Rough Fuzzy Hybridization
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Rough Fuzzy Hybridization
{{No footnotes, date=April 2009 Rough fuzzy hybridization is a method of hybrid intelligent system or soft computing, where Fuzzy set theory is used for linguistic representation of patterns, leading to a ''fuzzy granulation'' of the feature space. Rough set In computer science, a rough set, first described by Polish computer scientist Zdzisław I. Pawlak, is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the ''lower'' and the ''upper'' approximati ... theory is used to obtain dependency rules which model informative regions in the granulated feature space. External links Case generation Fuzzy logic ...
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Hybrid Intelligent System
Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as: * Neuro-symbolic systems * Neuro-fuzzy systems * Hybrid connectionist-symbolic models * Fuzzy expert systems * Connectionist expert systems * Evolutionary neural networks * Genetic fuzzy systems * Rough fuzzy hybridization * Reinforcement learning with fuzzy, neural, or evolutionary methods as well as symbolic reasoning methods. From the cognitive science perspective, every natural intelligent system is hybrid because it performs mental operations on both the symbolic and subsymbolic levels. For the past few years, there has been an increasing discussion of the importance of A.I. Systems Integration. Based on notions that there have already been created simple and specific AI systems (such as systems for computer vision, speech synthesis, etc., or software that employs some of the models mentioned above) and ...
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Soft Computing
Soft computing is a set of algorithms, including neural networks, fuzzy logic, and evolutionary algorithms. These algorithms are tolerant of imprecision, uncertainty, partial truth and approximation. It is contrasted with hard computing: algorithms which find provably correct and optimal solutions to problems. __TOC__ History The theory and techniques related to soft computing were first introduced in 1980s. The term "soft computing" was coined by Lotfi A. Zadeh. See also * Emergence * Synthetic intelligence * Watson (computer) IBM Watson is a question-answering computer system capable of answering questions posed in natural language, developed in IBM's DeepQA project by a research team led by principal investigator David Ferrucci. Watson was named after IBM's founder ... Notable journals * ''Soft Computing'' *''Applied Soft Computing'' References Soft computing {{Compu-ai-stub ...
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Fuzzy Set
In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an ''L''-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of ''L''-relations when ''L'' is the unit interval , 1 In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition—an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval , 1 Fuzzy sets generali ...
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Feature Space
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern recognition, classification and regression. Features are usually numeric, but structural features such as strings and graphs are used in syntactic pattern recognition. The concept of "feature" is related to that of explanatory variable used in statistical techniques such as linear regression. Classification A numeric feature can be conveniently described by a feature vector. One way to achieve binary classification is using a linear predictor function (related to the perceptron) with a feature vector as input. The method consists of calculating the scalar product between the feature vector and a vector of weights, qualifying those observations whose result exceeds a threshold. Algorithms for classification from a feature vector include ...
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Rough Set
In computer science, a rough set, first described by Polish computer scientist Zdzisław I. Pawlak, is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the ''lower'' and the ''upper'' approximation of the original set. In the standard version of rough set theory (Pawlak 1991), the lower- and upper-approximation sets are crisp sets, but in other variations, the approximating sets may be fuzzy sets. Definitions The following section contains an overview of the basic framework of rough set theory, as originally proposed by Zdzisław I. Pawlak, along with some of the key definitions. More formal properties and boundaries of rough sets can be found in Pawlak (1991) and cited references. The initial and basic theory of rough sets is sometimes referred to as ''"Pawlak Rough Sets"'' or ''"classical rough sets"'', as a means to distinguish from more recent extensions and generalizations. Information system framework Let I = (\mathbb,\mat ...
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