The concept of triadic thinking is given. From the perspective of triadic thinking, the basic ideas ofthree-way decision is introduced, that is, to explain and deal with an whole system through three independent and relevant parts, reasonably divide the whole system into three parts, and take effective strategies to deal with each part, so as to obtain the required results. Then, several related models and specific applications of three-way decision are summarized. Finally, the research status of three-way decision is analyzed and the future research direction is prospected from two aspects of model and application.

Overlap function is closely related to continuous triangular norm and general overlap function is a further extension of overlap function.There are several important applications of (general) overlap function, such as image processing, data classification, uncertain multi-attribute decision making and so on. In this paper, the fuzzy rough set model based on continuous triangular norm is extended, a new kind of fuzzy rough set model is proposed by using (general) overlap function and its residual implication, and the basic properties of the new fuzzy upper and lower approximation operators are analyzed and studied. At the same time, a new uncertainty multi-attribute decision making method is proposed by using the fuzzy upper and lower approximation operators, and the feasibility and effectiveness of the new method is illustrated by a specific case.

Aiming at the characteristics of three-way decision making method and the temporal problem of air combat target intention recognition,a three-way decision making model based on sequential intention recognition is proposed. By establishing the mathematical model of the combination of multi-class and three-way decision making and target intention recognition, while combining the sequential thought, the process of intention recognition is divided into several stages according to the time sequence. In each stage, the target intention recognition result of the current stage is obtained by using the multi-class and three-way decision making target intention recognition model. For the target with no intention identified, based on the updated target information, the recognition is carried out by delay decision, which improves the accuracy of intention recognition and reduces the risk loss of false identification. Finally, the effectiveness of the proposed algorithm is verified by simulation experiments.

By using score function and accuracy function, a novel three-way decision model based on Bayesian decision theory under single-valued neutrosophic information is proposed, in which the loss functions are single-valued neutrosophic numbers. Finally, an algorithm is given and the effectiveness of the proposed model and algorithm is shown by an example, and comparison analysis was made with the existing model.This model highlights the significance of the uncertain membership degree single-valued neutrosophic numbers.

For the problem that most existing classification methods based on neighborhood covering directly classify samples according to the nearest neighborhood. The certain classification methods do not consider the differences between each neighborhood, which may lead to classification mistakes. Local density is introduced to characterize the differences between each neighborhood, and a classification method by integrating density and neighborhood covering reduction(D-NCR) is proposed in this paper. First, the redundant neighborhoods are eliminated by the neighborhood covering reduction. Then, the weighted distance from the test sample to the neighborhood center is defined through local density of neighborhood center. Finally, two classification strategies are proposed for different test samples based on the weighted distance. Experimental results on UCI data sets demonstrate the effectiveness of the proposed method.

The Pawlak's conflict analysis model is generalized to the incomplete information systems, three-way conflict analysis based on incomplete information systems is studied with the thought of three-way decision. Firstly, the missing value are processed and the incomplete information systems are transformed into the complete information systems. Secondly, the conflict relationship of agents is discussed, and the conflict analysis model in incomplete information systems is established by the concept of conflict similarity distance. Finally, the threshold of the tri-partition of the agents is computed by the decision-theoretic rough sets, so as to get the most reasonable tri-partition decision result.

In order to further broaden the scope of application of real-valued concept lattice, multi-granularity idea is combined with real-valued formal contexts to propose real-valued class-attribute block and multi-granularity real-valued formal context.Then, the transformation relationship between real-valued concepts from fine conceptual knowledge space to coarse conceptual knowledge space or coarse conceptual knowledge space to fine conceptual knowledge space is analyzed as well as the reasoning relation between decision rules under different granularity spaces. The obtained results on multi-granularity real-valued concepts and decision rules can not only further improve the theory of real-valued concept lattice, but also generalize the existing method of multi-granularity formal concept analysis.