In-depth analysis and simulation study of an innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS

In this paper, an innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS is presented in-depth and studied through simulation comparison with the original method. The TOPSIS method provides the principle of compromise that the chosen alternative should have the shortest distance from the ideal solution and, simultaneously, the farthest distance from the negative ideal solution. However, the TOPSIS method does not always produce results in harmony with this principle due to an oversimplified definition of its aggregation function which does not grasp the contradictory nature of the principle's formulation. Our approach addresses this issue through the introduction of a fuzzy set representation of the closeness to the ideal and to the negative ideal solution for the definition of the aggregation function which is modeled as the membership function of the intersection of two fuzzy sets. This model enables a parameterization of the method according to the risk attitude of the decision maker. Thus, a class of methods is formulated whose different instances correspond to different risk attitudes of the decision makers. In order to define some clear advises for decision makers facilitating a proper parameterization of the method, a comparative analysis of the proposed class of methods with the original TOPSIS method is performed according to well defined simulation techniques. The results of the simulation experiment show on the one hand that there is no direct correspondence between the proposed class of methods and TOPSIS, and on the other hand that it is adequate to distinguish three instances that correspond respectively to risk-averse, risk-neutral and risk-seeking decision makers. Finally, a numerical example pertaining to the problem of service provider selection is presented to illustrate the application of the proposed class of methods and its functioning.