In logic, a many-valued logic is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued, the finite-valued with more than three values, and the infinite-valued, such as fuzzy logic and probability logic.
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 contrast to classical or digital logic, which operates on discrete values of either 1 or 0.
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.
In mathematics, fuzzy sets are somewhat like sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh and Dieter Klaua 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 L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are used now in different areas, such as linguistics, decision-making, and clustering, are special cases of L-relations when L is the unit interval [0, 1].
Lotfi Aliasker Zadeh was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley.
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large Industrial control systems which are used for controlling processes or machines.
In classical logic, propositions are typically unambigously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition one is equal to one is regarded as simply true, by the Law of Identity. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than wholly true or wholly false. Consider My coffee is hot.
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 any number of dimensions is possible.
The expression computational intelligence (CI) usually refers to the ability of a computer to learn a specific task from data or experimental observation. Even though it is commonly considered a synonym of soft computing, there is still no commonly accepted definition of computational intelligence.
A fuzzy concept is a 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 vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether. It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics. The inverse of a "fuzzy concept" is a "crisp concept".
"Something 4 the Weekend" is the third single by Super Furry Animals. The title track is a more mellow reworking of the song "Something For the Weekend" from the band's debut album Fuzzy Logic. The original version is included as the last track on the single. It reached #18 on the UK Singles Chart on its release in July 1996. "Something 4 The Weekend" replaces the original album version of the song on the American release of Fuzzy Logic.
George Jiří Klir was a Czech-American computer scientist and professor of systems sciences at Binghamton University in Binghamton, New York.
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-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning.
Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. It started in 1965 after the publication of Lotfi Asker Zadeh's seminal work Fuzzy sets. A fuzzy subset A of a set X is a function A:X→L, where L is the interval [0,1]. This function is also called a membership function. A membership function is a generalization of a characteristic function or an indicator function of a subset defined for L = {0,1}. More generally, one can use a complete lattice L in a definition of a fuzzy subset A .
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 form
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 special case of a convex, normalized fuzzy set of the real line. Just like Fuzzy logic is an extension of Boolean logic, fuzzy numbers are an extension of real numbers. Calculations with fuzzy numbers allow the incorporation of uncertainty on parameters, properties, geometry, initial conditions, etc.
In logic, an infinite-valued logic is a many-valued logic in which truth values comprise a continuous range. Traditionally, in Aristotle's logic, logic other than bivalent logic was the norm, as the law of the excluded middle precluded more than two possible values for any proposition. Modern three-valued logic allows for an additional possible truth value and is an example of finite-valued logic in which truth values are discrete, rather than continuous. Infinite-valued logic comprises continuous fuzzy logic, though fuzzy logic in some of its forms can further encompass finite-valued logic. For example, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification of fuzzy logic.
