Two new kinds of protoconcepts based on three-way decisions model.

With the development of formal concept analysis, classical concept lattice cannot solve some problems in practice because of its strict conditions. Protoconcept, which is an extension of the formal concept, provides a new method of data processing. Three-way decisions is more in line with human cognition. Not like the decision of two ways, three-way cognition expands its scope of application. However, up to now, protoconcept is influenced by two-way decisions which leads to the restrictions of its applications. Hence, it is urgent to find a method to generalize protoconcept from the framework of two-way decisions. To give the solution to this urgent problem, the main contributions of this paper are the following: First, using the combination of protoconcept and three-way decisions, two models of three-way protoconcept are obtained. The algorithms for searching three-way protoconcept are built. Second, we investigate the constructions of three-way protoconcepts in double Boolean algebra. Third, the relationships between protoconcepts and three-way protoconcepts are found. Moreover, using examples that come from the real world, we explain the main results obtained above and show some applications. The two models for protoconcepts provided in this paper generalize the fields of thought from two-way decisions to three-way decisions. This follows that they are more in line with human thinking. Hence, the two models will certainly generalize the applications of protoconcept theory in the future. [ABSTRACT FROM AUTHOR]