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Research on the Generalized Decision Reducts and the Acquisition ofOptimal Decision Rules in Generalized Decision Information System

This paper discusses generalized decision reducts and the acquisition of optimal decision rules in general (con- sistent or inconsistent) decision information systems. The properties and relationship between Pawlak reducts with respect to definite information and generalized decision reducts based on indefinite information were analysed and revealed re- spectively. Secondly, the computation approach of reducts and optimal decision rules based on discernibility functions were given. Last but not the least, a type of improved discernibility matrix was constructed, which can be used to com- pute generalized decision reducts and generalized decision core as well as Pawlak reducts and core. The discussions in this paper considered the consistency of information systems, in making a distinction between Pawlak reducts and gener- alized reducts. This work improved and generalized the relevant study by senior researchers. Moreover, some misunder- standings in the computation of cores in information systems have also been clarified from mathematical point of view.