Theoretical Research And Application Of Multigranulation Rough Set

Rough Set Theory is a powerful mathematical tool which can be used to deal withvague, uncertain and inconsistency information.In Pawlak’s rough set model, most of theresearches are used to deal with the problem in Complete Information Systems.However,inactual problem,systems delt by people are usually Incomplete Information Systems.Therefore, the study of how to use the rough set theory in Incomplete Information Systemshas become an important topic. But existing research work are all based on a single kind ofgranulation constructor, so Qian fromed the view of granular computing, pointed out that weoften need to describe concurrently a target concept through multi binary relations on theuniverse according to a user’s requirements or targets of problem solving. Therefore, theyproposed the concept of Multi-granulation Rough Set model. On this basis, to deal with theincomplete information system through the multigranulation approach, the tolerancerelations, similarity relations and limited tolerance relations are employed to constructoptimistic and pessimistic multigranulation rough set model, and applied the variableprecision multigranulation rough set based on limited tolerance relation to the evaluation ofHigher Education. The study of practical cases shows the effectiveness of the proposedmethod, the results are as following:(1) Aiming at the shortcomings of existing variable precision multigranulation roughset model cannot distinguish the two objects which have the same few known attributes andmore unknown attributes, this paper proposes an improved limited and variable precisionrough set model. Compared with the existing model, the study of practical cases shows thismodel can get accurate and reasonable results.(2) In this paper, to deal with the incomplete information system throughthe multigranulation approach, the tolerance relations, similarity relations and limitedtolerance relations are employed to construct optimistic and pessimistic multigranulationrough set model, respectively; Not only are the basic properties about these multigranulationrough sets analyzed, but also the relationships among them discussed. It is shown that,regardless of the method of optimistic multigranulation rough set model orpessimistic multigranulation rough set model, the limited tolerance relations basedmultigranulation lower approximations fall between the tolerance and similarity relations based multigranulation lower approximations, the limited tolerance relations basedmultigranulation upper approximations fall between similarity and the tolerance relationsbased multigranulation upper approximations. Such results are consistent with those insingle-granulation based rough sets model.(3) In incomplete information systems, multigranulation rough set model can use aplurality of different binary relations to approximate the target, and the variable precisionrough set is more suitable for processing noise data, this paper combines the characteristicsof these two models, proposed a variable precision multigranulation rough set based onlimited tolerance relation, including variable precision optimistic multigranulation rough setmodel and variable precision pessimistic multigranulation rough set, and discussed theproperties and relationships among them; At last, it is proved that variable precisionmultigranulation rough set based on limited tolerance relation has a higher approximationaccuracy than the classical rough set model.(4) This paper studied the attribute reduction of the variable precision multigranulationrough set based on limited tolerance relation in incomplete information system, presented adistributed algorithm of attribute reduction based on attribute signigicance, analysised theacquisition of decision rules on variable precision multigranulation rough set, and appliedthis algorithm to the evaluation of Higher Education. The study of practical cases shows theeffectiveness of the proposed method.