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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.
The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. [2] [3] Fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. [4] Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical ...
IEEE STANDARD 1855-2016, IEEE Standard for Fuzzy Markup language (FML), is a technical standard developed by the IEEE Standards Association. [1] FML allows modelling a fuzzy logic system in a human-readable and hardware independent way.
The structure of a fuzzy system is expressed by the input and output variables and the rule base, while the parameters of a fuzzy system are the rule parameters (defining the membership functions, the aggregation operator and the implication function) and the mapping parameters related to the mapping of a crisp set to a fuzzy set, and vice ...
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 ...
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.
FML was designed and developed by Giovanni Acampora during his Ph.D. course in Computer Science, at University of Salerno, Italy, in 2004.The original idea inspired Giovanni Acampora to create FML was the necessity of creating a cooperative fuzzy-based framework aimed at automatically controlling a living environment characterized by a plethora of heterogeneous devices whose interactions were ...