The inclusion measure and information energy for hesitant fuzzy sets and their application in decision making
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Inclusion measure of hesitant fuzzy sets is an important subject in the theory of hesitant fuzzy set, and it has been studied and widely used in clustering analysis and decision making. In this paper, we aim at constructing inclusion measure for hesitant fuzzy sets based on fuzzy sets. The axiomatical definition of inclusion measure for hesitant fuzzy sets is firstly proposed, and we construct a new inclusion relation for hesitant fuzzy sets. Based on this new inclusion relation, different inclusion measures based on the inclusion measures of fuzzy sets for hesitant fuzzy sets are further constructed. In addition, in order to describe the fuzziness degree of HFSs, information energy for HFSs is introduced. Finally, a real example about hesitant fuzzy multi-attribute decision making is used to illustrate the validity and applicability of the proposed inclusion measures and information energies.
Abstract
Inclusion measure of hesitant fuzzy sets is an important subject in the theory of hesitant fuzzy set, and it has been studied and widely used in clustering analysis and decision making. In this paper, we aim at constructing inclusion measure for hesitant fuzzy sets based on fuzzy sets. The axiomatical definition of inclusion measure for hesitant fuzzy sets is firstly proposed, and we construct a new inclusion relation for hesitant fuzzy sets. Based on this new inclusion relation, different inclusion measures based on the inclusion measures of fuzzy sets for hesitant fuzzy sets are further constructed. In addition, in order to describe the fuzziness degree of HFSs, information energy for HFSs is introduced. Finally, a real example about hesitant fuzzy multi-attribute decision making is used to illustrate the validity and applicability of the proposed inclusion measures and information energies.
참고문헌 (33)
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