Graph-based For Pessimistic Multi-granulation Rough Set And Simple Closure Space

It is an era of rapid development of information technology,with the popularity of the Internet,the data acquired by people in more diverse ways,and the amount of information has exploded.In face of large quantity information,how to extract useful information has become an urgent problem to be solved,so the dimensional reduction of data has become hot issues.As a pre-processing part of the data,attribute reduction has become the most primary work.Therefore,This paper combines with the vertex coverage theory of graph,the graph-based granularity reduction problems in pessimistic multi-granularition rough sets are studied.Then,according to existing connection between formal context and simple closure space,the association between skill reduction and minimum intersection generation group is discussed.Based on this,the directed edges are used to build partial order relation between attributes,and bulid its incidence matrices to discuss the problem of skill reduction in simple closure space.This paper mainly involves the following three aspects:（1）For complete and incomplete information systems,two kinds of concept of the graph induced in pessimistic multi-granularity rough set are proposed separately,and the graph characteristics of granularity reduction are given.On this basis,the significance of granularity is depicted by the graph method,and the relevant algorithms of granularity reduction are designed.Finally,the effectiveness of the proposed algorithm is verified by numerical experiments with the pessimistic approximate multi-granularition rough set as an example.（2）This paper combines the concept of intersectional irreducible elements of minimum intersection generation group of concept lattices,and the connection between skill reduction of simple closure space and attribute reduction of formal contexts is discussed.First of all,the dual set of knowledge basis A is defined,the essence of skill reduction based on conjunctive model is provided.Then,the concept of irreducible element in skill contexts is presented,the equivalency between A and intersectional irreducible elements is demonstrated.Finally,a method of skill reduction is given.（3）Based on the relationship between skill reduction and intersection irreducible elements,the partial order relation between skill and skill is established through directed edge,its characters are discussed.On this basis,the incidence matrix of graph is constructed,and the judging theory of intersectional irreducible element and intersectional reducible element are presented.Finally,the skill reduction is studied based on incidence matrix.