Research On Rough Set Model Under Partial Order Relation And Its Application

Many disordered phenomena usually include ordered talcs in the confused andcomplicated nature, as things' development has scqucncc, extension of concept hasmagnitude. For people, order is a kind of beauty, so that they found the theory oforder relation for research in the area of mathematics. Now, the perfecter part ofstudying order relation theory is partial order relation. For one thing, as a kind ofclassical order, it grows with scholars' attention. For the other thing, people researchactively the phenomena of partial order relation from nature, however it is difficultto study bccause of incomplete partial information and so on.In 1982, Rough Set theory proposed by the professor Z.Pawlak of Polandscientist. As one of mathematical tool for characterizing the vague and uncertainproblems, it can deal efficiently with all kinds of incomplete information, likeimprecision, inconsistency, insufficiency. It can also find underlying knowledge anddiscover underlying rules. Compared with the traditional method of uncertain dataprocesses, the most significant feature of Rough Set theory is that it doesn't need anyexperience information of data. Under the original data, it bases on equivalencerelation to directly classify universe, and use the concept of upper and lowerapproximation to describe objects. Now, it was been widely used in the areas ofmachine learning, knowledge discovery, decision analysis, finance data analysis,artificial intelligence, data mining, pattern recognition, etc.There is a discovery with attention on the application research of Rough Settheory. On one hand, the start of Rough Set is classifying objects of universe, itrepresents the idea of information granulation in Granular Computing. On the otherhand, it usually based on a training sample set when it characters incompleteinformation, so it is required to follow disciplinarian of statistics as selectingsamples, and is possible to make combination between Bayes method of probabilitystatistics and Rough Set theory.Based on the background, this paper combines the idea of Granular Computingwith Bayes method to extend the classical Rough Set theory, and makes the new rough set model under partial order relation. The structure of new model: foundation—partial order relation, core theory—Rough Set theory, guiding idea—GranularComputing, applying method—Bayes theory. Therefore, the paper introduces theRough Set theory as the core of new model, narrates its researching status and basicconcept firstly. Secondly, it represents the studying status of Partial Order Relation,Granular Computing and Bayes theory respectively, then gives relation betweenthose theories and Rough Set theory. At the end of the paper, it discusses basicconcept, model structuring and analysis of examples under the new model.