Ranking Hesitant Fuzzy Sets Within Allowable Error And Its Application To Multi-attribute Decision Making

Hesitant fuzzy set.(HFS)is an effective mathematical tool to show the hesitancy and uncertainty.Multi-attribute decision making problem is an important filed in the application of HFSs.In this paper,we propose a hesitant fuzzy multi-attribute decision making algorithm and apply the algorithm to an example of multi-attribute decision making problems,more details are as follows:(1)Considering the influence of subjectivity in membership degree making process,this paper compares hesitant fuzzy elements(HFEs)by introducing allowable error 5.Based on the definition of possibility degree of intervals a ≥ b,we propose the definition of possibility degree of HFEs h1≥h2,and discuss its desirable properties by the equivalent definition of the possibility degree.We introduce the lexicographical order of HFEs within allowable error based on the possibility degree P>,and extent it to HFSs.Moreover,we give a multi-attribute decision making algorithm,the core of the algorithm is based on the pair-wise comparison between alternatives within allowable error.(2)To assess the algorithm comprehensively by existing order,we define the ranking vector and transformation function to making different,methods in one dimension.We propose the reliability degree of different orders and study its properties.Finally.we establish comprehensive assessment method to test the proposed algorithm based on the ranking vector,transformation function and reliability degree.