The Feature Description of Formal Context Based on the Relationships among Concept Lattices

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.

Universal and macro-areal patterns in the lexicon

This paper investigates universal and areal structures in the lexicon as manifested by colexification patterns in the semantic domains of perception and cognition, based on data from both small and large datasets. Using several methods, including weighted semantic maps, formal concept lattices, correlation analysis, and dimensionality reduction, we identify colexification patterns in the domains in question and evaluate the extent to which these patterns are specific to particular areas. This paper contributes to the methodology of investigating areal patterns in the lexicon, and identifies a number of cross-linguistic regularities and of area-specific properties in the structuring of lexicons.

Rule Reductions of Decision Formal Context Based on Mixed Information

Three-way concept lattice extracts knowledge from positive and negative information separately. However, some applications require to mix positive and negative information for management and representation explicitly. In this paper, rule acquisition of FCA is extended based on mixed information. Firstly, two types of mixed concept lattices are studied. Then the relationships between mixed concept and classical concept, three-way concept are explored in depth. Secondly, mixed decision rules are investigated thoroughly. And the weak-basis is put forward to approximate to the basis of mixed decision rules. Finally, the comparison of mixed decision rules and three-way decision rules is perfectly discussed.

Neutrosophic three-way concept lattice and its application in conflict analysis

The theory of three-way concept analysis has been developed into an effective tool for data analysis and knowledge discovery. In this paper, we propose neutrosophic three-way concept lattice by combining neutrosophic set with three-way concept analysis and present an approach for conflict analysis by using neutrosophic three-way concept lattice. Firstly, we propose the notion of neutrosophic formal context, in which the relationships between objects and attributes are expressed by neutrosophic numbers. Three pairs of concept derivation operators are proposed. The basic properties of object-induced and attribute-induced neutrosophic three-way concept lattices are examined. Secondly, we divide the neutrosophic formal context into three classical formal contexts and propose the notions of the candidate neutrosophic three-way concepts and the redundant neutrosophic three-way concepts. Two approaches of constructing object-induced (attribute-induced) neutrosophic three-way concept lattices are presented by using candidate, redundant and original neutrosophic three-way concepts respectively. Finally, we apply the neutrosophic formal concept analysis to the conflict analysis and put forward the corresponding optimal strategy and the calculation method of the alliance.

Matrix-based reduction approach for one-sided fuzzy three-way concept lattices

Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders. Furthermore, approaches to granular matrix-based reductions are investigated, by which granular consistent sets, and granular reducts via discernibility Boolean matrices are tectonically put forward. At last, the demonstrated results are performed by several experiments which enrich the research of three-way concept analysis.

Gradation of Fuzzy Preconcept Lattices

Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.