Attribute Reduction Based On Information Entropy For Incomplete Fuzzy Information System

Rough set theory is a mathematical tool to deal with imprecise, inconsistent and incomplete data. Attribute reduction is an important part of rough set theory.Attribute reduction in complete information system that has unambiguous objectives has been defined in many studies. However, the incompleteness of information and fuzziness of objective exist widely in real life which confines the application of classical rough set theory. Therefore, the research of attribute reduction for incomplete and fuzzy information system is of great significance.Attribute reduction based on information entropy for incomplete and fuzzy information system is studied in this dissertation, with incomplete and fuzzy condition information system and incomplete and fuzzy decision information system as objects,rough set theory and fuzzy set theory as tools. The main contents of this dissertation are as follows:(1)Aming the phenomenon of lacking and float data in condition attributes, the concept of incomplete and fuzzy condition information system is proposed, and then a new binary relation for dividing condition attributes is also given, and the information entropy is improved, then the method for computing improved information entropy is given. On this basis, the attribute reduction algorithm based on improved information entropy for incomplete and fuzzy condition information system is proposed, and the extraction algorithm of decision-making rules is studied accordingly. The theoretical analysis and example illustrate the feasibility of the algorithms.(2)The attribute reduction algorithm based on information entropy in complete information system is extended to the incomplete and fuzzy decision information system. Formula of information entropy is extended, and the extended information entropy is computed by limited tolerance relation, then the corresponding algorithm is given. On this basis, the attribute reduction algorithm based on extended information entropy for incomplete and fuzzy decision information system is designed, and the extraction of decision-making rules is given accordingly. The theoretical analysis and example illustrate the feasibility of the algorithms.