TOPSIS Evaluation System of Logistics Transportation Based on an Ordered Representation of the Polygonal Fuzzy Set

Abstract

The polygonal fuzzy set is an effective tool to approximate the general fuzzy set by means of a finite number of ordered real numbers. It not only overcomes the shortcomings (which does not satisfy the closeness) of arithmetic operations of fuzzy sets based on Zadeh extension principle, but also realizes the non-linear operation of general fuzzy sets by an ordered representation of the polygonal fuzzy set. In this paper, the definition, geometric interpretation, ordered representation and arithmetic operations of the polygonal fuzzy sets are introduced for the first time, and the method of solving polygonal fuzzy sets and their ordered representation based on convex fuzzy sets are given by an example. Second, a new Euclidean metric of polygonal fuzzy sets is proposed, and the approximation accuracy of polygonal fuzzy sets to convex fuzzy sets is discussed. In addition, the linear function describing transportation cost index information of logistics companies is obtained through the ordered representation of Gauss membership function, and according to the ordered representation a new normalization method for the polygonal decision matrix is given. Finally, the method of solving the positive (negative) ideal solution and degree of relative closeness of the polygonal decision matrix is suggested by the weighted Euclidean distance. Then a new TOPSIS evaluation system is established, and the effectiveness of the proposed method is illustrated by an example of logistics transportation.