An Enhanced Type-Reduction Algorithm for Type-2 Fuzzy Sets

Authors:
C. -Y. Yeh;W. -H. R. Jeng;S. -J. Lee
Affiliations:
Department of Electrical Engineering , National Sun Yat-Sen University, Kaohsiung, Taiwan;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2011

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Abstract

Karnik and Mendel proposed an algorithm to compute the centroid of an interval type-2 fuzzy set efficiently. Based on this algorithm, Liu developed a centroid type-reduction strategy to carry out type reduction for type-2 fuzzy sets. A type-2 fuzzy set is decomposed into a collection of interval type-2 fuzzy sets by $alpha$-cuts. Then, the Karnik–Mendel algorithm is called for each interval type-2 fuzzy set iteratively. However, the initialization of the switch point in each application of the Karnik–Mendel algorithm is not a good one. In this paper, we present an improvement to Liu’s algorithm. We employ the previously obtained result to construct the starting values in the current application of the Karnik–Mendel algorithm. Convergence in each iteration, except the first one, can then speed up, and type reduction for type-2 fuzzy sets can be carried out faster. The efficiency of the improved algorithm is analyzed mathematically and demonstrated by experimental results.