An Improved Fuzzy TOPSIS Based on Fuzzy Sets with Three Kinds of Negations

The existing fuzzy TOPSIS methods are based on Zadeh fuzzy sets or various extended fuzzy sets, which hardly meet the need for using multiple negations to represent knowledge. In response to this problem, this work investigates an improved fuzzy TOPSIS method, which is rooted in FScom that investigates different negative relations, namely, contradictory negation relation, opposite negation relation and medium negation relation. Firstly, we propose a class of distance formulas satisfying the axiomatic definition of the distance measure on FScom and study the properties of the proposed distance formulas. Secondly, the traditional fuzzy ideal solution is improved by adding fuzzy medium ideal solution. And then the fuzzy ideal solution based on FScom are proposed, including fuzzy negative ideal solution, fuzzy medium ideal solution, and fuzzy negative ideal solution. Finally, the fuzzy TOPSIS method based on the distance of FScom is developed. Besides, this method is applied to rank network quality for verifying its effectiveness and practicability.