Research On Robust Fuzzy Concept Lattice

Formal concept analysis is a mathematical tool for data analysis and knowledge discovery proposed by German mathematician Wille in the 1980 s.Concept lattice,as the core structure of formal concept analysis,reflects the generalization and instantiation relation between concepts,being regarded as a high simplified description of the objective world.Concept lattice has been widely used in medical diagnosis,knowledge representation,personalized recommendation and so on.The information in real life is usually vague or uncertain.In order to solve practical problems more effectively,in recent years,many scholars have combined fuzzy set theory with formal concept analysis,and put forward a variety of fuzzy concept lattice models,such as L-fuzzy concept lattice,variable threshold concept lattice,L-fuzzy three-way concept lattice,intuitionistic fuzzy three-way concept lattice,etc.However,the above fuzzy concept lattice models only studied the construction of concept lattice under fuzzy formal context,without considering the robustness of the models.Therefore,slight disturbance of data will have a huge impact on the construction of fuzzy concept lattice,which is not conducive to the process and analysis of fuzzy information.In this paper,the robustness of fuzzy concept lattice is studied and two kinds of fuzzy concept lattice models with stronger robustness are proposed.The main research results of this paper are as follows:(1)This paper proposed robust variable threshold concept lattice by improving variable threshold concept lattice.We firstly introduced tolerance threshold into variable threshold concept lattice,proposed robust variable threshold concept,and finally constructed robust variable threshold concept lattice.The results show that robust variable threshold concept lattice can eliminate the concepts that lack robustness and improve the robustness of variable threshold concept lattice.In addition,we discussed the relationship between robust variable threshold concept lattice and variable threshold concept lattice,and it is proved that variable threshold concept lattice is a special case of robust variable threshold concept lattice.(2)Robust variable threshold concept lattice is extended,and robust three-way concept lattice is proposed.Three-way decision is applied to fuzzy context,and double threshold three-way concept operators are defined.Accordingly,robust three-way concept and robust three-way concept lattice are constructed,and relevant properties of robust three-way concept lattice are analyzed.The results show that the flexible selection of threshold can reduce the influence of data noise and improve the robustness of the model.