Determining the Optimal Fuzzifier Range for Alpha-Planes of General Type-2 Fuzzy Sets

Type-2 fuzzy sets (T2 FSs) are capable of handling uncertainty more efficiently than type-1 fuzzy sets (T1 FSs). The fuzzifier parameter plays an important role in the final cluster partitions in fuzzy c-means (FCM), interval type-2 (IT2) FCM, general type-2 (GT2) FCM, and other fuzzy clustering algorithms. In general, fuzzifiers are chosen for a given dataset based on experience. In this paper, we adaptively compute suitable values for the range of the fuzzifier parameter for each α-plane of GT2 FSs for a given data set. The footprint of uncertainty (FOU) for each α-plane is obtained from the given data set using histogram based membership generation. This is iteratively processed to give the converged values of fuzzifier parameters for each α-plane of GT2 FSs. Experimental results for several data sets are given to validate the effectiveness of our proposed method.

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