finger. A more complex situation is when a domain concept is expressed using different words in different situations. For example, the domain concept Value-Change can be expressed in many ways: The temperature rose: the verb rose is used for a Value-Change in temperature which increases the value. The temperature fell: the verb fell is used for a Value-Change in temperature which decreases the value. The rain got heavier: the phrase got heavier is used for a Value-Change in precipitation amount when the precipitation is rain. Sometimes words can communicate additional contextual information, for example: The temperature plummeted: the verb plummeted is used for a Value-Change in temperature which decreases the value, when the change is rapid and large. Contextual information is especially significant for vague terms such as tall. For example, a 2m tall man is tall, but a 2m tall horse is small. == Linguistic perspective == Lexical choice modules must be informed by linguistic knowledge of how the system's input data maps onto words. This is a question of semantics, but it is also influenced by syntactic factors (such as collocation effects) and pragmatic factors (such as context). Hence NLG systems need linguistic models of how meaning is mapped to words in the target domain (genre) of the NLG system. Genre tends to be very important; for example the verb veer has a very specific meaning in weather forecasts (wind direction is changing in a clockwise direction) which it does not have in general English, and a weather-forecast generator must be aware of this genre-specific meaning. In some cases there are major differences in how different people use the same word; for example, some people use by evening to mean 6PM and others use it to mean midnight. Psycholinguists have shown that when people speak to each other, they agree on a common interpretation via lexical alignment; this is not something which NLG systems can yet do. Ultimately, lexical choice must deal with the fundamental issue of how language relates to the non-linguistic world. For example, a system which chose colour terms such as red to describe objects in a digital image would need to know which RGB pixel values could generally be described as red; how this was influenced by visual (lighting, other objects in the scene) and linguistic (other objects being discussed) context; what pragmatic connotations were associated with red (for example, when an apple is called red, it is assumed to be ripe as well as have the colour red); and so forth. == Algorithms and models == A number of algorithms and models have been developed for lexical choice in the research community, for example Edmonds developed a model for choosing between near-synonyms (words with similar core meanings but different connotations). However such algorithms and models have not been widely used in applied NLG systems; such systems have instead often used quite simple computational models, and invested development effort in linguistic analysis instead of algorithm development.
SpreeAI
SpreeAI (stylized as SPREEAI) is an American fashion technology company headquartered in Incline Village, Nevada that develops artificial intelligence software for the apparel and retail industries, including photorealistic virtual try-on, AI-powered sizing recommendations, and digital model generation. Founded in 2022 by John Imah and Bob Davidson, the company achieved unicorn status in 2025 following a Series B round led by Davidson Group that valued the company at approximately US$1.5 billion. TechCrunch identified SpreeAI as one of the more than 100 new tech unicorns minted in 2025. Its board of directors includes supermodel Naomi Campbell and hospitality executive Larry Ruvo. == History == SpreeAI was founded in 2022 by John Imah and Bob Davidson with a focus on artificial intelligence applications in fashion retail. By 2024, the company had raised approximately US$60 million in venture funding. In May 2025, SpreeAI announced a Series B round led by Davidson Group; reporting at the time placed the company's valuation at approximately US$1.5 billion, making it one of a small number of fashion-technology companies to reach unicorn status. In January 2026, TechCrunch listed SpreeAI among the more than 100 new tech unicorns minted in 2025. == Technology == SpreeAI develops a suite of artificial intelligence tools for the apparel industry. Its consumer-facing platform allows shoppers to upload a single photograph or select a digital model and then visualize clothing items on that figure with photorealistic rendering, while a complementary sizing engine generates fit recommendations intended to reduce returns. The platform is designed for integration with online retailers so that shoppers can preview garments before purchase. The company has stated that its models were developed in part through research collaborations with the Massachusetts Institute of Technology and Carnegie Mellon University. == Leadership and board == John Imah, a Nigerian-American technology executive who previously held roles at Samsung, Twitch, Meta Platforms, and Snap Inc., is co-founder and chief executive officer. Co-founder Bob Davidson, through Davidson Group, led the company's Series B financing. The company's board of directors includes supermodel Naomi Campbell, who joined in 2024, and Las Vegas hospitality executive Larry Ruvo. == Partnerships == SpreeAI has formed partnerships across both academia and the fashion industry. Council of Fashion Designers of America (CFDA). In 2025, SpreeAI entered a partnership with the CFDA to support American designers and brands with AI-driven tools; the CFDA described SpreeAI as "a fashion technology leader delivering innovative solutions to help designers and brands thrive." Massachusetts Institute of Technology and Carnegie Mellon University. The company has cited ongoing research and talent collaborations with both institutions. Sergio Hudson and Kai Collective. In 2025, SpreeAI made what WWD described as its Met Gala debut through a custom collaboration with designer Sergio Hudson and Nigerian-British label Kai Collective; the collaboration paired Hudson's couture with SpreeAI's virtual try-on platform. == Recognition == In 2025, TechCrunch named SpreeAI among the new tech unicorns of the year. In 2025, SpreeAI was named an honoree in Inc.'s Best in Business awards, and CEO John Imah was included on Inc.'s list of 40 business leaders who "propelled their organizations to success." In 2025, Imah was named to the Observer's AI Power Index, a list of 100 leaders shaping the future of artificial intelligence. In 2025, Imah was included in AfroTech's Future 50, recognizing Black innovators in technology. SpreeAI and Imah have been the subject of profile coverage in The Washington Post, Rolling Stone UK, WWD, Vogue UA, L'Officiel Arabia, GQ South Africa, and Inc..
Perceptual computing
Perceptual computing is an application of Zadeh's theory of computing with words on the field of assisting people to make subjective judgments. == Perceptual computer == The perceptual computer – Per-C – an instantiation of perceptual computing – has the architecture that is depicted in Fig. 1 [2]–[6]. It consists of three components: encoder, CWW engine and decoder. Perceptions – words – activate the Per-C and are the Per-C output (along with data); so, it is possible for a human to interact with the Per-C using just a vocabulary. A vocabulary is application (context) dependent, and must be large enough so that it lets the end-user interact with the Per-C in a user-friendly manner. The encoder transforms words into fuzzy sets (FSs) and leads to a codebook – words with their associated FS models. The outputs of the encoder activate a Computing With Words (CWW) engine, whose output is one or more other FSs, which are then mapped by the decoder into a recommendation (subjective judgment) with supporting data. The recommendation may be in the form of a word, group of similar words, rank or class. Although many details are needed in order to implement the Per-C's three components – encoder, decoder and CWW engine – and they are covered in [5], it is when the Per-C is applied to specific applications, that the focus on the methodology becomes clear. Stepping back from those details, the methodology of perceptual computing is: Focus on an application (A). Establish a vocabulary (or vocabularies) for A. Collect interval end-point data from a group of subjects (representative of the subjects who will use the Per-C) for all of the words in the vocabulary. Map the collected word data into word-FOUs by using the Interval Approach [1], [5, Ch. 3]. The result of doing this is the codebook (or codebooks) for A, and completes the design of the encoder of the Per-C. Choose an appropriate CWW engine for A. It will map IT2 FSs into one or more IT2 FSs. Examples of CWW engines are: IF-THEN rules [5, Ch. 6] and Linguistic Weighted Averages [6], [5, Ch. 5]. If an existing CWW engine is available for A, then use its available mathematics to compute its output(s). Otherwise, develop such mathematics for the new kind of CWW engine. The new CWW engine should be constrained so that its output(s) resemble the FOUs in the codebook(s) for A. Map the IT2 FS outputs from the CWW engine into a recommendation at the output of the decoder. If the recommendation is a word, rank or class, then use existing mathematics to accomplish this mapping [5, Ch. 4]. Otherwise, develop such mathematics for the new kind of decoder. == Applications of Per-C == To-date a Per-C has been implemented for the following four applications: (1) investment decision-making, (2) social judgment making, (3) distributed decision making, and (4) hierarchical and distributed decision-making. A specific example of the fourth application is the so-called Journal Publication Judgment Advisor [5, Ch. 10] in which for the first time only words are used at every level of the following hierarchical and distributed decision making process: n reviewers have to provide a subjective recommendation about a journal article that has been sent to them by the Associate Editor, who then has to aggregate the independent recommendations into a final recommendation that is sent to the Editor-in-Chief of the journal. Because it is very problematic to ask reviewers to provide numerical scores for paper-evaluation sub-categories (the two major categories are Technical Merit and Presentation), such as importance, content, depth, style, organization, clarity, references, etc., each reviewer will only be asked to provide a linguistic score for each of these categories. They will not be asked for an overall recommendation about the paper because in the past it is quite common for reviewers who provide the same numerical scores for such categories to give very different publishing recommendations. By leaving a specific recommendation to the associate editor such inconsistencies can hope to be eliminated. How words can be aggregated to reflect each reviewer's recommendation as well as the expertise of each reviewer about the paper's subject matter is done using a linguistic weighted average. Although the journal publication judgment advisor uses reviewers and an associate editor, the word “reviewer” could be replaced by judge, expert, low-level manager, commander, referee, etc., and the term “associate editor” could be replaced by control center, command center, higher-level manager, etc. So, this application has potential wide applicability to many other applications. Recently, a new Per-C based Failure mode and effects analysis (FMEA) methodology was developed, with its application to edible bird's nest farming, in Borneo, has been reported. In addition, application of Per-C based method to educational assessment, for cooperative learning of students has been reported. In summary, the Per-C (whose development has taken more than a decade) is the first complete implementation of Zadeh's CWW paradigm, as applied to assisting people to make subjective judgments.
Neural architecture search
Neural architecture search (NAS) is a technique for automating the design of artificial neural networks (ANN), a widely used model in the field of machine learning. NAS has been used to design networks that are on par with or outperform hand-designed architectures. Methods for NAS can be categorized according to the search space, search strategy and performance estimation strategy used: The search space defines the type(s) of ANN that can be designed and optimized. The search strategy defines the approach used to explore the search space. The performance estimation strategy evaluates the performance of a possible ANN from its design (without constructing and training it). NAS is closely related to hyperparameter optimization and meta-learning and is a subfield of automated machine learning (AutoML). == Reinforcement learning == Reinforcement learning (RL) can underpin a NAS search strategy. Barret Zoph and Quoc Viet Le applied NAS with RL targeting the CIFAR-10 dataset and achieved a network architecture that rivals the best manually-designed architecture for accuracy, with an error rate of 3.65, 0.09 percent better and 1.05x faster than a related hand-designed model. On the Penn Treebank dataset, that model composed a recurrent cell that outperforms LSTM, reaching a test set perplexity of 62.4, or 3.6 perplexity better than the prior leading system. On the PTB character language modeling task it achieved bits per character of 1.214. Learning a model architecture directly on a large dataset can be a lengthy process. NASNet addressed this issue by transferring a building block designed for a small dataset to a larger dataset. The design was constrained to use two types of convolutional cells to return feature maps that serve two main functions when convoluting an input feature map: normal cells that return maps of the same extent (height and width) and reduction cells in which the returned feature map height and width is reduced by a factor of two. For the reduction cell, the initial operation applied to the cell's inputs uses a stride of two (to reduce the height and width). The learned aspect of the design included elements such as which lower layer(s) each higher layer took as input, the transformations applied at that layer and to merge multiple outputs at each layer. In the studied example, the best convolutional layer (or "cell") was designed for the CIFAR-10 dataset and then applied to the ImageNet dataset by stacking copies of this cell, each with its own parameters. The approach yielded accuracy of 82.7% top-1 and 96.2% top-5. This exceeded the best human-invented architectures at a cost of 9 billion fewer FLOPS—a reduction of 28%. The system continued to exceed the manually-designed alternative at varying computation levels. The image features learned from image classification can be transferred to other computer vision problems. E.g., for object detection, the learned cells integrated with the Faster-RCNN framework improved performance by 4.0% on the COCO dataset. In the so-called Efficient Neural Architecture Search (ENAS), a controller discovers architectures by learning to search for an optimal subgraph within a large graph. The controller is trained with policy gradient to select a subgraph that maximizes the validation set's expected reward. The model corresponding to the subgraph is trained to minimize a canonical cross entropy loss. Multiple child models share parameters, ENAS requires fewer GPU-hours than other approaches and 1000-fold less than "standard" NAS. On CIFAR-10, the ENAS design achieved a test error of 2.89%, comparable to NASNet. On Penn Treebank, the ENAS design reached test perplexity of 55.8. == Evolution == An alternative approach to NAS is based on evolutionary algorithms, which has been employed by several groups. An Evolutionary Algorithm for Neural Architecture Search generally performs the following procedure. First a pool consisting of different candidate architectures along with their validation scores (fitness) is initialised. At each step the architectures in the candidate pool are mutated (e.g.: 3x3 convolution instead of a 5x5 convolution). Next the new architectures are trained from scratch for a few epochs and their validation scores are obtained. This is followed by replacing the lowest scoring architectures in the candidate pool with the better, newer architectures. This procedure is repeated multiple times and thus the candidate pool is refined over time. Mutations in the context of evolving ANNs are operations such as adding or removing a layer, which include changing the type of a layer (e.g., from convolution to pooling), changing the hyperparameters of a layer, or changing the training hyperparameters. On CIFAR-10 and ImageNet, evolution and RL performed comparably, while both slightly outperformed random search. == Bayesian optimization == Bayesian Optimization (BO), which has proven to be an efficient method for hyperparameter optimization, can also be applied to NAS. In this context, the objective function maps an architecture to its validation error after being trained for a number of epochs. At each iteration, BO uses a surrogate to model this objective function based on previously obtained architectures and their validation errors. One then chooses the next architecture to evaluate by maximizing an acquisition function, such as expected improvement, which provides a balance between exploration and exploitation. Acquisition function maximization and objective function evaluation are often computationally expensive for NAS, and make the application of BO challenging in this context. Recently, BANANAS has achieved promising results in this direction by introducing a high-performing instantiation of BO coupled to a neural predictor. == Hill-climbing == Another group used a hill climbing procedure that applies network morphisms, followed by short cosine-annealing optimization runs. The approach yielded competitive results, requiring resources on the same order of magnitude as training a single network. E.g., on CIFAR-10, the method designed and trained a network with an error rate below 5% in 12 hours on a single GPU. == Multi-objective search == While most approaches solely focus on finding architecture with maximal predictive performance, for most practical applications other objectives are relevant, such as memory consumption, model size or inference time (i.e., the time required to obtain a prediction). Because of that, researchers created a multi-objective search. LEMONADE is an evolutionary algorithm that adopted Lamarckism to efficiently optimize multiple objectives. In every generation, child networks are generated to improve the Pareto frontier with respect to the current population of ANNs. Neural Architect is claimed to be a resource-aware multi-objective RL-based NAS with network embedding and performance prediction. Network embedding encodes an existing network to a trainable embedding vector. Based on the embedding, a controller network generates transformations of the target network. A multi-objective reward function considers network accuracy, computational resource and training time. The reward is predicted by multiple performance simulation networks that are pre-trained or co-trained with the controller network. The controller network is trained via policy gradient. Following a modification, the resulting candidate network is evaluated by both an accuracy network and a training time network. The results are combined by a reward engine that passes its output back to the controller network. == One-shot models == RL or evolution-based NAS require thousands of GPU-days of searching/training to achieve state-of-the-art computer vision results as described in the NASNet, mNASNet and MobileNetV3 papers. To reduce computational cost, many recent NAS methods rely on the weight-sharing idea. In this approach, a single overparameterized supernetwork (also known as the one-shot model) is defined. A supernetwork is a very large Directed Acyclic Graph (DAG) whose subgraphs are different candidate neural networks. Thus, in a supernetwork, the weights are shared among a large number of different sub-architectures that have edges in common, each of which is considered as a path within the supernet. The essential idea is to train one supernetwork that spans many options for the final design rather than generating and training thousands of networks independently. In addition to the learned parameters, a set of architecture parameters are learnt to depict preference for one module over another. Such methods reduce the required computational resources to only a few GPU days. More recent works further combine this weight-sharing paradigm, with a continuous relaxation of the search space, which enables the use of gradient-based optimization methods. These approaches are generally referred to as differentiable NAS and have proven very efficient in exploring the search space of ne
RIPAC (microprocessor)
RIPAC was a VLSI single-chip microprocessor designed for automatic recognition of the connected speech, one of the first of this use. The project of the microprocessor RIPAC started in 1984. RIPAC was aimed to provide efficient real-time speech recognition services to the italian telephone system provided by SIP. The microprocessor was presented in September 1986 at The Hague (Netherlands) at EUSPICO conference. It was composed of 70.000 transistors and structured as Harvard architecture. The name RIPAC is the acronym for "Riconoscimento del PArlato Connesso", that means "Recognition of the connected speech" in Italian. The microprocessor was designed by the Italian companies CSELT and ELSAG and was produced by SGS: a combination of Hidden Markov Model and Dynamic Time Warping algorithms was used for processing speech signals. It was able to do real-time speech recognition of Italian and many languages with a good affordability. The chip, issued by U.S. Patent No. 4,907,278, worked at first run.
Ordered weighted averaging
In applied mathematics, specifically in fuzzy logic, the ordered weighted averaging (OWA) operators provide a parameterized class of mean type aggregation operators. They were introduced by Ronald R. Yager. Many notable mean operators such as the max, arithmetic average, median and min, are members of this class. They have been widely used in computational intelligence because of their ability to model linguistically expressed aggregation instructions. == Definition == An OWA operator of dimension n {\displaystyle \ n} is a mapping F : R n → R {\displaystyle F:\mathbb {R} ^{n}\rightarrow \mathbb {R} } that has an associated collection of weights W = [ w 1 , … , w n ] {\displaystyle \ W=[w_{1},\ldots ,w_{n}]} lying in the unit interval and summing to one and with F ( a 1 , … , a n ) = ∑ j = 1 n w j b j {\displaystyle F(a_{1},\ldots ,a_{n})=\sum _{j=1}^{n}w_{j}b_{j}} where b j {\displaystyle b_{j}} is the jth largest of the a i {\displaystyle a_{i}} . By choosing different W one can implement different aggregation operators. The OWA operator is a non-linear operator as a result of the process of determining the bj. == Notable OWA operators == F ( a 1 , … , a n ) = max ( a 1 , … , a n ) {\displaystyle \ F(a_{1},\ldots ,a_{n})=\max(a_{1},\ldots ,a_{n})} if w 1 = 1 {\displaystyle \ w_{1}=1} and w j = 0 {\displaystyle \ w_{j}=0} for j ≠ 1 {\displaystyle j\neq 1} F ( a 1 , … , a n ) = min ( a 1 , … , a n ) {\displaystyle \ F(a_{1},\ldots ,a_{n})=\min(a_{1},\ldots ,a_{n})} if w n = 1 {\displaystyle \ w_{n}=1} and w j = 0 {\displaystyle \ w_{j}=0} for j ≠ n {\displaystyle j\neq n} F ( a 1 , … , a n ) = a v e r a g e ( a 1 , … , a n ) {\displaystyle \ F(a_{1},\ldots ,a_{n})=\mathrm {average} (a_{1},\ldots ,a_{n})} if w j = 1 n {\displaystyle \ w_{j}={\frac {1}{n}}} for all j ∈ [ 1 , n ] {\displaystyle j\in [1,n]} == Properties == The OWA operator is a mean operator. It is bounded, monotonic, symmetric, and idempotent, as defined below. == Characterizing features == Two features have been used to characterize the OWA operators. The first is the attitudinal character, also called orness. This is defined as A − C ( W ) = 1 n − 1 ∑ j = 1 n ( n − j ) w j . {\displaystyle A-C(W)={\frac {1}{n-1}}\sum _{j=1}^{n}(n-j)w_{j}.} It is known that A − C ( W ) ∈ [ 0 , 1 ] {\displaystyle A-C(W)\in [0,1]} . In addition A − C(max) = 1, A − C(ave) = A − C(med) = 0.5 and A − C(min) = 0. Thus the A − C goes from 1 to 0 as we go from Max to Min aggregation. The attitudinal character characterizes the similarity of aggregation to OR operation(OR is defined as the Max). The second feature is the dispersion. This defined as H ( W ) = − ∑ j = 1 n w j ln ( w j ) . {\displaystyle H(W)=-\sum _{j=1}^{n}w_{j}\ln(w_{j}).} An alternative definition is E ( W ) = ∑ j = 1 n w j 2 . {\displaystyle E(W)=\sum _{j=1}^{n}w_{j}^{2}.} The dispersion characterizes how uniformly the arguments are being used. == Type-1 OWA aggregation operators == The above Yager's OWA operators are used to aggregate the crisp values. Can we aggregate fuzzy sets in the OWA mechanism? The Type-1 OWA operators have been proposed for this purpose. So the type-1 OWA operators provides us with a new 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 type-1 OWA operator is defined according to the alpha-cuts of fuzzy sets as follows: 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 given as 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,\ldots ,n\;\}\to \{\;1,\ldots ,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,\ldots ,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},\ldots ,a_{n}}\right\}} . The computation of the type-1 OWA output is implemented by computing 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},\ldots ,A_{\alpha }^{n}}\right)} : Φ α ( A α 1 , … , A α n ) − {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)_{-}} and Φ α ( A α 1 , … , A α n ) + , {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)_{+},} where A α i = [ A α − i , A α + i ] , W α i = [ W α − i , W α + i ] {\displaystyle A_{\alpha }^{i}=[A_{\alpha -}^{i},A_{\alpha +}^{i}],W_{\alpha }^{i}=[W_{\alpha -}^{i},W_{\alpha +}^{i}]} . Then membership function of resulting aggregation fuzzy set is: μ G ( x ) = ∨ α : x ∈ Φ α ( A α 1 , ⋯ , A α n ) α α {\displaystyle \mu _{G}(x)=\mathop {\vee } _{\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)_{-}=\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)_{+}=\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}}}} Zhou et al. presented a fast method to solve two programming problem so that the type-1 OWA aggregation operation can be performed efficiently. == OWA for committee voting == Amanatidis, Barrot, Lang, Markakis and Ries present voting rules for multi-issue voting, based on OWA and the Hamming distance. Barrot, Lang and Yokoo study the manipulability of these rules.