An Entropy of Interval Type-2 Fuzzy Sets

Abstract:

The entropy shows the fuzzy degree of a fuzzy set (FS) and can be used in various areas. Aiming at the characteristics of the fuzzy entropy and type-2 fuzzy sets (IT2 FSs), we introduce a new entropy of IT2 FSs in this paper. At first, we select an axiomatic definition for it. Then, considering a fact that the operations of IT2 FSs depend on the upper membership functions (UMFs) and lower membership functions (LMFs), we propose a calculation formula and verify it accords with the four axioms of the selected definition. Finally, we use an example to illuminate its reasonable performance.

• Periodical: Applied Mechanics and Materials (Volumes 321-324)
• Pages: 1999-2003
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.321-324.1999
• Online since: June 2013
• Authors: Gao Zheng, Shi Wei Yin
• Keywords: Entropy, Fuzzy Logic, Fuzzy Measure, Interval type-2 Fuzzy Set

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