Problems with the defuzzification method and a new representation using Lukasiewicz logic

Document Type

Conference Proceeding

Publication Date

1-1-1995

Abstract

We show that the common defuzzification method has some major deficiencies in regard to certain formal logical properties among rules like and-equivalence, contrapositive-equivalence, chaining-property, etc. To correct this problem, we present a new method for representing a function y = g(x) using a rule set based on Lukasiewicz's logic Lx. The method introduces two sets of normalized fuzzy concepts {Aj:1 ≤ j ≤ N} and {Cj:1 ≤ j ≤ N}, a set of rules of the form rj = 'if x is Aj then y is Cj' or 'if x is not Aj then y is Cj' where Aj and Cj have non-decreasing linear membership functions, and an and/or formula φ(r1, r2, ..., rN) over the rules ri, without involving negation, which describes how to combine the results of inference from the individual rules rj to obtain the final value of y. Our rules satisfy the logical properties in regard to the various equivalences when applicable.

Publication Source (Journal or Book title)

IEEE International Conference on Fuzzy Systems

First Page

1833

Last Page

1840

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