Uncertainty Measurement And Attribute Reduction Of Incomplete Interval-valued Information Systems

Incomplete interval-valued information systems are extended models of single-valued information systems.The processing of interval valued information system is helpful to extend the application of rough set theory.Uncertainty measurement can supply new viewpoints for analyzing date to help us disclose the substantive characteristics of date sets.Attribute reduction can remove irrelevant redundant attributes on the premise of keeping the classification ability of the universe.In this paper,the uncertainty mea-surement and attribute reduction of incomplete interval-valued information systems are studied systematically and deeply.Based on the entropy theory of incomplete interval-valued information systems,the uncertainty measurement problem is studied in this paper.According to the weak sim-ilarity relation between incomplete interval values,the information entropy and rough entropy of knowledge are proposed.An example is given to shows that the rough entropy is more accurate than roughness in measuring the uncertainty of knowledge.In view of the incomplete interval-valued information system,proposed the incom-plete interval-valued information system based on discernibility matrix attribute reduc-tion method.And the distribution of reduction method in the incomplete interval-valued fuzzy decision system is introduced,including ?-lower assignment reduction and ?-upper assignment reduction.The decision theorem and identification function of distribution reduction are given,and the feasibility of this method is verified by example.Evidence theory is a kind of effective uncertain reasoning method in the information fusion technology.There are many similarities in the rough set theory and the Dempster-Shafer theory of evidence.In this paper,we introduce evidence theory into incomplete interval-valued information system based on weak similarity relation,and discuss method of attribute reduction based on evidence theory in incomplete interval-valued information system by combining trust function and likelihood function.