Research On Uncertain Decision And Application Based On Extended Rough Set

Rough set theory proposed by Pawlak in Poland is a good mathematical tool for dealing with fuzzy and uncertain data.Compared with fuzzy set and evidence theory that those theory need somebody to set parameter,the characteristic of rough set theory is that it does not need any prior knowledge or additional information,so it has a good application prospect in multiple attribute decision making problems.Classical rough set theory is based on equivalence relation that has a strict request on data,So classical rough set theory is not good at dealing with the practical application.In this paper,we will propose two kind of extended rough set that they are rough set based dominance relation and rough set combined with support vector machine,At the same time,we will solve the uncertain multi-attribute decision making problem according to the two kinds of extended rough set's advantage and have achieved good results.In some practical problems,there are many decision information systems based on dominance relation.For example,for two listed company that whose financial indexes have preference information project investment problem,decision makers generally think this company is better if the company has lower asset-liability ratio and higher mercantile rate of return.At this time,the order of preference attributes is important decision information,but the classical rough set theory can't do anything about it.This thesis will present the basic concepts of rough set based on dominance relation first,then,we will propose a reduction method based on information entropy and mutual information,in the end,we will present uncertainty reasoning about a new object using evidence theory.At the same time,this thesis will put a interval order rough set based the relationship between interval number and possibility degree so that we can sort the uncertain object better.In reality,it's very difficult to control data collection and data procession,however,rough set is sensitive to data quality resulting in it's prediction accuracy isn't satisfied.At the same time,the basic principle of the support vector machine is to enhance the generalization ability by minimizing the structure risk.In addition,support vector machine can be good at dealing with high dimension data.Therefore,in this thesis,we will consider combining the rough set and support vector machine to solve personal credit evaluation question.