Three-way decisions based multi-attribute decision-making with utility and loss functions

The traditional multi-attribute decision-making (MADM) methods are based on two-way decisions (2WD), i.e., acceptance and rejection. In contrast, three-way decisions (3WD) add a deferred decision to effectively handle MADM problems by reducing decision risks. In the past 3WD models have been broadly explored considering losses and utilities associated with the decisions, but none of the studies considered loss and utility together. Also, the existing studies lack the influence of decision-makers on outcomes. Accordingly, this paper presents a novel 3WD model based on a similarity measure, integrating the hybrid information of MADM matrix, utility and loss values along with the influence of decision-makers. First, the two states are formed by the fuzzy c-mean clustering algorithm. Second, the similarity class for each alternative is constructed based on the Jaccard index. With reference to the equivalence classes formed, conditional probabilities are further calculated and 3WD decision rules are studied. Finally, considering both expected utility and losses associated with the alternatives we propose a novel 3WD model for solving MADM problems. The effectiveness of the proposed approach is demonstrated with the help of an illustrative example. The proposed 3WD-MADM model is further verified from different perceptions through comparative and experimental analysis.