A novel three-way decision model under multiple-criteria environment

Three-way decisions provide a new research perspective for solving decision-making problems. Under a multiple-criteria environment, this paper proposes a novel decision model based on the combination of three-way decisions and multi-criteria decision-making (MCDM). MCDM-based three-way decisions extend the range of applications of three-way decisions to MCDM problems and provide new calculation methods of loss functions and decision rules in view of the difference of alternatives. First, we define two concepts of relative loss functions and inverse loss functions to illustrate several properties of loss functions in three-way decisions, and we subsequently establish calculation methods of loss functions and thresholds with the aid of evaluation values of criteria. In consideration of all of the criteria in MCDM problems, we propose an aggregation method of loss functions to reflect the comprehensive losses of alternatives. By establishing the key steps and algorithm of the MCDM-based three-way decisions, three-way decision rules of all of the alternatives are obtained. Finally, an empirical example of project investment is utilized to validate the effectiveness and superiority of the proposed model.