A Multi-Valued Rough Neutrosophic Approach for Multi-Criteria Decision-Making: Application in Hospital Selection

Decision-making problems are often characterized by complexity and uncertainty, presenting significant challenges for individuals or organizations. Traditional aggregation methods often struggle with the imprecise, inconsistent, and unclear data found in these situations. To address these issues, this study proposes a new multi-criteria decision-making method based on Multi-Valued Rough Neutrosophic Numbers. We first introduce the fundamental operational laws for multi-valued rough neutrosophic numbers, based on t-norm and t-conorm. Subsequently, we establish four new multi-valued rough neutrosophic number-based aggregation operators: the Multi-Valued Rough Neutrosophic Arithmetic Mean Operator, the Weighted Multi-Valued Rough Neutrosophic Arithmetic Mean Operator, the Multi-Valued Rough Neutrosophic Geometric Mean Operator, and the Weighted Multi-Valued Rough Neutrosophic Geometric Mean Operator. We also prove that these proposed aggregation operators satisfy desirable properties, including monotonicity, idempotency, and boundedness. To determine the optimal weights of criteria, we utilize the Shapley fuzzy measure, capturing the significance and contribution of each criterion. Following this, specific score and accuracy functions are developed to facilitate the ranking of alternatives. Finally, a numerical illustration derived from a real-world hospital selection context is presented to demonstrate the effectiveness and practical utility of the proposed approach.