Rough Set Theory And Method Research In Incomplete Data Analysis

The classical rough set theory was first proposed by Poland professor Pawlak; it isconstructed on the basis of strict indiscernibility (equivalence) relation (reflective,symmetric, transitive) which is based on the assumption of complete information systems,i.e., there are no unknown values in the information table. However, the lack of data isalways exit in data processing. Therefore, research on how to expand the rough set inincomplete information systems is very important for the development of rough set theory.In this paper, research on incomplete information system, use the classical rough setmodels and their properties to deeply investigated rough set in incomplete informationsystem. There are two primary innovations as follows:(1) Rough set model based on tolerance relation, has been widely used to deal withincomplete information systems. However, this model is not so perfect because not all of theelements in a tolerant class are mutually tolerant, but they are tolerant with the generatingelement of this class. To mend this limitation, the compatible relation is re-defined and then,the concept of maximal complete compatible class in incomplete information system ispresented for the purpose that any two elements in the same compatible module aremutually compatible. Furthermore, two methods are put forward in the interest of selectingoptimal compatible class for an object, which can be used in knowledge reduction. Besides,coverings on universe produced by tolerance and compatible relations are deeplyinvestigated and compared. Finally, a medical decision table is analyzed, and some compactrules are mined.(2) When the incomplete information system with both absent and missing unknownvalues, the characteristic class which was proposed by Grzymala-Busse was studied. Thelimitation of characteristic class was point out such that not any two elements in acharacteristic class were mutually tolerant. The technique of maximal consistent blocks wasintroduced into characteristic class, and then the concept of characteristic consistent blockwas proposed. Not only the basic properties about characteristic consistent blocks basedrough sets was deeply investigated, but also the relationship between characteristicconsistent blocks and characteristic relation based rough sets was analyzed. The resultsshowed that by comparing with the characteristic relation, the greater lower approximation and smaller upper approximation could be obtained by characteristic consistent blockapproach.