The SMAA-TWD model: A novel stochastic multi-attribute three-way decision with interrelated attributes in triangular fuzzy information systems

As a decision model to depict the human cognitive process, three-way decision (TWD) offers a reasonable semantic interpretation for solving practical multi-attribute decision-making (MADM) problems. Due to the complexity of the decision-making environment, uncertainties usually exist in multi-attribute three-way decision making problems. To stress these uncertainties simultaneously, a novel stochastic multi-attribute TWD model that incorporates TWD, ∊-almost stochastic dominance, and stochastic multiobjective acceptability analysis (SMAA) is proposed for dealing with stochastic MADM problems with interrelated attributes in triangular fuzzy information systems. First, based on the ∊-almost stochastic dominance, a novel ∊-almost stochastic dominance degree is proposed for measuring the quantitative relationship of two triangular fuzzy numbers. Second, a novel stochastic TWD model is presented, in which the set of two states, conditional probability, and relative loss, can be obtained according to an information system. Third, the Choquet integral with respect to bi-capacity is utilized to aggregate the expected losses of three actions to strengthen their interpretability. Fourth, a SMAA-TWD model is proposed for multi-attribute TWDs with interrelated attributes in triangular fuzzy information systems. Finally, an application to medical diagnosis is given, and a comparative analysis is performed to verify the applicability and effectiveness of the proposed model.