Complex spherical fuzzy TOPSIS based on entropy

Abstract

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a traditional approach, which is quite powerful since it shows the best and worst alternatives at the same time, for solving multi-criteria group decision-making (MCGDM) problems. On the other hand, the theory of complex spherical fuzzy set (CSFS) has a noticeable advantage over the other set theories which process the uncertain data since this theory includes the abstinence part of uncertain information in addition to satisfaction and dissatisfaction in two-dimensional data. This paper proposes to merge the feasible and remarkable structure of the CSFS with the excellent tendencies of the traditional TOPSIS where the information about the weights of both the decision-makers (DMs) and criteria are completely unknown. So, we establish a novel TOPSIS method under the complex spherical fuzzy environment by calculating the weights of both the DMs and criteria objectively with the novel entropy measure function that we constructed for this method. Furthermore, we give a numerical example to explain the proposed method step by step. Finally, we compare the solutions to the current problem with the various existing MCGDM methods to provide the capabilities and validity of the presented method. We also give a sensitivity analysis by changing the entropy to demonstrate the robustness of the weights of the criteria under the prevailing entropy measure function.