On the Variance of Interval Type-2 Fuzzy Sets

This article presents some theoretical considerations about the variance of a fuzzy set and introduces a covering-based algorithm for computing the bounds of the variance of an interval Type-2 fuzzy set. The proposed algorithm obtains the bounds of all possible variances of an interval Type-2 fuzzy set unlike other algorithms, which are based on the center of centroid of an interval Type-2 fuzzy set to obtain a relative variance that is proven to be always bigger than the absolute variance. A comparison to the relative variance of an interval Type-2 fuzzy set is given through different examples, where the proposed algorithm shows better precision than the KM algorithm.