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

Zeeshan Ali, Tahir Mahmood and Miin-Shen Yang
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Zeeshan Ali: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Tahir Mahmood: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Miin-Shen Yang: Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan

Mathematics, 2020, vol. 8, issue 10, 1-19

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.

Keywords: fuzzy sets; complex spherical fuzzy sets; Bonferroni mean operators; TOPSIS method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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