An Extended Type-Reduction Method for General Type-2 Fuzzy Sets

作者：Xie, Bing Kun^*; Lee, Shie Jue

来源：IEEE Transactions on Fuzzy Systems, 2017, 25(3): 715-724.

DOI：10.1109/TFUZZ.2016.2567454

• Interval type-2 fuzzy sets
• Karnik-Mendel algorithm
• type-reduction
• type-2 fuzzy sets
• alpha-plane

A centroid type-reduction strategy for computing the centroids of type-2 fuzzy sets based on decomposed a-planes was proposed by Liu. However, it cannot be applied to type-2 fuzzy sets with concave secondary membership functions. In this paper, we extend the Liu's method so that the centroids of type-2 fuzzy sets with concave secondary membership functions can be derived. For each decomposed a-plane, we convert it into a group of interval type-2 fuzzy sets. The union of the centroids of its member interval type-2 fuzzy sets constitutes the centroid of the a-plane. Then, the weighted union of the centroids of the decomposed a-planes becomes the centroid type-reduced set of the original type-2 fuzzy set. When dealing with type-2 fuzzy sets with convex secondary membership functions, our proposed method is reduced to the Liu's method.

• 出版日期2017-6
• 单位中山大学