On the Variance of Interval Type-2 Fuzzy Sets

• Published in: IEEE transactions on fuzzy systems Vol. 31; no. 7; pp. 2320 - 2330
• Main Authors: Figueroa-Garcia, Juan Carlos, Ramos-Cuesta, Jennifer Soraya, Hernandez-Perez, German
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-07-2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Centroids; Fuzzy sets; Indexes; Interval type-2 fuzzy sets; Measurement uncertainty; Optimization; Switches; Three-dimensional displays; Uncertainty; uncertainty measures; variance
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2022.3223761

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.