The Research Of Multigranulation Rough Sets And Knowledge Redution In Incomplete Information System

Rough set theory is an effective mathematical tool, which can be used to analyze and deal with imprecise, incomplete and inconsistent information. By comparing with the evidence theory, the fuzzy set theory and the probability theory, such theory does not need any prior knowledge besides the data itself. With the development of twenty years, rough set theory has been widely used in machine learning, financial analysis, approximate reasoning, data mining, expert system, decision analysis, imagine processing, medical diagnosis and soPresently, the researching of rough set theory includes:expansions of rough set theory, knowledge acquisition and reducts, uncertainty measure of the knowledge. It should be noticed that the approaches to knowledge acquisition and the algorithms of finding reducts are crucial topics in the researching of rough set theory. Since the classical rough set theory is constructed on the basis of the indiscernibiltity relation (equivalence relation), it is too restrictive and lack of flexibility, and then the researching of different types of expanded rough set models is important to the development of the rough set theory. Now, many researchers have done excellent jobs on multigranulation rough set, dominance-based rough set, variable precision rough set and fuzzy set in complete information system. Nevertheless, the single researching results obtained by above works have the limitations such that accuracy and flexibility. In this thesis, multigranulation rough set and the corresponding several types of the expanded rough set models have been deeply investigated in incomplete information systems.(1) By considering that optimistic rough set is too loose while pessimistic rough set is too strict, the fusion of multigranulation rough set, variable precision rough set and incomplete information system is presented and then the concept of variable precision multigranulation rough set model is constructed. On the basis of the tolerance relation based variable precision rough set and multigranulation rough set, the concept of variable precision multigranulation rough set is proposed, which includes variable precision optimistic and pessimistic rough sets, respectively. Both these two models are expansions of tolerance relation based variable precision rough set and multigranulation rough set. The reduct about the new proposed variable precision multigranulation rough set model is also discussed by the heuristic algorithm. The efficiency of the reduct is analyzed and then draw the conclusions: with the increase of the threshold b, the efficiency of the reduct of the proposed variable precision multigranulation rough set has the downward trend, but with the monotonically increase of the threshold b, the efficiency of the reduct has not the monotonically downward trend strictly; the efficiency of the reduct of the variable precision pessimistic multigranulation rough set is higher than the variable precision optimistic multigranulation rough set; the reducts of the variable precision optimistic and pessimistic rough sets does not exist certain inclusion relation.(2) By considering the order relation of the attribute values and the multigranulation association problem of the attribute of the rough set in incomplete information system, the fusion of multigranulation rough set, tolerance precision rough set and incomplete information system is presented and then the concept of tolerance relation based multigranulation rough set model is constructed. The idea of multigranulation is introduced into incomplete information system, a family of tolerance relations are used to approximate the fuzzy concepts, then the optimistic and pessimistic multigranulation rough fuzzy sets are proposed. The new proposed models are expansions of classical multigranulation rough sets and tolerance relation based rough fuzzy set, which makes multigranulation method deal with fuzzy information effectively. Moreover, the efficiency of the reduct of tolerance based optimistic and pessimistic multigranulation rough sets are compared and then draw the conclusions that the efficiency of the reduct of the limited tolerance relation is higher than the extended tolerance relation; pessimistic multigranulation (?)-upper approximate distribute reduct is a inadvisable reduct in practical engineering.(3) By considering the present fuzzy rough set is based on one and only one fuzzy binary relation, without considering the distributive fuzzy information process, the fusion of multigranulation rough set, tolerance precision rough set and fuzzy information system is presented and then the concept of tolerance relation based multigranulation fuzzy rough set model is constructed, and then the properties about the new model are discussed; in fuzzy information system, with the idea of multigranulation, the decision rule of logical connective "or" are acquired; the reduct of tolerance based optimistic and pessimistic multigranulation rough fuzzy sets are researched and then draw the conclusions that under the framework of tolerance based multigranulation, the pessimistic lower approximate can get smaller lower approximate than the optimistic lower approximate; the pessimistic upper approximate can get larger upper approximate than the optimistic upper approximate, i.e., the approximate accuracy of optimistic is lager than the approximate accuracy of pessimistic.