A Novel Approach towards Interval Type-2 Fuzzy c-Means using Multiple Kernels and Using Adaptively Calculated Fuzzifier Values

Abstract

In this dissertation, we propose an adaptive hybrid clustering method, where fuzzy c-means with multiple kernels (FCM-MK) has been combined with interval type-2 fuzzy c-means. In the proposed method, multiple Gaussian kernels are used. The resolution-specific weight, the membership values, and the cluster prototypes are decided in situ. In the calculation of the cluster prototypes, uncertainty associated with the fuzzifier parameter m is considered. In doing so, a pattern set is extended to interval type-2 fuzzy sets using two fuzzifiers m1 and m2, creating a footprint of uncertainty (FOU) for the fuzzifier m. This is followed by type reduction and defuzzification for obtaining the final location of the prototypes. Various experimental results are shown to validate the effectiveness of the proposed clustering method. It has been also shown that time complexity of proposed algorithm is greater than interval type-2 FCM by only a constant factor, meaning there is no significant increase in time complexity. So, we are able to achieve better results than interval type-2 FCM at same time complexity.

Type-2 fuzzy sets are preferred over type-1 sets as they are capable of addressing uncertainty more efficiently. Fuzzifier values play pivotal role in managing these uncertainties; still selecting appropriate value of fuzzifier has been a tedious task. Generally, based on observation, a particular value of fuzzifier is chosen from a given range of values for a given dataset. To tackle this issue, we have tried to adaptively compute suitable fuzzifier values of interval type-2 fuzzy c-means for a given pattern. Information is extracted from individual data points using histogram approach and this information is further processed to give us the two fuzzifier values m1 and m2. These obtained values are bounded within some upper and lower bounds based on existing methods.