Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decisionmaking experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.