Novel Hamacher aggregation operators with applications to the AHP-COPRAS method for spherical fuzzy environment

Abstract Spherical fuzzy set (SFS) theory has a broad and powerful structure to handle ambiguous and uncertain information in decision-making (D-M) theory. Analytic hierarchy process (AHP) is one of the well-known multi-criteria decision-making (MCDM) methods weighting the (sub-)criteria by processing pairwise comparisons of (sub-)criteria. Besides, The Complex Proportional Assessment (COPRAS) is a traditional multi-criteria group decision-making (MCGDM) method that handles proportional and direct reliance on the weights and the utility degree of analyzed adaptations on a frame of the attributes. This paper aims to integrate the AHP method and COPRAS method to construct a novel group decision-making method that determines the best alternative by calculating both unknown weights of criteria and decision makers (DMs). For this aim, to use in the weight calculations, we first show the shortcomings of the Hamacher operations given for spherical fuzzy numbers, and we reconstruct these operations appropriate for the nature of spherical fuzzy numbers. This reconstruction ensures that the aggregation operators process more accurately the data given in the problem. Then, we integrate the AHP method and the COPRAS method to solve the MCGDM problems under Hamacher aggregation (HA) operators based on reconstructed Hamacher operations in the spherical fuzzy environment. This integration allows us to subjectively calculate the weights of criteria using the AHP method and to find the ranking result after computing the weights of the DMs using the COPRAS method. Furthermore, we give a numerical example related to the location selection for a tech-center to explain the proposed method step by step and to demonstrate the practical applicability. Additionally, we solve two different real-life problems such as “determination of serving petrol station selection during COVID-19 lockdown” and “renewable energy location selection” which are given with spherical fuzzy information to demonstrate the applicability and practicality of the proposed method. Also, another problem “enterprise resource planning system selection” given and solved in fuzzy set theory is handled, and so a comparison different from the spherical fuzzy environment is provided. The results of these case studies are compared with traditional fuzzy set-based solutions, highlighting the superiority of the proposed method in terms of validity, robustness, and sensitivity. The comprehensive results confirm that the integration of AHP and COPRAS within the spherical fuzzy framework provides an efficient, reliable, and adaptable solution for complex decision-making scenarios.