| Information systems provide a convenient and useful tool for representing a set of ob-jects with a group of attributes. Knowledge discovery in information system as a hot issue ininformation science field has always been the core topic in artificial intelligent.Knowledge reduction is one of the most key issues of knowledge discovery. Knowledgereduction is deleting the attributes which are unrelated or unimportant (redundant attributes)with the classification ability of the knowledge base unchanged. Based on rough set theory,fuzzy set theory and intuitionistic fuzzy set theory, this paper studies the issues of attributereductions in information systems by the means of matrix and dependence space. The maincontent of this paper can be generalized as follows:1. Aiming at variable precision rough set model and fuzzy rough set model, the matrixalgorithm of (β) upper、lower distribution reduction and decision reduction are introduced.2. Possible assignment reduction and distribution reduction in inconsistent ordered deci-sion information system are considered in terms of dependence space. The novel judgementtheorems for judging assignment consistent sets are established in ordered decision informationsystem with the theory of dependence space. Moreover, we obtain a necessary condition thatmakes a set be a distribution consistent set, which is demonstrated is not sufficient.3. Based on dependence space, we discuss the problem of lower assignment reduction ofα level. Finally, the judgement theorems for judging lower assignment consistent sets of α levelare established in incomplete and fuzzy objective information system.4. The approximate reductions of dominance intuitionistic fuzzy information system arediscussed. The judgment theorems for judging approximate consistent sets using matrices the-ory are presented, then, based on the theory of dependence space, we give another new methodto calculate the reductions. Furthermore, we prove the equivalency of the two approaches. |
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