text stringlengths 12 14.7k |
|---|
Fuzzy measure theory : Fuzzy Measure Theory at Fuzzy Image Processing Archived 2019-06-30 at the Wayback Machine |
Fuzzy number : A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function. A fuzzy number is thus a speci... |
Fuzzy number : Fuzzy set Uncertainty Interval arithmetic Random variable |
Fuzzy number : Fuzzy Logic Tutorial |
Fuzzy pay-off method for real option valuation : The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation ... |
Fuzzy pay-off method for real option valuation : The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the thre... |
Fuzzy pay-off method for real option valuation : The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding in... |
Fuzzy relation : A fuzzy relation is the cartesian product of mathematical fuzzy sets. Two fuzzy sets are taken as input, the fuzzy relation is then equal to the cross product of the sets which is created by vector multiplication. Usually, a rule base is stored in a matrix notation which allows the fuzzy controller to ... |
Fuzzy routing : Fuzzy routing is the application of fuzzy logic to routing protocols, particularly in the context of ad-hoc wireless networks and in networks supporting multiple quality of service classes. It is currently the subject of research. |
Fuzzy routing : Dynamic routing List of ad hoc routing protocols |
Fuzzy routing : Hui Liu et al., An Adaptive Genetic Fuzzy Multi-path Routing Protocol for Wireless Ad Hoc Networks Runtong Zhang, A Fuzzy Routing Mechanism In Next-Generation Networks |
Fuzzy set : In mathematics, fuzzy sets (also known as 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, Salii (1965) defined a more general kind of structure called an "... |
Fuzzy set : A fuzzy set is a pair ( U , m ) where U is a set (often required to be non-empty) and m : U → [ 0 , 1 ] a membership function. The reference set U (sometimes denoted by Ω or X ) is called universe of discourse, and for each x ∈ U , the value m ( x ) is called the grade of membership of x in ( U , m... |
Fuzzy set : As an extension of the case of multi-valued logic, valuations ( μ : V o → W _\to ) of propositional variables ( V o _ ) into a set of membership degrees ( W ) can be thought of as membership functions mapping predicates into fuzzy sets (or more formally, into an ordered set of fuzzy pairs, called a fuzzy ... |
Fuzzy set : A fuzzy number is a fuzzy set that satisfies all the following conditions: A is normalised; A is a convex set; The membership function μ A ( x ) (x) achieves the value 1 at least once; The membership function μ A ( x ) (x) is at least segmentally continuous. If these conditions are not satisfied, then A is ... |
Fuzzy set : The use of set membership as a key component of category theory can be generalized to fuzzy sets. This approach, which began in 1968 shortly after the introduction of fuzzy set theory, led to the development of Goguen categories in the 21st century. In these categories, rather than using two valued set memb... |
Fuzzy set : The fuzzy relation equation is an equation of the form A · R = B, where A and B are fuzzy sets, R is a fuzzy relation, and A · R stands for the composition of A with R . |
Fuzzy set : A measure d of fuzziness for fuzzy sets of universe U should fulfill the following conditions for all x ∈ U : d ( A ) = 0 if A is a crisp set: μ A ( x ) ∈ (x)\in \ d ( A ) has a unique maximum iff ∀ x ∈ U : μ A ( x ) = 0.5 (x)=0.5 μ A ≤ μ B ⟺ \leq \mu _\iff μ A ≤ μ B ≤ 0.5 \leq \mu _\leq 0.5 μ A ≥ μ ... |
Fuzzy set : There are many mathematical constructions similar to or more general than fuzzy sets. Since fuzzy sets were introduced in 1965, many new mathematical constructions and theories treating imprecision, inexactness, ambiguity, and uncertainty have been developed. Some of these constructions and theories are ext... |
Fuzzy set : == References == |
Fuzzy set operations : Fuzzy set operations are a generalization of crisp set operations for fuzzy sets. There is in fact more than one possible generalization. The most widely used operations are called standard fuzzy set operations; they comprise: fuzzy complements, fuzzy intersections, and fuzzy unions. |
Fuzzy set operations : Let A and B be fuzzy sets that A,B ⊆ U, u is any element (e.g. value) in the U universe: u ∈ U. Standard complement μ ¬ A ( u ) = 1 − μ A ( u ) (u)=1-\mu _(u) The complement is sometimes denoted by ∁A or A∁ instead of ¬A. Standard intersection μ A ∩ B ( u ) = min (u)=\min\(u),\mu _(u)\ Standard ... |
Fuzzy set operations : μA(x) is defined as the degree to which x belongs to A. Let ∁A denote a fuzzy complement of A of type c. Then μ∁A(x) is the degree to which x belongs to ∁A, and the degree to which x does not belong to A. (μA(x) is therefore the degree to which x does not belong to ∁A.) Let a complement ∁A be def... |
Fuzzy set operations : The intersection of two fuzzy sets A and B is specified in general by a binary operation on the unit interval, a function of the form i:[0,1]×[0,1] → [0,1]. For all x ∈ U: μA ∩ B(x) = i[μA(x), μB(x)]. |
Fuzzy set operations : The union of two fuzzy sets A and B is specified in general by a binary operation on the unit interval function of the form u:[0,1]×[0,1] → [0,1]. For all x ∈ U: μA ∪ B(x) = u[μA(x), μB(x)]. |
Fuzzy set operations : Aggregation operations on fuzzy sets are operations by which several fuzzy sets are combined in a desirable way to produce a single fuzzy set. Aggregation operation on n fuzzy set (2 ≤ n) is defined by a function h:[0,1]n → [0,1] |
Fuzzy set operations : Fuzzy logic Fuzzy set T-norm Type-2 fuzzy sets and systems De Morgan algebra |
Fuzzy set operations : Klir, George J.; Bo Yuan (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall. ISBN 978-0131011717. |
Fuzzy set operations : L.A. Zadeh. Fuzzy sets. Information and Control, 8:338–353, 1965 |
Fuzzy Sets and Systems : Fuzzy Sets and Systems is a peer-reviewed international scientific journal published by Elsevier on behalf of the International Fuzzy Systems Association (IFSA) and was founded in 1978. The editors-in-chief (as of 2010) are Bernard De Baets of the Department of Data Analysis and Mathematical Mo... |
Fuzzy Sets and Systems : Fuzzy control system Fuzzy Control Language Fuzzy logic Fuzzy set |
Fuzzy subalgebra : Fuzzy subalgebras theory is a chapter of fuzzy set theory. It is obtained from an interpretation in a multi-valued logic of axioms usually expressing the notion of subalgebra of a given algebraic structure. |
Fuzzy subalgebra : Consider a first order language for algebraic structures with a monadic predicate symbol S. Then a fuzzy subalgebra is a fuzzy model of a theory containing, for any n-ary operation h, the axioms ∀ x 1 , . . . , ∀ x n ( S ( x 1 ) ∧ . . . . . ∧ S ( x n ) → S ( h ( x 1 , . . . , x n ) ) ,...,\forall x_(... |
Fuzzy subalgebra : The fuzzy subgroups and the fuzzy submonoids are particularly interesting classes of fuzzy subalgebras. In such a case a fuzzy subset s of a monoid (M,•,u) is a fuzzy submonoid if and only if s ( u ) = 1 )=1 s ( x ) ⊙ s ( y ) ≤ s ( x ⋅ y ) where u is the neutral element in A. Given a group G, a fuz... |
Fuzzy subalgebra : Klir, G. and Bo Yuan, Fuzzy Sets and Fuzzy Logic (1995) ISBN 978-0-13-101171-7 Zimmermann H., Fuzzy Set Theory and its Applications (2001), ISBN 978-0-7923-7435-0. Chakraborty H. and Das S., On fuzzy equivalence 1, Fuzzy Sets and Systems, 11 (1983), 185-193. Demirci M., Recasens J., Fuzzy groups, fuz... |
FuzzyCLIPS : FuzzyCLIPS is a fuzzy logic extension of the CLIPS (C Language Integrated Production System) expert system shell from NASA. It was developed by the Integrated Reasoning Group of the Institute for Information Technology of the National Research Council of Canada and has been widely distributed for a number ... |
FuzzyCLIPS : FuzzyCLIPS GitHub Repository (compatible with CLIPS 6.10) FuzzyCLIPS source code compatible with CLIPS 6.24 and CLIPS 6.31 (by CLIPS maintainer) NASA sponsorship of FuzzyCLIPS. NASA conference discussion FuzzyCLIPS. Textbook that discusses fuzzy aspects and CLIPS, the basis for FuzzyCLIPS. NASA firm inform... |
High-performance fuzzy computing : High-performance fuzzy computing (HPFC) is those technologies able to exploit supercomputers and computer clusters to perform high performance fuzzy logic computations. Thus HPFC is just a special case of the much more general high-performance computing. In the specific case of fuzzy ... |
High-performance fuzzy computing : (in English) Rapid prototyping of high performance fuzzy computing applications using high level GPU programming for maritime operations support (in English) Speedup of Implementing Fuzzy Neural Networks with high-dimensional inputs through Parallel Processing on Graphic Processing Un... |
IEEE 1855 : IEEE STANDARD 1855-2016, IEEE Standard for Fuzzy Markup language (FML), is a technical standard developed by the IEEE Standards Association. FML allows modelling a fuzzy logic system in a human-readable and hardware independent way. FML is based on eXtensible Markup Language (XML). The designers of fuzzy sy... |
IEEE 1855 : Official website (https://standards.ieee.org/ieee/1855/5418/) |
Linear partial information : Linear partial information (LPI) is a method of making decisions based on insufficient or fuzzy information. LPI was introduced in 1970 by Polish–Swiss mathematician Edward Kofler (1911–2007) to simplify decision processes. Compared to other methods the LPI-fuzziness is algorithmically simp... |
Linear partial information : Any Stochastic Partial Information SPI(p), which can be considered as a solution of a linear inequality system, is called Linear Partial Information LPI(p) about probability p. It can be considered as an LPI-fuzzification of the probability p corresponding to the concepts of linear fuzzy lo... |
Linear partial information : The MaxEmin Principle To obtain the maximally warranted expected value, the decision maker has to choose the strategy which maximizes the minimal expected value. This procedure leads to the MaxEmin – Principle and is an extension of the Bernoulli's principle. The MaxWmin Principle This prin... |
Linear partial information : Despite the fuzziness of information, it is often necessary to choose the optimal, most cautious strategy, for example in economic planning, in conflict situations or in daily decisions. This is impossible without the concept of fuzzy equilibrium. The concept of fuzzy stability is considere... |
Linear partial information : Considering a given LPI-decision model, as a convolution of the corresponding fuzzy states or a disturbance set, the fuzzy equilibrium strategy remains the most cautious one, despite the presence of the fuzziness. Any deviation from this strategy can cause a loss for the decision maker. |
Linear partial information : Tools for establishing dominance with linear partial information and attribute hierarchy Archived 2011-09-28 at the Wayback Machine Linear Partial Information with applications Linear Partial Information (LPI) with applications to the U.S. economic policy Practical decision making with Line... |
Łukasiewicz logic : In mathematics and philosophy, Łukasiewicz logic ( WUUK-ə-SHEV-itch, Polish: [wukaˈɕɛvitʂ]) is a non-classical, many-valued logic. It was originally defined in the early 20th century by Jan Łukasiewicz as a three-valued modal logic; it was later generalized to n-valued (for all finite n) as well as ... |
Łukasiewicz logic : The propositional connectives of Łukasiewicz logic are → ("implication"), and the constant ⊥ ("false"). Additional connectives can be defined in terms of these: ¬ A = d e f A → ⊥ A ∨ B = d e f ( A → B ) → B A ∧ B = d e f ¬ ( ¬ A ∨ ¬ B ) A ↔ B = d e f ( A → B ) ∧ ( B → A ) ⊤ = d e f ⊥ → ⊥ \neg A&=_... |
Łukasiewicz logic : The original system of axioms for propositional infinite-valued Łukasiewicz logic used implication and negation as the primitive connectives, along with modus ponens: A → ( B → A ) ( A → B ) → ( ( B → C ) → ( A → C ) ) ( ( A → B ) → B ) → ( ( B → A ) → A ) ( ¬ B → ¬ A ) → ( A → B ) . A&\rightarrow (... |
Łukasiewicz logic : A hypersequent calculus for three-valued Łukasiewicz logic was introduced by Arnon Avron in 1991. Sequent calculi for finite and infinite-valued Łukasiewicz logics as an extension of linear logic were introduced by A. Prijatelj in 1994. However, these are not cut-free systems. Hypersequent calculi f... |
Łukasiewicz logic : Infinite-valued Łukasiewicz logic is a real-valued logic in which sentences from sentential calculus may be assigned a truth value of not only 0 or 1 but also any real number in between (e.g. 0.25). Valuations have a recursive definition where: w ( θ ∘ ϕ ) = F ∘ ( w ( θ ) , w ( ϕ ) ) (w(\theta ),w(\... |
Łukasiewicz logic : Using exactly the same valuation formulas as for real-valued semantics Łukasiewicz (1922) also defined (up to isomorphism) semantics over any finite set of cardinality n ≥ 2 by choosing the domain as any countable set by choosing the domain as . |
Łukasiewicz logic : The standard real-valued semantics determined by the Łukasiewicz t-norm is not the only possible semantics of Łukasiewicz logic. General algebraic semantics of propositional infinite-valued Łukasiewicz logic is formed by the class of all MV-algebras. The standard real-valued semantics is a special M... |
Łukasiewicz logic : Łukasiewicz logics are co-NP complete. |
Łukasiewicz logic : Łukasiewicz logics can be seen as modal logics, a type of logic that addresses possibility, using the defined operators, ◊ A = d e f ¬ A → A ◻ A = d e f ¬ ◊ ¬ A \Diamond A&=_\neg A\rightarrow A\\\Box A&=_\neg \Diamond \neg A\\\end A third doubtful operator has been proposed, ⊙ A = d e f A ↔ ¬ A A\le... |
Łukasiewicz logic : Rose, A.: 1956, Formalisation du Calcul Propositionnel Implicatif ℵ0 Valeurs de Łukasiewicz, C. R. Acad. Sci. Paris 243, 1183–1185. Rose, A.: 1978, Formalisations of Further ℵ0-Valued Łukasiewicz Propositional Calculi, Journal of Symbolic Logic 43(2), 207–210. doi:10.2307/2272818 Cignoli, R., “The a... |
Membership function (mathematics) : In mathematics, the membership function of a fuzzy set is a generalization of the indicator function for classical sets. In fuzzy logic, it represents the degree of truth as an extension of valuation. Degrees of truth are often confused with probabilities, although they are conceptua... |
Membership function (mathematics) : For any set X , a membership function on X is any function from X to the real unit interval [ 0 , 1 ] . Membership functions represent fuzzy subsets of X . The membership function which represents a fuzzy set A ~ is usually denoted by μ A . . For an element x of X , the value... |
Membership function (mathematics) : See the article on Capacity of a set for a closely related definition in mathematics. One application of membership functions is as capacities in decision theory. In decision theory, a capacity is defined as a function, ν from S, the set of subsets of some set, into [ 0 , 1 ] , suc... |
Membership function (mathematics) : Defuzzification Fuzzy measure theory Fuzzy set operations Rough set |
Membership function (mathematics) : Zadeh L.A., 1965, "Fuzzy sets". Information and Control 8: 338–353. [1] Goguen J.A, 1967, "L-fuzzy sets". Journal of Mathematical Analysis and Applications 18: 145–174 |
Monoidal t-norm logic : In mathematical logic, monoidal t-norm based logic (or shortly MTL), the logic of left-continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic of commutative bounded integral residuated... |
Monoidal t-norm logic : In fuzzy logic, rather than regarding statements as being either true or false, we associate each statement with a numerical confidence in that statement. By convention the confidences range over the unit interval [ 0 , 1 ] , where the maximal confidence 1 corresponds to the classical concept ... |
Monoidal t-norm logic : Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for MTL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all MTL-algebras — that is, all algebras for which the logic is sound Linear semantics... |
Monoidal t-norm logic : Hájek P., 1998, Metamathematics of Fuzzy Logic. Dordrecht: Kluwer. Esteva F. & Godo L., 2001, "Monoidal t-norm based logic: Towards a logic of left-continuous t-norms". Fuzzy Sets and Systems 124: 271–288. Jenei S. & Montagna F., 2002, "A proof of standard completeness of Esteva and Godo's monoi... |
MV-algebra : In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation ⊕ , a unary operation ¬ , and the constant 0 , satisfying certain axioms. MV-algebras are the algebraic semantics of Łukasiewicz logic; the letters MV refer to the many-valued logic of Łuka... |
MV-algebra : An MV-algebra is an algebraic structure ⟨ A , ⊕ , ¬ , 0 ⟩ , consisting of a non-empty set A , a binary operation ⊕ on A , a unary operation ¬ on A , and a constant 0 denoting a fixed element of A , which satisfies the following identities: ( x ⊕ y ) ⊕ z = x ⊕ ( y ⊕ z ) , x ⊕ 0 = x , x ⊕ y = y ⊕ x... |
MV-algebra : A simple numerical example is A = [ 0 , 1 ] , with operations x ⊕ y = min ( x + y , 1 ) and ¬ x = 1 − x . In mathematical fuzzy logic, this MV-algebra is called the standard MV-algebra, as it forms the standard real-valued semantics of Łukasiewicz logic. The trivial MV-algebra has the only element 0 and... |
MV-algebra : C. C. Chang devised MV-algebras to study many-valued logics, introduced by Jan Łukasiewicz in 1920. In particular, MV-algebras form the algebraic semantics of Łukasiewicz logic, as described below. Given an MV-algebra A, an A-valuation is a homomorphism from the algebra of propositional formulas (in the la... |
MV-algebra : MV-algebras were related by Daniele Mundici to approximately finite-dimensional C*-algebras by establishing a bijective correspondence between all isomorphism classes of approximately finite-dimensional C*-algebras with lattice-ordered dimension group and all isomorphism classes of countable MV algebras. S... |
MV-algebra : There are multiple frameworks implementing fuzzy logic (type II), and most of them implement what has been called a multi-adjoint logic. This is no more than the implementation of an MV-algebra. |
MV-algebra : Chang, C. C. (1958) "Algebraic analysis of many-valued logics," Transactions of the American Mathematical Society 88: 476–490. ------ (1959) "A new proof of the completeness of the Lukasiewicz axioms," Transactions of the American Mathematical Society 88: 74–80. Cignoli, R. L. O., D'Ottaviano, I. M. L., Mu... |
MV-algebra : Daniele Mundici, MV-ALGEBRAS. A short tutorial D. Mundici (2011). Advanced Łukasiewicz calculus and MV-algebras. Springer. ISBN 978-94-007-0839-6. Mundici, D. The C*-Algebras of Three-Valued Logic. Logic Colloquium '88, Proceedings of the Colloquium held in Padova 61–77 (1989). doi:10.1016/s0049-237x(08)70... |
MV-algebra : Stanford Encyclopedia of Philosophy: "Many-valued logic"—by Siegfried Gottwald. |
Noise-based logic : Noise-based logic (NBL) is a class of multivalued deterministic logic schemes, developed in the twenty-first century, where the logic values and bits are represented by different realizations of a stochastic process. The concept of noise-based logic and its name was created by Laszlo B. Kish. In its... |
Noise-based logic : The logic values are represented by multi-dimensional "vectors" (orthogonal functions) and their superposition, where the orthogonal basis vectors are independent noises. By the proper combination (products or set-theoretical products) of basis-noises, which are called noise-bit, a logic hyperspace ... |
Noise-based logic : In the paper, where noise-based logic was first introduced, generic stochastic-processes with zero mean were proposed and a system of orthogonal sinusoidal signals were also proposed as a deterministic-signal version of the logic system. The mathematical analysis about statistical errors and signal ... |
Noise-based logic : Noise-based logic gates can be classified according to the method the input identifies the logic value at the input. The first gates analyzed the statistical correlations between the input signal and the reference noises. The advantage of these is the robustness against background noise. The disadva... |
Noise-based logic : All the noise-based logic schemes listed above have been proven universal. The papers typically produce the NOT and the AND gates to prove universality, because having both of them is a satisfactory condition for the universality of a Boolean logic. |
Noise-based logic : The string verification work over a slow communication channel shows a powerful computing application where the methods is inherently based on calculating the hash function. The scheme is based on random telegraph waves and it is mentioned in the paper that the authors intuitively conclude that the ... |
Noise-based logic : Preliminary schemes have already been published to utilize noise-based logic in practical computers. However, it is obvious from these papers that this young field has yet a long way to go before it will be seen in everyday applications. |
Noise-based logic : Homepage of noise-based logic at Texas A&M University Kish cypher at Scholarpedia |
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... |
Ordered weighted averaging : An OWA operator of dimension n is a mapping F : R n → R ^\rightarrow \mathbb that has an associated collection of weights W = [ w 1 , … , w n ] ,\ldots ,w_] lying in the unit interval and summing to one and with F ( a 1 , … , a n ) = ∑ j = 1 n w j b j ,\ldots ,a_)=\sum _^w_b_ where b j ... |
Ordered weighted averaging : F ( a 1 , … , a n ) = max ( a 1 , … , a n ) ,\ldots ,a_)=\max(a_,\ldots ,a_) if w 1 = 1 =1 and w j = 0 =0 for j ≠ 1 F ( a 1 , … , a n ) = min ( a 1 , … , a n ) ,\ldots ,a_)=\min(a_,\ldots ,a_) if w n = 1 =1 and w j = 0 =0 for j ≠ n F ( a 1 , … , a n ) = a v e r a g e ( a 1 , … , a n ) ,\l... |
Ordered weighted averaging : The OWA operator is a mean operator. It is bounded, monotonic, symmetric, and idempotent, as defined below. |
Ordered weighted averaging : 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 . \sum _^(n-j)w_. It is known that A − C ( W ) ∈ [ 0 , 1 ] . In addition A − C(max) = 1, A − C(ave) = ... |
Ordered weighted averaging : 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... |
Ordered weighted averaging : 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. |
Ordered weighted averaging : Liu, X., "The solution equivalence of minimax disparity and minimum variance problems for OWA operators," International Journal of Approximate Reasoning 45, 68–81, 2007. Torra, V. and Narukawa, Y., Modeling Decisions: Information Fusion and Aggregation Operators, Springer: Berlin, 2007. Maj... |
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 computing : 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 po... |
Perceptual computing : 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 Public... |
Perceptual computing : Computational intelligence Expert system Fuzzy control system Fuzzy logic Granular computing Rough set Type-2 fuzzy sets and systems Vagueness |
Perceptual computing : F. Liu and J. M. Mendel, “Encoding words into interval type-2 fuzzy sets using an Interval Approach,” IEEE Trans. on Fuzzy Systems, vol. 16, pp 1503–1521, December 2008. J. M. Mendel, “The perceptual computer: an architecture for computing with words,” Proc. of Modeling With Words Workshop in the... |
Perceptual computing : Freeware MATLAB implementations of Per-C are available at: http://sipi.usc.edu/~mendel/software. |
Possibility theory : Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively. Professor Lotfi Zadeh... |
Possibility theory : For simplicity, assume that the universe of discourse Ω is a finite set. A possibility measure is a function Π from 2 Ω to [0, 1] such that: Axiom 1: Π ( ∅ ) = 0 Axiom 2: Π ( Ω ) = 1 Axiom 3: Π ( U ∪ V ) = max ( Π ( U ) , Π ( V ) ) for any disjoint subsets U and V . It follows that, like pro... |
Possibility theory : Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, possibility theory uses two concepts, the possibility and the necessity of the event. For any set U , the necessity measure is defined by N ( U ) = 1 − Π ( U ¯ ) ) . In the above formula,... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.