Knowledge Reductions Of Information System With Fuzzy Targets

Rough set theory is a new mathematical tool to deal with fuzzy and uncertain information. Rough set theory has been made rapid progress in thories and practical applications since Pawlak, a Polish mathematician, firstly put up with rough set theory in 1982. Especially because of its successful application in knowledge diacovery in 1980s and 1990s, it is valued throughout international world. Nowadays, rough set theory has been successfully applied to many fields such as artificial intelligence, knowledge and data discovery, pattern recognition and classification and failure detection.This paper mainly focuses on konwledge discoveries in information system with fuzzy targets. It includes the follow three research works: first, rough approximation of fuzzy set under usual binary relation is investigated based on rough approximation of fuzzy set in Pawlak information system and a series of attributes about approximation of fuzzy set are derived,which are similar to those attributes under classical equivalent relation. Second, based on the theory and method of knowledge reduction and knowledge discovery in information systems with fuzzy targets, the definition of information systems with fuzzy multi-group targets is introduced and the method of knowledge reduction in this kind of information system is presented. Finally, the method of fuzzy classification in fuzzy information system is brought forward and the definition of information system with pure fuzzy targets is given. Moreover, two methods of knowledge reductions in this information system, consistent classification reduction and consistent maximal decision reduction, are derived.