L -fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms

In this paper, the basic ideas underlying fuzzy logic are introduced into the study of three-way formal concept analysis. This leads naturally to the notion of L -fuzzy three-way concepts. The L -fuzzy three-way operators and their inverse are defined and their properties are given. Based on these operators, two types of L -fuzzy three-way concepts are defined and the corresponding three-way concept lattices are constructed. A possibility theory reading of L -fuzzy three-way concepts is also provided. Moreover, the corresponding fuzzy inference method is studied. Two coherent fuzzy inference methods, the lower approximate fuzzy inference and the upper approximate fuzzy inference, are proposed, respectively.