An Alternative Approach for Computing the Union and Intersection of Fuzzy Sets: A Basis for Design of Robust Fuzzy Controllers
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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 TagakiSugeno 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”.
Fourier Series , Fuzzy Overlap , Triangular Pulses , Polygonal Waveform
Olunloyo, V.O.S, Ajofoyinbo, A.M & Badiru, A.B (2008) An Alternative Approach for Computing the Union and Intersection of Fuzzy Sets: A Basis for Design of Robust Fuzzy Controllers. 7th WSEAS International Conference on Artificial Intelligence,Knowledge Engineering and Data Bases (AIKED'08), Held at University of Cambridge, UK.