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

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 -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.