The Study Of Three-way Semiconcepts And Algorithms In Two Forms Of Formal Contexts

In 1991,Luksch et al.proposed a new "concept" structure—classical semiconcepts.Classical semiconcepts only need to study on the relationship between objects and attributes in one direction,and relax the restrictions of operators in formal concept analysis.Once the theory of Semiconcept was presented,many researchers have paid their attentions to it.However,classical semiconcepts only study the exact relationship between objects and at-tributes,but there are also cases of fuzzy relations in practical applications.Due to the influence of two-way decisions,there are few researches on the combination of classical semiconcepts and other theories,which affects the development of classical semiconcepts.In order to enrich the theory of classical semiconcepts,the thinking mode is extended from two-way decisions to three-way decisions.We discuss the classical semiconcepts with three-way decisions.Since the classical formal context and fuzzy formal context are widely used,this thesis will conduct the following research on classical semiconcepts:1.For a classical formal context,the model of three-way decisions is introduced into classical semiconcepts,and operators are used to divide the discussed universal set into three parts.Thus,two kinds of three-way semiconcepts—OE—semiconcept and AE—semiconcept are proposed.This paper discusses the basic properties of three-way semiconcepts in lattice theory,and analyses the relationships between three-way semiconcepts,and three-way concepts and classical semiconcepts,and gives some algorithms for constructing two kinds of three-way semiconcepts respectively.Examples are used to verify the effectiveness of the algorithms.2.For a fuzzy formal context,the theory of classical semiconcepts is combined with fuzzy set theory and three-way decisions.The fuzzy relation between objects and attributes is defined by the membership degree in the fuzzy set.And the fuzzy three-way semioperators are defined according to the threshold value.And the definitions of two forms of fuzzy three-way semicon-cepts—fuzzy OE—semiconcept and fuzzy AE—semiconcept are proposed.It gives a partial ordered relation and upper and lower bounds of fuzzy three-way semiconcepts,respectively.The algorithm process of generating the fuzzy three-way semiconcepts is given.At last,using some examples to illustrate the process of these algorithms.