A Development of the Circular Non-linear Diophantine Fuzzy Set and Their Application in Cloud Services Provider Selection

Selecting a reliable Cloud Service Provider (CSP) is a complex multi-criteria decision-making (MCDM) problem due to conflicting criteria and uncertainty in expert evaluations. Traditional methods often fail to handle circular uncertainty and non-linear hesitancy effectively. To address this, we propose a novel framework combining the Combined Compromise Solution (CoCoSo) method with Circular Non-Linear Diophantine Fuzzy Sets (Cir N-LDFSs). Cir N-LDFSs integrate circular intuitionistic and circular linear Diophantine fuzzy sets, modeling uncertainty through membership function (MF) and non-membership function (NMF) as center coordinates, enabling precise evaluation of subtle variations in expert opinions. Frank-based aggregation operators, including the circular Non-Linear Diophantine fuzzy frank weighted average (Cir N-LDFFWA) operator, are developed to aggregate expert preferences efficiently. The CoCoSo method is applied to rank CSP alternatives, solving multi-criteria group decision-making (MCGDM) problems. The proposed approach offers clear advantages, including robust handling of uncertainty, improved ranking stability, computational efficiency, and flexibility, as demonstrated in CSP selection, providing accurate and reliable decision support in complex and uncertain environments.