An Object-Induced Fuzzy Three-Way Concept Lattice Analysis Based on Two Thresholds

The model of three-way decision has achieved a big success both in theories and applications. This paper implements the idea of three-way decision to a fuzzy formal context, and a novel model for generating an object-induced fuzzy three-way concept (fuzzy OE-concept) lattice based on two thresholds is proposed. More specifically, this paper first analyzes the fuzzy OE-concept lattice proposed by Long and Xu, and points out that the so called “boundary region” cannot help in acquiring useful information for concepts. Based on this, the authors are motivated to dig deeper into this theory, and introducing a pair of “fuzzy boundary operators” for determining the “boundary region” of each concept. Furthermore, this paper redefines object-induced fuzzy three-way operator and fuzzy three-way inverse operator, and fuzzy OE-concept, and their properties are then discussed. Lastly, an example is presented to exhibit this model.