Open AccessA method for converting entropy to inclusion measure of interval type-2 fuzzy sets
Author(s) -
Gangtie Zheng,
Jing Wang
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1423/1/012063
Subject(s) - defuzzification , fuzzy number , type 2 fuzzy sets and systems , mathematics , fuzzy set operations , fuzzy classification , fuzzy measure theory , fuzzy set , fuzzy mathematics , membership function , fuzzy logic , entropy (arrow of time) , data mining , artificial intelligence , computer science , physics , quantum mechanics
As tools for dealing with universal fuzziness in human thinking, traditional fuzzy sets, namely type-1 fuzzy sets, are not able to directly model uncertainties about membership functions, however type-2 fuzzy sets can make up for this deficiency. Interval type-2 fuzzy sets, the simplified cases of general type-2 fuzzy sets, are practical because its membership functions and operations are greatly simplified. The inclusion measure and entropy of fuzzy sets are two important parameters with application prospects, the former describes the degree to which a fuzzy set is included in another, the latter shows the quantity of fuzzy information in a fuzzy set. It is important to make in-depth research on the two measures. In this paper, we mainly discuss the relationship of the inclusion measure and entropy of interval type-2 fuzzy sets proposed by Zheng et al., and present a theorem that converts the entropy to the inclusion measure of interval type-2 fuzzy sets. The conclusion provides the basis for further research.