TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Zeeshan Ali; Tahir Mahmood; Miin-Shen Yang

doi:10.3390/math8101739

journal article Open Access Oct 10, 2020

TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Zeeshan Ali

Tahir Mahmood

Miin-Shen Yang

Mathematics Vol. 8 No. 10 pp. 1739 · MDPI AG

View at Publisher Save 10.3390/math8101739

Abstract

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

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Details

Published: Oct 10, 2020
Vol/Issue: 8(10)
Pages: 1739
License: View

Authors

Z

Zeeshan Ali

Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

T

Tahir Mahmood

Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

M

Miin-Shen Yang

Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan

Cite This Article

Zeeshan Ali, Tahir Mahmood, Miin-Shen Yang (2020). TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators. Mathematics, 8(10), 1739. https://doi.org/10.3390/math8101739

TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

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