Entropy Measure Of Hesitant Fuzzy Information And Its Application

In order to give a mathematical description of the uncertainty of information,Zadeh proposed the fuzzy set theory in 1965.Since then,various generalizations of fuzzy set have emerged according to the need of practical problems.Hesitant fuzzy set as one of the generalizations of fuzzy set extends the membership of each element from a single value in[0,1]to a set of finite different values in[0,1].Further,in order to reflect the psychological behavior of decision makers more objectively in the decision-making process,people introduce probability into the hesitant fuzzy set and give the concept of probabilistic hesitant fuzzy set.At the same time,entropy,as a tool to describe the degree of uncertainty of information,has been widely used in both hesitant fuzzy set and probabilistic hesitant fuzzy set.Some research has been done along this direction,the main work can be summarized as follows:1.The axiomatic definition of entropy based on the hesitant fuzzy set is given,and the parameterized hesitant fuzzy entropy is proposed and verified.At the same time,the parameterized hesitant fuzzy entropy is compared with the existing hesitant fuzzy entropies by specific examples,and the results show that the proposed entropy is effective and superior in describing the uncertainty of information.In addition,combining with the parameterized hesitant fuzzy entropy and the idea of TOP SIS,a new multi-attribute decision-making method is constructed.The practicability and feasibility of the method and proposed entropy are illustrated by an practical example.2.The axiom of entropy based on probabilistic hesitant fuzzy element is improved,and the order-α probabilistic hesitant fuzzy entropy is constructed.Then,it has been shown that the proposed entropy can identify the probabilistic hesitant fuzzy information effectively,and the introduction of parameters α makes the proposed entropy more flexible.Finally,the practicality of the proposed entropy in multi-attribute decision problem is verified by the method of classical operator.