Research On Approaches To Knowledge Reduction Of Interval Information Systems Based On Fuzzy Rough Set Theory

Rough set theory, proposed by Polish mathematician Z.Pawlak in1982, is a data analysistheory. It can effectively deal with ambiguity and uncertainty knowledge, discover implicitknowledge and reveal potential law. Reduction is not only an important part of data miningbut also one of the core issues of rough set theory. A variety of attributes reduction theoriesand algorithms were proposed by researchers for different information systems. Based on thebinary fuzzy relation over the universe, the attributes reduction method of intervalinformation systems and interval ordered information systems was studied. The main contentof this paper can be summarized as follows:1、Discussed the fuzzy information entropy reduction of interval information systems andthe fuzzy positive domain reduction of interval decision table from the perspective of fuzzyinformation theory. First, a fuzzy tolerance relation was defined based on the similaritymeasure between objects in interval information systems. And the upper and lowerapproximation of decision classes based on the fuzzy tolerance relation were given. Secondly,the definition of the significance of condition attributes and the relative significance ofcondition attributes were given in interval information systems and interval decision table bythe introduction of fuzzy information entropy and fuzzy relative positive domain and fuzzyapproximate quality. And on this basis, a heuristic algorithm for calculating fuzzy informationentropy reduction in interval information systems and fuzzy relative positive domainreduction in interval decision table was given.2、Discussed the fuzzy information entropy reduction of interval ordered informationsystems and the fuzzy lower approximate distribution reduction of interval ordered decisiontable from the perspective of dominance-based fuzzy rough set. First, we detailed analysis theapproach of computing a valued preference relation between any two objects with respect toeach criterion in interval ordered information systems. Secondly, the approach of fuzzyinformation entropy reduction in interval ordered information systems was given. Thirdly, thefuzzy lower approximate distribution reduction was defined in interval ordered decision tablebased on the fuzzy lower approximation of the upward and downward unions of decisionclasses. By the introduction of fuzzy conditional significance and the relative fuzzyconditional significance, a heuristic algorithm for calculating fuzzy information entropyreduction and fuzzy lower approximate distribution reduction was given, and an example wasgiven to prove the effectiveness of the algorithm. Finally, a ranking approach for all objectsbased on fuzzy granular was given in interval ordered information systems.