The General Relationship Is Quasi-fuzzy Rough Set Model

In the model of Pawlak fuzzy rough set,dual relation in the univers of discourse is equivalence relation, but dual relation is not always equivalence in the real questions. the application of the model of Pawlak rough set is limited , To the limitation of the data in realization, which weakened the equivalent relation and confined the application of the Pawlak fuzzy rough set, this paper brought about the new conception of equasi-common relation and equasi-generalized approximate space. With the replacement the successor neighbourhood by the equivalence class, we builded a fuzzy rough model under the equasi-common relation.Although the area of application is enlarged,"RA A RA" is not always right for any dual relation R and fuzzy set Ain the model of fuzzy rough set under the common relation. "RA A RA "is necessary for that the theory of rough set is applied information proccess. we notice that if R were reflexive relation,"RA A RA" would right, for thisreason, we brought about equasi-common relation (which is only reflexive relation ), we builded the model of fuzzy rough set under the equasi-common relation , It is not only enlarged the area of application of the model of Pawlakfuzzy rough set but also make sure that "RA A RA" which is the necceearyfor information proccess is right.In the model of fuzzy rough set under the equasi-common relation, we defined many conceptions such as equasi-generalized fuzzy rough equal , equasi-generalized fuzzy rough inclusion, and discussed their characters.With the replacement the equivalence class by the predecessor neighbourhood .we defined another model of fuzzy rough set under the equasi-common relation. We compared these two models and found that the twomodels are coincident when dual relation was symmetric.The author defined many conceptions which are similar to conceptions in the model of fuzzy rough set under the equasi-common relation and disccussed their characters in the fuzzy rough model under the equasi-common fuzzy relation by the equal process .and defined the conception of the equasi-generalized fuzzy rough equality,the equasi-generalized fuzzy rough inclusion, fuzzy set,the approximation about equasi-generalized approximate space according to the parameter, the fuzzy set of approximate space and the roughness of the parameter about the fuzzy set in equasi-generalized approximate space, then disscussed their character.Secondly this paper builded another fuzzy rough set model under equasi-common relation with the replacement equivalence class by the predecessor neighbourhood. We compared this two model and found that the two model is coincident when dual relation was symmetric.The author defined the approximate conception and disccussed their characters in the rough fuzzy model under the equasi-common fuzzy relation by the equal process.At the end , the author proved the concidence of three approximate operator which are the approximate operater in the fuzzy rough model under the equasi-coomon relation, the approximate operator in the fuzzy rough model under the equasi-common fuzzy relation and the approximate operator in the rough set under the common relation.