Determining the optimal fuzzifier range for alpha-planes of general type-2 fuzzy sets

Shreyas Kulkarni, Rishabh Agrawal, Frank Chung-Hoon Rhee

Abstract:

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 αplane 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.