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 ( $CSFN{S}_{f}S$ ) which is capable of handling two-dimensional vague information with parameterized ranking systems. First, we propose the basic notions for a theoretical development of $CSFN{S}_{f}Ss$ , including ranking functions, comparison rule, and fundamental operations (complement, union, intersection, sum, and product). Furthermore, we look into some properties of $CSFN{S}_{f}Ss$ . 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 $CSFN{S}_f$ -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 $CSFN{S}_f$ 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.