Uncertainty And Reduction Of A Multi-granulation Fuzzy Information System

This paper studies uncertainty and reduction of multi-granulation fuzzy information systems.First,a novel completion method of an incomplete fuzzy infor-mation system is proposed.Then,in an optimistic multi-granulation fuzzy system,the rough belongingness of a fuzzy set,and the fuzziness measure of an optimistic multi-granulation fuzzy approximation space are studied.We also discuss the optimistic multi-granulation conditional roughness of a fuzzy set with respect to another fuzzy set,the optimistic multi-granulation conditional entyopy of a decision attribute set with respect to a multi-granulation condition attribute set and the properties of the reduction of a consistent optimistic multi-granulation decision information system based on the conditional entropy.For ?-consistent optimistic multi-granulation decision information systems,we give a special conditional entropy and use it to analyse the reduction of ?-consistent optimistic multi-granulation decision information systems.Finally,we give various uncertainty measures for pessimistic multi-granulation fuzzy information systems.