Enhancing Multi-criteria Decision-making: A Fusion of Three-Way Decision and Fuzzy Bayesian Rules

In the realm of multi-criteria decision-making (MCDM), the need for robust methodologies that can effectively handle uncertainty and ambiguity is paramount. This research paper presents an innovative approach that combines the power of three-way decision (3WD) with the flexibility of fuzzy Bayesian rule, offering a novel perspective and a promising solution to address complex decision problems. By employing fuzzy membership functions, we capture the inherent uncertainty in decision variables and obtain conditional probabilities for each region. Rather than relying on a rule of tie-breaking, a distinct method is specified to partition alternatives based on the conditional probability of alternatives for each region, enabling a more precise and reliable partition of alternatives, eliminating the need for arbitrary tie-breaking rules. To evaluate and rank the alternatives within each region, loss and utility functions are applied. These functions enable the calculation of expected costs, facilitating a comprehensive assessment of the consequences associated with different choices. By incorporating loss and utility functions, decision-makers can quantitatively evaluate trade-offs and make informed decisions that align with their preferences and objectives. Through a specific numerical example, the effectiveness of the proposed methodology is demonstrated, comparing it with other existing methods. The proposed framework enhances decision-making processes by effectively handling uncertainty, ambiguity, and trade-offs.