An alternative approach for computing the union and intersection of fuzzy sets: a basis for design of robust fuzzy controllers

Authors:
V. O. S. Olunloyo;A. M. Ajofoyinbo;A. B. Badiru
Affiliations:
Department of Systems Engineering, Faculty of Engineering, University of Lagos, Lagos, Nigeria;Department of Systems Engineering, Faculty of Engineering, University of Lagos, Lagos, Nigeria;Department of Industrial & Information Engineering, University of Tennessee, Knoxville, TN
Venue:
AIKED'08 Proceedings of the 7th WSEAS International Conference on Artificial intelligence, knowledge engineering and data bases
Year:
2008

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Abstract

The capability of fuzzy sets to express gradual transition from membership to non-membership and vice versa has broad utility. The overlap between two or more adjoining fuzzy sets create very important fuzzy "patch" that deserves special attention. In the existing literature, Zadeh, Mamdani and Tagaki-Sugeno have established that the Min- and Max- operators can effectively be used for fuzzy interpolative inference. But what has not been done is to define an explicit expression for determining membership function in the overlap region. This paper addresses that concern, as it proposes an alternative approach to determination of membership function based on the Fourier series representation of the envelope of the fuzzy "patch".