A Multiattribute Decision-Making Framework: VIKOR Method with Complex Spherical Fuzzy N -Soft Sets

Abstract

In this paper, we set forth a framework for solving a multiattribute group decision-making (MAGDM) problem, namely, the selection of a firm for participation in a Saudi oil refinery project in Pakistan. This project will prove a key success factor for the economic growth of Pakistan due to its enormous economic impact on the energy sector, industrial development, commerce, transportation, and so on. This multiplicity justifies that several intricate components comprising both intrinsic and external attributes should be adequately evaluated for the selection of such a firm, that is, the formulation of this question as a MAGDM problem. Nonbinary evaluation with two-dimensional ambiguity and uncertainty in the parameters are general concerns in modern literature, and they fit into this problem. Within this context, one of the most superior and amenable theories (complex spherical fuzzy $N$ -soft sets, henceforth $C\mathcal{S}FN{S}_{f}Ss$ ) shall be used to formulate a new comprehensive method, known as complex spherical fuzzy $N$ -soft-VIKOR ( $C\mathcal{S}FN{S}_f$ -VIKOR) method. According to the general spirit of the benchmark technique, the normalized Euclidean distances and the weights of the attributes are jointly handled, and as consequence, two main features (“maximum group utility” and “minimum individual regret”) are acquired. The coefficient strategy with reference to group utility measure and individual regret measure of opponents are employed for the compromise measure. Armed with this novel tool, we single out the most feasible firm according to the preference order of the alternatives examined by the decision-makers on the subject of linear normalized weights of experts and attributes. Furthermore, a comparative analysis justifies the $C\mathcal{S}F$ -VIKOR method, and some results prove its capabilities and validity. Moreover, a sensitivity test certifies the stability of the proposed method.