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Containing order rough set methodology

In classical rough set theory, which gives definitions of indiscernibility relation, upper approximation, lower approximation, reduct and core, the main idea is approximating knowledge granules which come from decision attributes set employing knowledge granules from condition attributes set, hence generating rules. These knowledge granules are obtained according to equivalence relation in essence, it is possible there exist attributes which contain preference order relation among their values and correlate semantically with other attributes, such attributes are called criteria. Rough set methodology involved in this paper takes into account these information which criteria carry, deduces rules containing order information, and discusses to keep rules set more complete and consistent. In this paper we introduce definition of containing order rough set (CORS) methodology and other concerned notations, formalizes method of data analysis and rules generation, moreover provide a more rational approximation quality measure and four principles of generating rules.