A Fast Geometric Method for Defuzzification of Type-2 Fuzzy Sets
IEEE Transactions on Fuzzy SystemsPublished 1 August 2008
Simon Coupland, Robert John
Citations110
SJR quartileQ1
SJR score3.61
SNIP2.80
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TL;DR
A new method for assessing the accuracy of the membership function of a type-2 fuzzy set and the differences between the new approach and type-reduction are discussed, identifying the origin of this massive improvement in execution speed.
Abstract
Generalized type-2 fuzzy logic systems cannot currently be used for practical problems because the amount of computation required to defuzzify a generalized type-2 fuzzy set is too large. This paper presents a new method for defuzzifing a type-2 fuzzy set. The new much faster technique is based on geometric representations and operations. The results of a real world example contained in this paper show this new approach to be over 200,000 times faster than type-reduction. We present a new method for assessing the accuracy of the membership function of a type-2 fuzzy set. This method is used to show that the new representation used by the defuzzifier is not detrimental to the accuracy of the set. We also discuss the differences between the new approach and type-reduction, identifying the origin of this massive improvement in execution speed.
Keywords
Computer Science
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning-III
12,148 Citations1975L. A. Zadeh
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776 Citations1976M. Mizumoto, Kokichi Tanaka
This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊓, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzies form a distributive lattice under ⊢ and ⊡.
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