vikor method based supplier selection under nonlinear diophantine rough fuzzy environment

Abstract

Uncertainty and imprecision are inherent in real-world decision-making problems, requiring robust mathematical frameworks for accurate modeling. This paper introduces a novel approach by integrating vikor method with Non-Linear Diophantine Rough Fuzzy Sets (NLDRFS) to enhance information representation and processing in uncertain environments. The proposed model leverages the flexibility of rough fuzzy sets to handle vagueness, while the vikor method provide a smooth, nonlinear aggregation mechanism that improves decision-making efficiency. Furthermore, the Diophantine structure introduces a new dimension of mathematical rigor, allowing a more precise approximation of uncertainty. We explore theoretical properties, develop algebraic operations, and illustrate practical applications in multi-criteria decision-making (MCDM) and pattern recognition. Comparative analyses demonstrate that our proposed framework outperforms existing rough fuzzy set models in handling complex uncertainties.