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A Method for Converting Inclusion Measure to Entropy of Interval Type-2 Fuzzy Sets

In order to model imprecise information better, more and more scholars use type-2 fuzzy sets, among which interval type-2 fuzzy sets have practical application value, the reasons lie in that their secondary grades are all 1 and there are some fast algorithms for their operations. Inclusion measure and entropy are considered as two basilic parameters in fuzzy set theory because of their versatility, and those of interval type-2 fuzzy sets have become research hotspots nowadays. This paper mainly studies the relationship between the inclusion measure and entropy of interval type-2 fuzzy sets presented by Zheng et al., proposes and proves a transformation theorem that the former can be converted to the latter within the constraints of their axiomatic definitions. The result offers a reference for the theoretical research and practical application in the future.