| The theory of rough sets is proposed by Pawlak in practice of classificationand data analysis with imprecise and incomplete information. The rough set conceptcan be of some importance, primarily in some branches of artificial intelligence, suchas reasoning, automatic classification, pattern recognition, learning algorithms, etc. Inrecent years, with the development of rough set theory, the idea of rough set leads to afurther research and applications in classification theory, cluster analysis, measurementtheory, etc.The key of the rough set theory is deal with the approximation of an arbitrarysubset of a universe by two subsets called lower and upper approximations. Thereare mainly two methods for the development of this theory, the constructive and alge-braic(axiomatic) approaches. In constructive methods, lower and upper approximationsare not primitive notions. They are constructed from other concepts, such as binary re-lations on a universe, partitions and coverings of a universe, and partially ordered sets,lattice, Boolean algebras and their subalgebras, etc.The main aim of the paper is to construct new models of rough fuzzy sets and fuzzyrough sets by the constructive method. After the accuracy of fuzzy concepts with levelsets, A new model of rough set is obtained by the use of Pawlak rough set theory andrepresentation theorem. In the paper, the rough fuzzy set model in the interval [0,1] isdiscussed at first. Secondly, the fuzzy rough set model in the interval [0,1] is proposed.Thirdly, the rough fuzzy set model in F lattice is defined. fourthly, the fuzzy rough setmodel in F lattice is obtained.In this paper, the uncertainty measurement of rough fuzzy sets and fuzzy rough setsis also discussed. The fuzziness of the uncertainty is measured with fuzzy entropy. Theuncertainty measurement called rough entropy is obtained on the basis of informationentropy. |
PDF Full Text Request