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
Recommended Citation
Kundu, S., & Chen, J. (1995). Problems with the defuzzification method and a new representation using Lukasiewicz logic. IEEE International Conference on Fuzzy Systems, 4, 1833-1840. Retrieved from https://repository.lsu.edu/eecs_pubs/2437