Research On Attribute Reduction In Interval-Valued Information Systems Based On Connection-degree Tolerance Relation

Rough set theory was proposed by the Polish mathematician Professor Pawlak in 1982.It is a mathematical tool for dealing with incomplete,uncertain and inaccurate data.It is widely used in data mining,machine learning,decision support and analysis,and imagery processing,expert systems,approximate reasoning and many other fields.In recent years,the majority of scholars have promoted the Pawlak rough set model a lot.Among them,knowledge discovery based on interval-valued information system has become one of the important directions of rough set theory and its application research.Due to the strict requirements of the equivalence relation in the Pawlak rough set model,there are limitations in processing interval-valued data.Therefore,based on the tolerance relation between reflexivity and symmetry,this paper studies the attribute reduction method in interval-valued information system,and discusses the similarity of interval numbers in depth.The main work is reflected in the following aspects.(1)Based on the connection degree in the set pair analysis,the similarity between the objects in the interval-valued information system is proposed,which indicates the distribution of the similarity of the interval numbers of the two objects under different attributes.Furthermore,the concept of connection-degree tolerance relation and connection-degree tolerance class are proposed in the interval-valued information systems.A new classification criterion is established and it is proved that the classification ability is between variable precision tolerance relation and two-parameters tolerance relation.Finally,the methods of reduction of connection-degree classification reduction and dependency intensity reduction based on connection-degree tolerance relation are proposed.(2)In practice,considering the uncertainty of the endpoint of the interval number,the triangular norm is introduced into the operation of the interval number,so that the width of the interval number can be appropriately increased,and more effective information that may be lost is retained.Firstly,a new length of interval number and intersection and union algorithm for interval are defined,and the related properties are discussed.Secondly,applying the new algorithm to the similarity of interval numbers,a generalized similarity of interval numbers is proposed,which enhances the application range of interval number similarity.Finally,based on the generalized similarity,connection-degree tolerance relation is discussed,which enhances the generalization ability of the compatibility degree of the connection degree.(3)Taking education and teaching management as an example,the attribute reduction method of interval-valued information system based on the connection-degree tolerance relation is applied to practice.