Abstract
Regarding the problem of the existing intuitionistic fuzzy entropy formulas in ordering the partial entropy, the constraint condition that is consistent with the intuitionistic facts is proposed in this paper, the axiomatic definition of entropy which fully reflects the intuition and fuzziness of intuitionistic fuzzy sets is given, and the improved intuitionistic fuzzy entropy formula is constructed according to the entropy axiomatic definition and its properties are studied. Finally, we compare the improved formula with the existing intuitionistic fuzzy entropy formulas, and the result turns out that the improved formula can solve the problem in the entropy ordering theoretically and practically.
Highlights
Atanassov extended the fuzzy set theory given by Zadeh [1] to the intuitionistic fuzzy set theory [2]
Definition 4 fully reflects the ambiguity of the known information and the intuition of the unknown information of the intuitionistic fuzzy sets, where the fuzziness is reflected by the constraint condition (3), and the intuition is embodied by the constraint condition (5)
The results calculated by the entropy formula proposed in this paper are consistent with intuitionistic facts, which shows that it is better than the entropy formula (17)
Summary
Atanassov extended the fuzzy set theory given by Zadeh [1] to the intuitionistic fuzzy set theory [2]. Based on the study of Burillo and Bustince, Szmidt and Kacprzyk proposed the axiomatic definition of intuitionistic fuzzy entropy which can reflect the intuition and fuzziness and constructed an entropy formula by using the geometric meaning of intuitionistic fuzzy sets [13], which provides different points of views for many scholars to build new intuitionistic fuzzy entropy formulas [14,15,16,17]. The authors construct a new intuitionistic fuzzy entropy formula which fully reflects the fuzziness and intuition based on the pioneering study of Szmidt and Kacprzyk [13] and prove that the formula has two better properties
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