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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 membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of much uncertainty.
Fuzzy logic is an important concept in medical decision making. Since medical and healthcare data can be subjective or fuzzy, applications in this domain have a great potential to benefit a lot by using fuzzy-logic-based approaches. Fuzzy logic can be used in many different aspects within the medical decision making framework.
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 an indicator function (also called a characteristic function) of a subset defined for L = {0, 1}.
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 (true or false, respectively).
A systematic study of particular t-norm fuzzy logics and their classes began with Hájek's (1998) monograph Metamathematics of Fuzzy Logic, which presented the notion of the logic of a continuous t-norm, the logics of the three basic continuous t-norms (Łukasiewicz, Gödel, and product), and the 'basic' fuzzy logic BL of all continuous t-norms ...
Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets [13] (see also fuzzy set theory). Fuzzy logic can play a significant role in artificial intelligence programming, for example because it can model human cognitive processes more easily ...
The place of defuzzification in a fuzzy control system A particular defuzzification method. 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 typically needed in fuzzy control systems.
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 the fuzzy measure (also capacity, see [1]), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals.