Enhancement of the Defining Interrelationships Between Ranked Criteria II method using interval grey numbers for application in the grey-rough MCDM model

Multi-Criteria Decision-Making (MCDM) represents a critical area of research, particularly in artificial intelligence, through the modeling of real-world decision-making scenarios.Numerous methods have been developed to address the challenges of integrating non-quantitative, incomplete, and imprecise information under conditions of uncertainty.This paper presents the enhancement of the Defining Interrelationships Between Ranked Criteria II (DIBR II) method by incorporating interval grey numbers, in accordance with the principles of Grey theory, its arithmetic operations, and the DIBR II methodology.The enhancement includes the of a conviction degree to reflect decision-makers' or experts' confidence in their assertions.The application of this enhanced method is demonstrated through an illustrative example, following the procedural steps.Additionally, its efficacy is validated in a real-world scenario involving the selection of Lean organization system management techniques, utilizing the Rough Multi-Attributive Border Approximation Area Comparison (Rough MABAC) method.The results indicate that the enhanced DIBR II method is effective in determining criteria weight coefficients, offering a more nuanced distribution compared to traditional crisp methods.Furthermore, when implemented in a multi-criteria model, it yields a more refined ranking of alternatives, contingent on the degree of confidence in the given claims.