Three-way cognitive concept learning via multi-granularity

The key strategy of the three-way decisions theory is to consider a decision-making problem as a ternary classification one (i.e. acceptance, rejection and non-commitment). Recently, this theory has been introduced into formal concept analysis for mining three-way concepts to support three-way decisions in formal contexts. That is, the three-way decisions have been performed by incorporating the idea of ternary classification into the design of extension or intension of a concept. However, the existing methods on the studies of three-way concepts are constructive, which means that the three-way concepts had been formed by defining certain concept-forming operators in advance. In order to reveal the essential characteristics of three-way concepts in making decisions from the perspective of cognition, it is necessary to reconsider three-way concepts under the framework of general concept-forming operators. In other words, axiomatic approaches are required to characterize three-way concepts. Motivated by this problem, this study mainly focuses on three-way concept learning via multi-granularity from the viewpoint of cognition. Specifically, we firstly put forward an axiomatic approach to describe three-way concepts by means of multi-granularity. Then, we design a three-way cognitive computing system to find composite three-way cognitive concepts. Furthermore, we use the idea of set approximation to simulate cognitive processes for learning three-way cognitive concepts from a given clue. Finally, numerical experiments are conducted to evaluate the performance of the proposed learning methods.