An overlap function-based three-way intelligent decision model under interval-valued fuzzy information systems

One of the expression forms of uncertain information are interval-valued fuzzy information systems (IFISs). Whereas, psychological experiments show that psychological behaviors of decision maker (DM) affect the decision results under uncertain information. Consequently, the main research objectives of this paper are two-fold: 1. To study how to portray the influence of psychological behaviors on decision-making under IFISs, so that the decision-making process is more realistic. 2. To investigate how to efficiently solve decision -making problems in the context of IFISs. Three-way decision (3WD) theory and fuzzy rough sets (FRSs) are effective tools for solving uncertain information. For that reason, this paper develops a 3WD model based on prospect theory (PT) under IFISs, which can provide the best decision action for objects from a viewpoint of optimization. First, an attribute-oriented interval fuzzy set is introduced, which establish a bridge between the state sets in 3WD and the reference points in PT. Furthermore, conditional probability of an object is reasonably estimated by interval-valued fuzzy rough sets (IVFRSs). Meanwhile, an attribute-oriented relative value model is proposed, which can get the prospect values of an object under each action. Second, an intelligent 3WD model is developed from a viewpoint of information granularity. Finally, through the search of the existing literature, relevant research data is obtained, and then case research method, qualitative and quantitative combination method, control variable method are adopted in turn to design the case study, comparative and experimental analyses. In short, the developed model not only expands the development of related theories, 3WD, PT, FRSs, but also offers new methods for solving the decision-making problems under IFISs, which has important practical guidance significance.