Group decision-making method with Pythagorean fuzzy rough number for the evaluation of best design concept

A rough set is important for the reduction of attributes of an information system, since it approximates a subset of a universal set based on some binary connection. A Pythagorean fuzzy set, on the other hand, provides specific information about the extent to which a statement is true or false. Both of these theories address various types of uncertainty and can be combined to maximize their combined advantages. In the current study, we aim to build a broader structure of fuzzy rough numbers, known as Pythagorean fuzzy rough numbers. The proposed framework addresses some of the limitations of traditional fuzzy rough numbers and provides a more practical and effective solution for dealing with uncertainty in decision-making. Our main objective is to develop a new method based on Pythagorean fuzzy rough numbers, the Analytic Hierarchy Process (AHP), and the Technique of Ranking by Similarity to Ideal Solution (TOPSIS) method. The suggested approach is tested on a case study which involves the selection of a product design concept for a new heat exchanger. The Pythagorean fuzzy rough AHP technique is implemented to assess the significance of each factor in the design process, and the Pythagorean fuzzy rough TOPSIS approach is used to rank the design concepts in order of their overall quality. The outcomes demonstrates that the suggested methodology efficiently assesses design concepts, making it helpful for the design industry in decision-making process. This study highlights the importance of integrating the AHP-TOPSIS method based on Pythagorean fuzzy rough numbers for a comprehensive evaluation of design concepts, taking into account both qualitative and quantitative factors to aid complex decision-making processes. The proposed method is thoroughly compared with some other existing decision-making methods.