Research On Picture Fuzzy Rough Set Model And Its Extension

With the rapid advent of massive data and complex applications,mankind is facing the challenge of scientific modeling and intelligent decision-making of massive data.The research and development of the basic theory of artificial intelligence has become a key problem to be solved in the current information age.The proposal of rough set provides a new method for mathematical modeling and calculation.It abstracts human objective knowledge into multiple data relationships for processing.The essence of constructing the rough set model is the relational reasoning and knowledge discovery of information under multiple relations.Aiming at the shortcomings of the intuitionistic fuzzy rough set model for complex data processing,this paper proposes the picture fuzzy rough set model,at the same time,the extended model of picture fuzzy rough set is studied.The work of this paper is as follows:(1)Firstly,the picture fuzzy similarity relation is defined,the picture fuzzy approximate space is constructed,and the picture fuzzy rough set model is established by constructive method.The characteristics of the model and reduction strategies are studied in depth.The uncertainty measurements of the model are carried out by using the knowledge granularity and entropy method,and the mathematical relationship between information measurement and knowledge is obtained.The reduction algorithm of picture fuzzy rough set is proposed and the model is verified by a specific example.(2)In view of the problem that picture fuzzy information over dual-universes can not be described and mined,the picture equivalent fuzzy relation over dual-universes is defined and the picture fuzzy rough set model over dual-universes is established by using the constructive method.The properties of the model and the reduction principle are further studied,and the attribute reduction algorithm of the picture fuzzy rough set over dual-universes is proposed and the model is verified by a specific example.The picture fuzzy rough set model proposed in this paper provides a theoretical support for the classification and calculation of picture fuzzy information.The model and its extended theory are of great significance for the further study of picture fuzzy reasoning mechanism and the improvement of the basic theory of artificial intelligence.