Order Relation Of Fuzzy Multisets And Its Application In Anonymous Multi-attribute Group Decision Making

Multi-attribute decision making problems are ubiquitous in management,economy,military and other fields.Because of the fuzziness of human thinking and the complexity of decision making environment and decision making problems,decision makers often use triangular fuzzy numbers,interval numbers,intuitionistic fuzzy numbers,trapezoidal fuzzy numbers and hesitant fuzzy sets to describe uncertain decision making information.In order to make the decisions made as correct as possible,in addition to the need to further improve the decision making methods used,it is also necessary to rely on collective wisdom,that is,group decision making.In order to eliminate interference in the group decision process,experts are often required to participate in the decision making in an anonymous form,which may result in the evaluation values given by different experts being the same.The fuzzy multisets allows the elements in the domain to the same or different membership values appear multiple times,and the fuzzy multisets is used to describe the anonymous multi-attribute group decision information,which can reflect the most realistic decision situation.It can be seen that this paper has important practical significance for the research of anonymous multi-attribute group decision making methods.The specific contents are as follows:(1)The definition of the priority axiom of fuzzy multisets and the pretreatment of the fuzzy multisets are given.Three methods for obtaining the order relations of the fuzzy multisets are proposed,namely,the ordered priority degree method considering the single value of the fuzzy multiple elements,the projection priority degree method considering the whole and the combination priority degree method considering the individual and global characteristics of the fuzzy multiple elements.(2)Under the condition that the attribute weight is completely unknown,a new method based on the maximum deviation method to obtain the objective weight of the attribute is proposed.(3)The anonymous multi-attribute group decision making problem is transformed into the problem of ranking fuzzy multisets.The anonymous multi-attribute group decision making methods based on ordered priority degree,projection priority degree and combination priority degree are proposed respectively.Among these three methods,additive consistency fuzzy preference relation is constructed.Consequently,consistency of decision information is maintained throughout the decision making process,and consequently consensus is reached among decision makers.Finally,the feasibility and practicability of each of the above methods are proved by examples.The research on anonymous multi-attribute group decision making will help to improve the theory of multi-attribute group decision making and enrich the theory and method of uncertain decision-making.