The Extended TOPSIS Based on Trapezoid Fuzzy Linguistic Variables

Abstract The purpose of this paper is to extend the TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method for solving multiple attribute decision making (MADM) problems with trapezoid fuzzy linguistic variables. To begin with, this paper introduces the concept of the trapezoid fuzzy linguistic variables, and defines the distance between two trapezoid fuzzy linguistic variables in order to deal with trapezoid fuzzy linguistic variables directly. This paper proposed a combined weight to highlight the importance of weights. Then, the combined weights of each attribute can be determined by the maximizing deviation method and the non-linear weighted comprehensive method. Furthermore, the relative closeness degree is defined based on the TOPSIS method to determine the ranking order of all alternatives by calculating the distances to both the positive ideal solution and negative ideal solution, respectively. Finally, an illustrative example is given to verify the feasibility and effectiveness of this method.