Entropy-based operations on fuzzy sets

Imre J. Rudas, M. Okyay Kaynak

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In this paper, by using a fuzzy entropy approach, three sets of new generalized operators are presented. After a general discussion on fuzzy entropy, the concept of elementary entropy function of a fuzzy set is introduced. Using this mapping, the generalized intersections and unions are defined as mappings that assign the least and the most fuzzy membership grade to each of the elements of the domain of the operators, respectively. It is shown that these operators can be constructed from the conventional min and max operations. Next, two modified sets of operations are introduced. The second part of the paper investigates the applicability of the new operators in fuzzy logic controllers. Simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers. It is concluded that the first set of operators does not provide stable control, but the performance of the fuzzy controller can be improved by using the modified operations for a class of plants.

Original languageEnglish
Pages (from-to)33-40
Number of pages8
JournalIEEE Transactions on Fuzzy Systems
Volume6
Issue number1
DOIs
Publication statusPublished - Dec 1 1998

Keywords

  • Fuzzy control
  • Fuzzy entropy
  • T-operators

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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