Some Recent Defuzzification Methods

Some Recent Defuzzification Methods

Harendra Kumar (Gurukula Kangari University, India)
DOI: 10.4018/978-1-5225-1848-8.ch002
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Defuzzification is a process that converts a fuzzy set or fuzzy number into a crisp value or number. Defuzzification is used in fuzzy modeling and in fuzzy control system to convert the fuzzy outputs from the systems to crisp values. This process is necessary because all fuzzy sets inferred by fuzzy inference in the fuzzy rules must be aggregated to produce one single number as the output of the fuzzy model.There are numerous techniques for defuzzifying a fuzzy set; some of the more popular techniques are included in fuzzy logic system. In the present chapter some recent defuzzification methods used in the literature are discussed with examples.
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Fuzzy set theory was introduced by Zadeh (1965). Fuzzy set is the extension of crisp set. In fuzzy, each and every element has the degrees of membership value which lies in [0,1]. Fuzzy set theory extends the classical set theory with memberships of its elements described by the classical characteristic function, to allow for partial membership described by a membership function. Thus, fuzzy set theory has great capabilities and flexibilities in solving many real-world problems which classical set theory does not intend or fails to handle. Fuzzy set theory was applied to control systems theory and engineering almost immediately after its birth. In many practical applications such as in fuzzy inference systems, the fuzzy results generated cannot be used as such to the applications, hence it is necessary to convert the fuzzy quantities into crisp quantities for further processing.

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