Research On Multi-attribute Decision-making Method Based On Hesitant Fuzzy Information

With the advancement of network technology,decision-makers have gradually expanded from a small number of relevant experts to a larger decision-making group,while the existing group decision-making methods are only suitable for small groups and no longer meet the needs.At the same time,the ambiguity and complexity of things continue to increase,and precise numbers cannot accurately cover all the information of things,and are no longer suitable for decisionmaking problems with fuzzy preferences.Hesitant fuzzy sets allow decision makers to provide multiple possible values,improve the flexibility of decision makers’ assignments,and better describe decision makers’ preferences,so they have attracted widespread attention from scholars.However,most of the existing hesitant fuzzy distance measures will lead to distortion of the original information,and the calculation results of the hesitance degree do not conform to people’s intuitive feelings,hesitant fuzzy sets cannot describe decision information comprehensively and accurately.In this regard,the main research work in this thesis is as follows:First of all,considering that the existing hesitant fuzzy distance measures need to satisfy the condition of length consistency before calculating the distance between two hesitant fuzzy numbers,and most of the hesitant fuzzy distance measures do not reasonably consider the hesitance degree,they cannot effectively describe the degree of hesitation when decision makers give evaluation information.This thesis proposes a new hesitant fuzzy distance that avoids the distortion of the original information.It is proved by mathematics that it can satisfy the basic properties of the distance,and has higher accuracy and applicability than the existing distance.Then,based on the new distance,a hesitant fuzzy clustering algorithm is proposed.According to this algorithm,the members of the large group are clustered to obtain the group preference matrix of each scheme,and then the weight of the attribute is determined by the dispersion maximization weighting method.Finally,the hesitant fuzzy operator and the score function are used to calculate the comprehensive evaluation value of each scheme and sort them.This method can effectively solve the hesitant fuzzy multi-attribute large group decision-making problem,and the effectiveness of the proposed decision-making method is verified by example analysis.Finally,this thesis combines the Pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set to define the Pythagorean probabilistic hesitant triangular fuzzy set,the basic operations and scoring functions of the Pythagorean probability hesitant triangular fuzzy numbers are proposed,their comparison rules are given,the correlation operators are developed,and the multiattribute decision-making method is constructed accordingly.Through comparative analysis,the Pythagorean probabilistic hesitant triangular fuzzy set contains nonmembership information,probability information and triangular fuzzy information at the same time,which can describe decision information more comprehensively and accurately.