Multi-attribute decision-making using (p, q)-rung orthopair fuzzy Hamacher interactive aggregation operators

Compared to Fermatean fuzzy sets, Pythagorean fuzzy sets, and intuitionistic fuzzy sets, (p, q)-rung orthopair fuzzy sets ((p, q)-ROFSs) can display membership grades over a wider range, allowing them to present more confusing circumstances. This article elaborates the use of (p, q)-ROFS in engineering design for material selection. Material selection is a crucial part of engineering because it satisfies all of the object’s functional requirements. The design process’s crucial and time-consuming phase of material selection. The output, profitability, and reputation of a manufacturer can suffer from the choice of the incorrect material(s). An essential tool in the engineering design process for handling the complexity of material selection is multi-attribute decision-making (MADM). However, the outcomes of using the current MADM approaches are frequently inconsistent. To solve these issues, a novel aggregation method based on the truthness and falsity indices of (p, q)-ROFS is suggested for material selection in engineering design. We present (p, q)-rung orthopair fuzzy Hamacher interactive aggregation operators (AOs) that take advantage of (p, q)-ROFS and smooth approximation with interactive Hamacher operations. Based on the indicated AOs, in engineering design, a trustworthy MADM method is advised for material selection (MS). The main contributions of this article are as follows: (1) The aggregation operators for (p, q)-rung orthopair fuzzy numbers and their attributes have been studied using Hamacher norms. (2) MADM is established under (p, q)-rung orthopair fuzzy sets. A step-by-step explanation of the proposed method is given using an algorithm. (3) The developed method is then applied as a case study in the selection of materials for cryogenic storage tanks. (4) The results have been contrasted with the rankings obtained by several currently employed techniques. The authenticity analysis and comparison analysis are also intended to talk about the reliability and sanity of the best choice.