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.
Highlights
Multi-a ribute decision making (MADM) issues are inescapable in the field of decision making.In numerous functional applications, MADM plays a significant role in the procedure of decision making
Zadeh [1] characterized the idea of fuzzy sets (FSs) to clarify the imprecision and the doubt occurring during the assessment procedure
Properties we review some is defined as: existing notions, such as complex PFSs (CPFSs), complex spherical fuzzy sets (CSFSs) and Bonferroni mean is defined as: is defined as: to represent the universal set
Summary
Multi-a ribute decision making (MADM) issues are inescapable in the field of decision making. The theory of spherical fuzzy set (SFS), proposed by Mahmood et al [14], with a condition that the sum of squares of all grades cannot be exceeded from a unit interval, was used to resolve these issues. The theory of complex PFSs (CPFSs), with a condition in which the sum of squares of the grades of both real and imaginary parts cannot be exceeded from a unit interval, was proposed by Ullah et al [26] for coping with this kind of issue. 0.4ei2Π0.5 , 0.1ei2Π0.1 ), the IFS, PFS, PFS, CIFS, or CPFS are not able to investigate, because For coping with such issues, the theory of complex spherical fuzzy sets (CSFSs) is explored in this paper to examine proficiency and ability.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
