Regret Theory-Based Three-Way Decision Method on Incomplete Multiscale Decision Information Systems with Interval Fuzzy Numbers

In realistic decision-making environments, human behaviors bring influences to various decision-making procedures, and classic multiattribute decision-making approaches based on utility decisions own some deviations from actual situations. The behavioral decision theory modifies classic decision-making theories to make the new method more applicable. Regret theory, as one of the important components in behavioral decision theories, has been widely used in theories and applications. Based on regret theory, we establish a generalized three-way decision method on incomplete multiscale decision information systems with interval fuzzy numbers. First, we select an incomplete optimal subsystem for the incomplete multiscale information system, and convert the multiscale evaluation information into an interval fuzzy number by using a linguistic term set. Second, based on the probability distribution of evaluation values and tradeoff factors, we propose a target-dependent approximation estimation method for the incomplete interval fuzzy subsystem. Then, the regret–rejoicing preferences between objects are obtained. Finally, a tripartition and ranking method based on a max-bipartition and preference index is established. Moreover, the incompleteness experiments show that the decision-making results of our method can still maintain more than 97% consistency in an incomplete information system with a missing rate of at most 20%. In addition, the parameter analysis shows that the proposed method maintains an accuracy rate of more than 98% and a classification error rate of no more than 0.6%.