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This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then...
This paper explains how to compute normalized interval type-2 fuzzy sets in closed form and explains how the results reduce to well-known results for type-1 fuzzy sets and interval sets. Such normalized interval type-2 fuzzy sets may be needed in linguistic probability computations or multiple criteria decision analysis under uncertainty.
Subsethood and similarity measures are important concepts in fuzzy set (FS) theory. There are many different definitions of them, for both type-1 (T1) FSs and interval type-2 (IT2) FSs. In this paper, Rickard et al.'s definition of IT2 FS subsethood measure, extended from Kosko's T1 FS subsethood measure using the Representation Theorem, and Nguyen and Kreinovich's IT2 FS similarity measure, extended...
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