Research On Multi-Attribute Decision Making Based On Linguistic Z-Numbers

Due to the occurrence of certain uncertain situations in real life,randomness and ambiguity are inevitable.Most of the information on which decisions are based is uncertain.How to deal with fuzzy and uncertain information to make the results more accurate and reliable has become a key research direction since Zadeh proposed fuzzy numbers in the 1960 s.In order to make up for the shortcomings of fuzzy numbers in describing the reliability of information,Zadeh proposed Z-Numbers in 2011,(Z=(A,B)),including the constraints on the evaluation object and the corresponding confidence,where A and B are described in a natural language.In the process of decision-making,experts often choose to use linguistic words,phrases or sentences to express their preference for the options.Language-based multi-attribute decision-making occupies an increasingly important position in the decision-making field.And it is useful and significance for dealing with the complexity or uncertainty of the real world.This paper takes linguistic Z-numbers as the main line,and focuses on the operator of Linguistic Z-Numbers(LZNs)and Hesitant Uncertain Linguistic Z-Numbers(HULZNs),the defuzzification of LZNs,the distance measure of HULZNs and the concrete application of multi-attribute decision making method based on linguistic Z-numbers.The full text is divided into three parts,the specific work is as follows:In the first part,the related concepts of linguistic term sets,uncertain linguistic variables,Z-Numbers and classic fuzzy sets are mainly introduced,and specific explanations and graphic expressions are given around the related concepts of fuzzy sets,and the working principle of the MABAC decision-making method and the TOPSIS decision-making method are explained in detail,which lay the foundation for the research of Multi-attribute decision-making later.In the second part,the conversion between linguistic Z-Numbers(LZNs)and fuzzy numbers and the defuzzification of Z-Numbers are studied,and the Multi-attribute group decision model of Z-MABAC method in linguistic environment is constructed.First,according to the 7-point conversion rule,a one-to-one correspondence between linguistic terms and fuzzy numbers is established.Z=(A,B),this article uses the first part of the variable A constraint in LZNs to transform into trapezoidal fuzzy number,and the second part of B reliability measure into triangular fuzzy number.Secondly,based on the fuzzy expectation approximation invariance rule,a method of transforming Z-Numbers into classical fuzzy numbers is given,which greatly reduces the resistance of Z-Numbers in application.Based on the classic MABAC method again,the criterion weight is obtained through the objective weight method to construct a multi-criteria decision model in the linguistic Z-Numbers environment,and apply it to the selection of third-party logistics providers.Finally,this paper compares and analyzes with other decision-making methods to verify the effectiveness and feasibility of the proposed method.In the third part,we mainly discuss the problem of Multi-criteria decision making with Hesitant Uncertain Linguistic Z-Numbers(HULZNs).Firstly,based on the linguistic scale functions and the concept of Hesitant Uncertain Linguistic Z-Numbers,the relevant operators and distance measure of Hesitant Uncertain Linguistic Z-Numbers are defined.Secondly,based on part of the weight information,the decision-maker weight and criterion weight model are constructed,and the expert information is assembled through HULZPWA operator.Finally,a TOPSIS model under the environment of the Hesitant Uncertain Linguistic Z-Numbers is constructed,and the selection of green suppliers is taken as an example for analysis.