| Formal Concept Analysis is a kind of lattice theory based on formal context.It was proposed by German mathematician R.Wille in 1982 and has become a powerful mathematical tool in data analysis and knowledge discovery.Qi et al.combined formal concept analysis with three-way decision theory,proposed three-way concept analysis in 2014,and constructed a new model between objects and attributes in formal context.Three-way concept as an extension of formal concept,it is necessary to study the relationship between three-way concepts and classical concepts in a formal context.This paper studies the three-way concept problems in two different formal contexts,and proposes the construction methods of the three-way concepts in the two formal contexts.The main research content is as follows:1.As for a 0-1 formal context,firstly,present some properties of classical concepts and three-way concepts,respectively.Based on this,we systematically study the relationships between two types of three-way concepts and classical concepts.More specifically,we can obtain all object-induced three-way concepts and attribute-induced three-way concepts based on four relationships,where the four relationships are characterized by four theorems.After that,two algorithms are proposed to build an object-induced three-way concept lattice and an attribute-induced concept three-way lattice,respectively,and examples are given to verify these algorithms.2.Introduce the three-way concepts into the generalized one-sided formal context,based on positive operators and negative operators,define one-sided three-way operators and one-sided three-way concepts.Then discuss properties of one-sided three-way operators and one-sided three-way concepts in detail,we propose an algorithm to obtain all one-sided three-way concepts in a generalized one-sided formal context.Furthermore,base on one-sided three-way concept,we propose an approach to compute all granular reductions in a generalized one-sided formal context. |
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