Research On Fuzzy Multi-attribute Decision Making Methods Based On Axiomatic Fuzzy Sets

All aspects of our life require decision making.It refers to the process in which people choose an optimal scheme from several alternatives.In this respect,multi-attribute decisionmaking theory,as an important branch of modern decision theory and method research,has been widely used in many fields such as management,economy,military and engineering.Because of the complexity of decision-making environment and the ambiguity of human subjective cognition,attribute values are often difficult to be directly described by quantitative methods,thus qualitative analysis is required,which leads to the problem of fuzzy multi-attribute decision-making.Aiming at the problem of fuzzy multi-attribute decision-making with attribute values described in natural language,based on axiomatization of fuzzy sets theory,this thesis studies the theory and method of fuzzy multi-attribute decision-making,and obtains the following research results as follows:1.The order relation of axiomatization of fuzzy sets theory in the same fuzzy membership space is proposed by using the fuzzy mean of axiomatic fuzzy sets.When the attribute values of each alternative are represented by axiomatic fuzzy sets,the order relation between axiomatic fuzzy sets is applied to the order of different attribute values of each alternative.2.In view of the fuzzy multi-attribute decision-making problem in which attribute values are represented by linguistic value,the scheme is regarded as a special vector with axiomatic fuzzy sets as components.The four algorithms between axiomatic fuzzy sets are defined by the classical extension principle.According to these four algorithms,the Euclidean distance between two vectors is defined,and then the TOPSIS multi-attribute decision-making model based on axiomatic fuzzy sets is established.The effectiveness of the model is illustrated by an example.3.For the fuzzy multi-attribute decision-making problem where attribute values are represented by linguistic value,the projection similarity between two different vectors is defined from the projection angle.Based on such definition of projection similarity,the similarity between decision schemes is proposed,and a multi-attribute decision model based on projection similarity is established.The advantages and disadvantages of the two different decision models are compared,and the effectiveness of the model is illustrated by an example.