A fast type-reduction algorithm based on Binary-Search

Type-Reduction algorithms are very important for type-2 fuzzy sets and systems. We proposed in the present paper a new type-reduction algorithm based on EKM algorithm. In ordered sample sets, Binary-Search method can quickly finds witch points and calculate centroid of interval type-2 fuzzy set. Four type reduction algorithms (KM, EKM, MEKM and BEKM) are used to compare different type-2 fuzzy sets. Experiments show that four algorithms can accurately find switch points and get centroid of interval type-2 fuzzy set. However, the algorithm proposed in this paper is more efficient and its cycle time is the shortest.