Approximate Three-Way Concept Theory And Its Application Based On Formal Context

Professor Wille proposed Formal Concept Analysis(FCA)in 1982.FCA mainly includes formal context,formal concept and corresponding concept lattice.The im-portant data structure of FCA is concept lattice,which reflects the generalization and specialization relationship between formal concepts.Each node of a concept lattice is a formal concept.It consists of two parts:extension(an object set)and intension(an attribute set).In real life,obtaining the uncertain concept(approximate concept)from the formal context is an important research direction.Based on related research,this article discusses how to obtain approximate concept from the formal context,and proposes the construction method of approximate concept.The contents of this study include:First,in the formal context,three-way k-grade relationship based on the object set are defined.Approximate three-way concept based on the object set is proposed and its properties are studied,which is used to explain the problems in real life.According to the definition,the algorithm of approximate three-way concept based on the object set is obtained,and the relationship between approximate three-way concept based on the object set and three-way concept,approximate concept,join-irreducible element,meet-irreducible element and other special elements is discussed.Second,in the formal context,three-way k-grade relationship based on the at-tribute set are defined,and approximate three-way concept based on the attribute set is proposed.According to the definition,the algorithm of approximate three-way concept based on attribute is obtained,and the relationship between approximate three-way concept based on attribute set and three-way concept,approximate con-cept,join-irreducible element,meet-irreducible element and other special elements is discussed.Last,construct a new formal context from the original formal context,that is,subposition or apposition of formal context.Approximate three-way concept is con-structed in subposition or apposition of formal context,and the relationship between approximate three-way concept of the original formal context and its subposition or apposition is studied.We get the equivalent relationship between approximate three-way concept of the original formal context and approximate concept of its subposition or apposition,and we can obtain approximate three-way concept from its subposition or apposition.The research of this paper will further enrich and perfect the theoretical system of formal concept analysis,promote the theoretical development of the new research field of three-way concept analysis,and provide more help for practical decision-making.