Hybrid Decision-Making Frameworks under Complex Spherical Fuzzy N-Soft Sets

Abstract

This paper presents the novel concept of complex spherical fuzzy N-soft set (CSFNSfS) which is capable of handling two-dimensional vague information with parameterized ranking systems. First, we propose the basic notions for a theoretical development of CSFNSfSs, including ranking functions, comparison rule, and fundamental operations (complement, union, intersection, sum, and product). Furthermore, we look into some properties of CSFNSfSs. We then produce three algorithms for multiattribute decision-making that take advantage of these elements. We demonstrate their applicability with the assistance of a numerical problem (selection of best third-party app of the year). A comparison with the performance of Pythagorean N-soft sets speaks for the superiority of our approach. Moreover, with an aim to expand the range of techniques for multiattribute group decision-making problems, we design a CSFNSf-TOPSIS method. We use a complex spherical fuzzy N-soft weighted average operator in order to aggregate the decisions of all experts according to the power of the attributes and features of alternatives. We present normalized-Euclidean distances (from the alternatives to both the CSFNSf positive and negative ideal solutions, respectively) and revised closeness index in order to produce a best feasible alternative. As an illustration, we design a mathematical model for the selection of the best physiotherapist doctor of Mayo hospital, Lahore. We conduct a comparison with the existing complex spherical fuzzy TOPSIS method that confirms the stability of the proposed model and the reliability of its results.