Applications of newly defined diamond Pythagorean fuzzy CODAS method via multi-criteria decision-making problems

The diverse decision values may fail to capture an accurate perspective when multiple decision-makers are part of the process. To address this challenge, this work introduces the diamond Pythagorean fuzzy set (Dia-PyFS), an advancement over both the Pythagorean fuzzy (PyFS) set and the interval-valued Pythagorean fuzzy set (IVPyFS). Due to the established extension of intuitionistic fuzzy sets into Pythagorean fuzzy sets, the Dia-PyFS model, a broader form of the diamond intuitionistic fuzzy set model, demonstrates enhanced performance. We then introduce the Dia-PyFS as an extension of PyFS. The Diamond Pythagorean fuzzy values that define the elements within Dia-PyFS may share a common norm. For Dia-PyFS, we define fundamental algebraic and arithmetic operations, including union, intersection, addition, multiplication, and scalar multiplication, and analyze their primary properties. Additionally, we propose some new Dia-PyF weighted average and geometric aggregation operators as well as explore their unique properties. We also then propose several algebraic operations between Dia-PyFVs using general triangular t-norms and t-conorms. To transform input values represented by Dia-PyFs into a single output value, we also introduce specific weighted aggregation operators based on these algebraic methods. Additionally, the Dia-PyFS framework builds upon the “combinative distance-based assess” (CODAS) methodology, which relies on both Euclidean and Hamming distances. To illustrate the applicability of this new approach, the feasibility and suitability of the Dia-PyFS set approach for choosing the best options are demonstrated by the summary and comparative analysis of the produced reports.