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, epsilon-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 epsilon-almost stochastic dominance, a novel epsilon-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 prob-ability, 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 pro-posed 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.