A Three-Way Decision Methodology With Regret Theory via Triangular Fuzzy Numbers in Incomplete Multiscale Decision Information Systems

The three-way decision theory provides a three-way philosophical thinking to solve problems, and the regret theory quantifies the risk preferences of decision makers under different psychological behaviors. On the one hand, the combination of these two theories makes models more practical by considering the psychological behaviors of decision makers. On the other hand, we can effectively combine the advantages of the three-way decision theory with the regret theory to highlight the interpretability of decision-making processes. In this article, we propose a novel approximate estimation method for incomplete utility values via the regret theory and establish a wide sense of a three-way decision model on incomplete multiscale decision information systems. First, the degree of consistency for each scale is measured via using the dependence degree, then the optimal subsystem is selected by evaluating the scale selection cost. Furthermore, the incomplete multiscale evaluation information is transformed into triangular fuzzy numbers via linguistic term sets. Second, in light of fuzzy evaluation values and tradeoff factors, an estimation method for incomplete fuzzy subsystems is constructed, which can be used to calculate the utility difference and regret-rejoicing values for pairwise comparisons. Finally, from the perspective of human cognition, the tripartition and the corresponding decision rules are built by the tolerance degree, and the ranking of objects is calculated by the relative closeness degree. Additionally, multiaspect comparative and experimental analyses are performed by extensive experiments, and the feasibility, validity, and stability of the constructed model are shown by parametric analyses.