Preference-based regret three-way decision method on multiple decision information systems with linguistic Z-numbers

Three-way decision theory (3WD) provides a reasonable solution to solve multi-criteria decision-making (MCDM) problems and reduces more decision risks than two-way decision (2WD). However, the impact of preferences on decision results has not been reasonably considered in 3WD. Thus, this paper proposes a preference-based regret 3WD model on multiple decision information systems (MDISs) with linguistic Z-numbers (LZNs) to address the defect. First of all, a Z-LINMAP method is proposed by extending LINMAP method into the LZNs environment to derive criteria weights, Z-number ideal solutions and preference coefficients. On the basis of preference coefficients, the consistency-order and inconsistency-order are defined and further the consistency and inconsistency equivalence classes are presented to derive the conditional probabilities of alternatives. Then, the regret loss functions based on regret theory are presented and the regret 3WD rules of a single decision information system are designed. Furthermore, the weighted expected regret loss function and loss score function are defined to classify and rank all alternatives for MDISs. Finally, the proposed 3WD model is applied to the image recognition case with human-computer interaction to verify the effectiveness, and the comparative and sensitivity analyses are carried out to demonstrate the feasibility of our model.