Research On Rough Set Models And Knowledge Reductions For Incomplete And Fuzzy Decision Information System

Rough set models and knowledge reductions for incomplete and fuzzy decisioninformation system (IFDIS in short) are systematically studied in this dissertation on thebasis of researches on extended model of rough set and knowledge reduction forincomplete information system, with IFDIS as the main discuss object, rough set theoryand fuzzy set theory as tools, and knowledge reduction as objective. A prototype system ofknowledge reductions for IFDIS is developed based on the various algorithms. Theprimary contributions are as follows:1. The concept of IFDIS is proposed by the definitions of incomplete informationsystem and complete fuzzy decision information system. The rough set models andknowledge reductions, based on tolerance relation, non-symmetrical similarity relation,limited tolerance relation and inclusion degree, are further studied.2. Improved-tolerance relation,γ-Tolerance relation and symmetrical similarityrelation are suggested; Rough set models and reductions for incomplete informationsystem and IFDIS based on these relations are studied.3. Variable rough set model and knowledge reduction for IFDIS are proposed. Thevariable rough set model is based on the general binary relation, thus tolerance relation,non-symmetrical (symmetrical) similarity relation, limited tolerance relation,improved-tolerance relation, valued limited tolerance relation andγ-tolerance relationmay be considered as its special cases. Inclusion degree-based rough set model for IFDISis defined, and knowledge reductions, based on (upper, lower) distributive compatiblereduction and maximum (minimum) distributive reduction, are studied.4. The properties of various rough set models are researched and all models arecompared with each other, which bring the conclusions: the improved-tolerance relationand limited tolerance relation-based rough set models are more rigorous than tolerancerelation-based rough set model, non-symmetrical similarity relation-based model is morerigorous than symmetrical similarity relation-based model which is more rigorous thanlimited tolerance relation-based model. Rough set model based onγ-tolerance is thegeneralization of tolerance relation-based rough set model under valid parameter. Bothvariable rough set model and inclusion degree-based rough set model are general rough setmodels for IFDIS. Four algorithms for various knowledge reducts are mainly studied:precision reduction algorithm, (upper, lower) compatible reduction algorithm, maximum(minimum) distributive reduction algorithm and discernibility matrix algorithm. Resultsshow that precision reduction algorithm, compatible reduction algorithm and maximum(minimum) distributive reduction algorithm are suitable for all knowledge reductionswhose computational complexities are almost O(|A|~3·|U|~2), while discernibility matrixalgorithm is only suitable for knowledge reductions for IFDIS based on tolerance relation and non-symmetrical (symmetrical) similarity relation.5. A prototype system of knowledge reductions for IFDIS is developed based on theabove-mentioned various algorithms, and some of the algorithms are validated.