Research On Incomplete Fuzzy Rough Set Model Extension Based On Dominance Relation And Its Application

As a new type of data analysis tool, rough set theory be used to deal with imprecise, uncertain, vague, incomplete, and other types of data, and it does not require any a priori information. Now it has been successfully applied in the data mining, financial management, fault diagnosis, pharmaceutical chemicals, and other fields.According to incomplete fuzzy decision information system with dominance relation, after analyzing the advantages and disadvantages of existing two dominance relations, a new total order dominance relation is built by using the probability distribution principle of the attribute value. This dominance relation is used to scientifically and reasonably improve the extended dominance relation by approximation quality and approximation accuracy and overcome the shortcoming that the limit dominance relation can not be used to compare all the objects on the domain. And further, based on the new dominance relation, the expression of the lower and upper approximation, the definition of relative reduction and specific calculation method are given. Finally, an example shows the effectiveness of the proposed method.Attribute reduction is one of the core contents of the rough set research. Attribute reduction algorithm based on discernibility matrix is one of the frequently used attribute reduction methods. About how to solve the minimal disjunctive normal form of the discernibility function constructed by a discernibility matrix, a new method with the simple basic principle, easy steps and simple operations in this thesis, is proposed that can be easily understood and programmed to get the minimal disjunctive normal form item by item. This method is proved by theorems that the approach can certainly get the minimal disjunctive normal form and all of the reductions. The method also adapts a dynamic information system with the objects gradually increasing. An example shows that the approach is correct and valid, finally.Proposed a rough set of expansion model, the ultimate goal is to export the decision rules to help decision makers make better decisions. About how to solve rules extraction in incomplete fuzzy information system, after analyzing existing rules extraction methods, in this thesis two types of decision rules based on a new total order dominance relation, namely,"at least" and "at most" are proposed. And further, how to simplify the two types of decision rules, namely, value reduction is also discussed in this thesis. At last, an example shows that the proposed methods of rules extraction and its simplification are correct and valid.