A series of information measures of hesitant fuzzy soft sets and their application in decision making

A hesitant fuzzy soft set is a hybrid model consist of a hesitant fuzzy set and a soft set. It can be considered an effective mathematical tool for dealing with vagueness and uncertainty. This study focuses on the measure of information fuzziness for hesitant fuzzy soft sets. First, we propose the concept of the relative entropy of hesitant fuzzy soft sets which is used to measure the discrimination information. Then, we introduce the symmetric cross-entropy of hesitant fuzzy soft sets considering the relative entropy. In addition, we provide the axiomatic definitions of the similarity measure and entropy of hesitant fuzzy soft sets. Meanwhile, we develop a novel similarity measure and an entropy formula of hesitant fuzzy soft sets by using the concept of the symmetric cross-entropy. Furthermore, we present two different decision-making methods for multi-attribute decision making and multi-attribute group decision making where multi-attribute index information is described by hesitant fuzzy soft sets. Finally, practical examples are presented in order to illustrate the validity and practicability of the similarity measure and entropy. We also compare and analyze our entropy and similarity measures with other measures.