Abstract
Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.
Highlights
In order to find an application carrier for lattice, formal concept analysis (FCA) was proposed by Wille in1982 [1,2]
Li et al gave the approximate concept lattice [14] based on incomplete data
The corresponding formal context is called type I-dual intersectable formal context). They studied the isomorphic relation between concept lattice and three-way concept lattices based on the dual intersectable formal context [34]
Summary
In order to find an application carrier for lattice, FCA was proposed by Wille in. 1982 [1,2]. In terms of lattice building, Qian et al proposed the method based formal context from the perspective of context [23]. Yang et al in 2020 proposed the method based on the composite of classical lattices from the perspective of lattice [24]. Inspired by 3WCA, some new three-way concept lattice models are proposed. Long et al studied attribute-induced three-way concept lattice in incomplete fuzzy formal context by double threshold construction method [32]. The corresponding formal context is called type I-dual intersectable formal context) They studied the isomorphic relation between concept lattice and three-way concept lattices based on the dual intersectable formal context [34].
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