Two Methods Of Constructing Crisp-fuzzy Concept Lattices

Formal concept analysis(FCA)describes a binary relation between a set of objects and a set of attributes through the basis of a formal context,which is reflecting the concept and conceptual hierarchy by a concept lattice.In addition,as a mathematical tool for data analysis and knowledge acquisition,FCA has been successfully applied in knowledge discovery,data mining,information extraction and software engineering.Classical formal concept analysis is not suitable for fuzzy and uncertain problems.However,a fuzzy formal context can be represented those fuzzy and uncertain relationships among data.The researches of fuzzy concept lattices focus on the construction of fuzzy concept lattices,attribute reduction and rule extraction.Two-way decision only discusses two choices of acceptance and rejection.In a case of incomplete information,the choices made by using two-way decision can not meet the needs of real life.Therefore,three-way decision can be suitable to deal with the practical problems because of adding a delayed decision besides a decision of acceptance and rejection.In this paper,the following works are done respectively.1.To improve the efficiency of constructing crisp-fuzzy concept lattices,a crisp-fuzzy concept lattices will be constructed by using a circle in a weighted graph.At the same time,an algorithm is given to generate all crisp-fuzzy concepts.Finally,an example is given to verify the feasibility and correctness of this algorithm.Because of the visualization of a graph,the introduction of a weighted graph not only saves the storage space for the operation of this algorithm,but also makes the process of generating fuzzy concepts more intuitive.2.To obtain crisp-fuzzy concept lattices,this paper introduces three-way decision into crisp-fuzzy concept lattices and constructs crisp-fuzzy three-way concept lattices.The crisp-fuzzy three-way concepts are defined.And some correspondent properties and theories are obtained.Furthermore,an algorithm is shown to generate all crisp-fuzzy three-way concepts.By using crisp-fuzzy three-way concepts in this paper,a non-commitment decision can be made even if a decision of acceptance and rejection can not be made from the raw fuzzy and uncertain information.