A Nonlinear Model to Solve Multiple Attribute Decision-Making Problems with Interval-Valued Neutrosophic Numbers

Cognitive processes can be effectively communicated through linguistic variables (LVs), offering a robust framework for conveying uncertain and incomplete data in multiple attribute decision-making (MADM) problems. This method surpasses conventional techniques in handling such complexities. Recognizing decision experts'(DEs) bounded rationality, particularly their cognitive limitations leading to potential losses, underscores the need for innovative cognitive decision-making strategies in MADM. This study introduces LVs to encapsulate uncertain and hesitant cognitive elements, followed by a mathematical programming approach to tackle MADM problems where attributes or cognitive preferences exhibit interdependence. To enhance this approach within an interval-valued neutrosophic numbers (IVNN) environment, an IVNN multi-attribute group decision-making problem is modeled as a nonlinear programming model. Through variable transformation and aggregation operator application, this model is refined into an equivalent nonlinear programming model. The proposed method empowers decision-makers (DMs) to identify optimal alternatives without relying solely on their expertise, as demonstrated by its successful application in resolving two real-world problems.