A New Approach to Decision Support System Through Application of Spherical Cubic Fuzzy Numbers

Abstract

This study discusses the methods used to deal with vagueness such as fuzzy sets (FSs), intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), picture fuzzy sets (PFSs), spherical fuzzy sets (SFSs), intuitionistic cubic fuzzy sets (ICFS) and Pythagorean cubic fuzzy sets (PCFSs). Moreover, the main contribution of this study is the introduction of spherical cubic fuzzy sets (SCFSs). In addition, score function, accuracy function and some operators and distance measures are defined for SCFSs that are handy in the processes of decision making. Different Hamacher operators are used to established multi-criteria decision-making methods for the assessment of business execution with spherical fuzzy information. Furthermore, several new operations are characterized through Dombi 𝑡̃-norm and Dombi 𝑡̃-conorms to get the best results during the decision criteria. Also, various characteristics of such operators are examined. The operators defined are averaging operators, geometric operators, Hamacher averaging operators, Hamacher geometric operators, Dombi averaging operators and Dombi geometric operatos which include simple fuzzy weighted operators, ordered weighted operators and hybrid weighted operators. Additionally, a new methodology with incomplete weight information for spherical cubic fuzzy (SCF) multi-criteria decision making (MCDM) is suggested using TOPSIS method. The maximum deviation model is also put forward to determine the criteria of weight values. Finally, each of the proposed operators, methods and models are compared to the existing methods and techniques. Thus, the proposed methods are verified to be more effective in different types of decision making processes.