A novel intuitionistic fuzzy three-way decision model based on an intuitionistic fuzzy incomplete information system

As a new method of granular computing, the three-way decision (3WD) approach has unique advantages in handling uncertain and imprecise problems. Based on decision-theoretic rough sets (DTRSs) and Bayesian minimum risk theory, conditional probability and loss function are the key research issues in 3WD. Many approaches for handling deterministic and complete information have been developed. However, few studies have focused on the construction of an intuitionistic fuzzy three-way decision (IF3WD) model for an intuitionistic fuzzy incomplete information system (IFIIS). In this paper, an IF3WD model based on an IFIIS is proposed to improve the ability to process complex fuzzy incomplete information systems, which extends the application range of the traditional 3WD. Concretely, we first propose a calculation method to measure the degree of information retention of missing data and describe it in two dimensions: coarse-grained and fine-grained. Next, an intuitionistic fuzzy number approximation (IFNA) strategy for missing data is presented. Then, a loss function with three states is given. Furthermore, combined with the Choquet integral, the interaction and influence between acceptance, rejection, and delay decision costs are investigated, and the corresponding IF3WD rules are induced. Finally, the rationality and effectiveness of our proposed model are verified through case analysis and are compared with those of existing methods.