Extension of TOPSIS model to the decision-making under complex spherical fuzzy information

Akram M., Kahraman C., Zahid K.

SOFT COMPUTING, vol.25, no.16, pp.10771-10795, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 16
  • Publication Date: 2021
  • Doi Number: 10.1007/s00500-021-05945-5
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.10771-10795
  • Keywords: Aggregated spherical fuzzy decision matrix, Complex spherical fuzzy sets, MCGDM, TOPSIS method
  • Istanbul Technical University Affiliated: Yes


This research article is devoted to present a decision-making approach pertaining the excellent tendencies of traditional TOPSIS method under the broader environment of complex spherical fuzzy sets (CSFSs). TOPSIS method is regarded as one of the authentic decision-making strategies that follows the scheme to point out the alternative acquiring favorable distances from the ideal solutions. On the other hand, the pre-eminent feature of the CSFS includes the tendency to handle both aspects of two-dimensional information involved in the satisfaction, abstinence and dissatisfaction nature of human decisions. This study aims to expand the number of multiple criteria group decision-making (MCGDM) techniques by presenting a strategy, named complex spherical fuzzy TOPSIS (CSF-TOPSIS) method that cumulates the novel features of complex spherical fuzzy sets with the potential of TOPSIS method. In proposed method, we merge the independent decisions of all experts about the capabilities of alternatives and priorities of criteria using the CSFWA operator. We rank the alternatives in an ascending order of revised closeness index, evaluated by deploying normalized Euclidean distance. We establish the proposed CSF-TOPSIS method by an explanatory numerical example for the selection of best water supply strategy for Nohoor village in Iran. Further, we conduct the comparative study with spherical fuzzy TOPSIS method and complex spherical fuzzy VIKOR method to explicate the adequacy of the proposed strategy and consistency of the results.