A Fast Method for Computing the Centroid of a Type-2 Fuzzy Set

作者：Wu, Hsin Jung^*; Su, Yao Lung; Lee, Shie Jue

来源：IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics , 2012, 42(3): 764-777.

DOI：10.1109/TSMCB.2011.2177085

• Enhanced Karnik-Mendel (KM) (EKM) algorithm
• KM algorithm
• type-2 fuzzy system
• type reduction
• alpha-plane representation

Type reduction does the work of computing the centroid of a type-2 fuzzy set. The result is a type-1 fuzzy set from which a corresponding crisp number can then be obtained through defuzzification. Type reduction is one of the major operations involved in type-2 fuzzy inference. Therefore, making type reduction efficient is a significant task in the application of type-2 fuzzy systems. Liu introduced a horizontal slice representation, called the alpha-plane representation, and proposed a type-reduction method for a type-2 fuzzy set. By exploring some useful properties of the alpha-plane representation and of the type reduction for interval type-2 fuzzy sets, a fast method is developed for computing the centroid of a type-2 fuzzy set. The number of computations and comparisons involved is greatly reduced. Convergence in each iteration can then speed up, and type reduction can be done much more efficiently. The effectiveness of the proposed method is analyzed mathematically and demonstrated by experimental results.

• 出版日期2012-6
• 单位中山大学