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

Fuzzy set theory is an effective tool for dealing with uncertainty. The basis for designing a fuzzy logic system is to establish a fuzzy rule base according to on-site experimental data or expert experience, but fuzzy rules themselves often have uncertainty. Using type-2 fuzzy set theory can effectively solve this problem. The advantage of type-2 fuzzy sets over type-l is that they have structures of three dimensions that can represent deeper levels of uncertainty, and enhance their ability to describe and handle the objective world nondeterminacy. Fuzzy measure theory is a meaningful subfield of fuzzy set theory. Among various frequently-used fuzzy measures, fuzzy inclusion measure and fuzzy entropy are two important parameters, which have good application prospects in risk assessment, image segmentation, pattern recognition, fuzzy clustering and other fields. Under certain conditions, the two can be converted into each other. This dissertation studies the transition relation of an inclusion measure between interval type-2 fuzzy sets and a typical entropy of interval type-2 fuzzy set, proposes a transformation theorem and proves it to underlie future theoretical research and practical applications.