# Category: Fuzzy logic

SQLf
SQLf is a SQL extended with fuzzy set theory application for expressing flexible (fuzzy) queries to traditional (or ″Regular″) Relational Databases. Among the known extensions proposed to SQL, at the
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 simpl
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.
Uncertainty theory
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Mathematical measures of the likelihood of an event b
Fuzzy architectural spatial analysis
Fuzzy architectural spatial analysis (FASA) (also fuzzy inference system (FIS) based architectural space analysis or fuzzy spatial analysis) is a spatial analysis method of analysing the spatial forma
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 mu
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 stru
Type-2 fuzzy sets and systems
Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the me
Łukasiewicz logic
In mathematics and philosophy, Łukasiewicz logic (/ˌluːkəˈʃɛvɪtʃ/ LOO-kə-SHEV-itch, Polish: [wukaˈɕɛvitʂ]) is a non-classical, many-valued logic. It was originally defined in the early 20th century by
Fuzzy control system
A fuzzy control system is a control system based on fuzzy logic—a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in
T-norm fuzzy logics
T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the system of truth values and functions called t-norm
Fuzzy cognitive map
A fuzzy cognitive map (FCM) is a cognitive map within which the relations between the elements (e.g. concepts, events, project resources) of a "mental landscape" can be used to compute the "strength o
Combs method
The Combs method is a rule base reduction method of writing fuzzy logic rules described by in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules. The Combs method takes advan
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.
Predicate (mathematical logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula , the symbol is a predicate which applies to the individual constant . Similarly,
Neuro-fuzzy
In the field of artificial intelligence, neuro-fuzzy refers to combinations of artificial neural networks and fuzzy logic.
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
Defuzzification
Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is t
Fuzzy differential equation
Fuzzy differential equation are general concept of ordinary differential equation in mathematics defined as differential inclusion for non-uniform upper hemicontinuity convex set with compactness in f
High-performance fuzzy computing
The term high-performance fuzzy computing (HPFC) refers to those technologies able to exploit supercomputers and computer clusters to perform high performance fuzzy logic computations. Thus HPFC is ju
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 curr
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 classic
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
Residuated Boolean algebra
In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, th
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, ra
Construction of t-norms
In mathematics, t-norms are a special kind of binary operations on the real unit interval [0, 1]. Various constructions of t-norms, either by explicit definition or by transformation from previously k
Fuzzy associative matrix
A fuzzy associative matrix expresses fuzzy logic rules in tabular form. These rules usually take two variables as input, mapping cleanly to a two-dimensional matrix, although theoretically a matrix of
Fuzzy Control Language
Fuzzy Control Language, or FCL, is a language for implementing fuzzy logic, especially fuzzy control. It was standardized by IEC 61131-7. It is a domain-specific programming language: it has no featur
T-norm
In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in
Sugeno integral
In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure. Let be a measurable space and let be an -measurable function. The Sugeno integral ove
Fuzzy rule
Fuzzy rules are used within fuzzy logic systems to infer an output based on input variables. Modus ponens and modus tollens are the most important rules of inference. A modus ponens rule is in the for
Vague set
In mathematics, vague sets are an extension of fuzzy sets. In a fuzzy set, each object is assigned a single value in the interval [0,1] reflecting its grade of membership. This single value does not a
European Society for Fuzzy Logic and Technology
The European Society for Fuzzy Logic and Technology (EUSFLAT) is a scientific association with the aims to disseminate and promote fuzzy logic and related subjects (sometimes comprised under the colle
Fuzzy electronics
Fuzzy electronics is an electronic technology that uses fuzzy logic, instead of the two-state Boolean logic more commonly used in digital electronics. Fuzzy electronics is fuzzy logic implemented on d
Fuzzy differential inclusion
Fuzzy differential inclusion is tha culmination of Fuzzy concept and Differential inclusion introduced by Lotfi A. Zadeh which became popular.,, , f(t,x(t)] is a fuzzy valued continuous function on eu
Fuzzy markup language
Fuzzy Markup Language (FML) is a specific purpose markup language based on XML, used for describing the structure and behavior of a fuzzy system independently of the hardware architecture devoted to h
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 sto
Ordered weighted averaging aggregation operator
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
Probabilistic database
Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databas
Random-fuzzy variable
In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contr
Residuated lattice
In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x\z and z/y, loosely analogous to division or implic
Rough fuzzy hybridization
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 fe
Uncertain inference
Uncertain inference was first described by C. J. van Rijsbergen as a way to formally define a query and document relationship in Information retrieval. This formalization is a logical implication with
BL (logic)
In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of
Evolving intelligent system
In computer science, an evolving intelligent system is a fuzzy logic system which improves the own performance by evolving rules. The technique is known from machine learning, in which external patter
Vagueness
In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of mi
Fuzzy Sets and Systems
Fuzzy Sets and Systems is a peer-reviewed international scientific journal published by Elsevier on behalf of the (IFSA) and was founded in 1978. The editors-in-chief (as of 2010) are Bernard De Baets
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 , satisfying certain axioms. MV-algebras are t
Fuzzy classification
Fuzzy classification is the process of grouping elements into a fuzzy set whose membership function is defined by the truth value of a fuzzy propositional function. A fuzzy class ~C = { i | ~Π(i) } is
Fuzzy finite element
The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case of a fuzzy set. The advantage of using fuzzy numb
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
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-readab
Fuzzy measure theory
In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is th
An adaptive neuro-fuzzy inference system or adaptive network-based fuzzy inference system (ANFIS) is a kind of artificial neural network that is based on Takagi–Sugeno fuzzy inference system. The tech
Fuzzy concept
A fuzzy concept is a kind of concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is
Fuzzy mathematics
Fuzzy mathematics is the branch of mathematics including fuzzy set theory and fuzzy logic that deals with partial inclusion of elements in a set on a spectrum, as opposed to simple binary "yes" or "no
Degree of truth
In classical logic, propositions are typically unambiguously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, bei
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 so
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value ma
Bates's chip
Bates's chip (also called a sloppy chip or fuzzy chip) is a theoretical chip proposed by MIT Media Lab's computer scientist Joseph Bates that would incorporate fuzzy logic to do calculations. The resu
Functional presence engine
A Functional Presence Engine, or FPE, is a probabilistic parsing mechanism that uses at least four components to respond to input patterns. It comprises a lexing system, a probabilistic fitness functi
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, o