Rough Sets Model Based Based On Dominance Relation

Worldwide,there has been a rapid growth in interest in rough set theory and its applications in recent years. There are lots of high一quality articles on rough sets that have been published in a variety of international journals. Rough Set Theory is a new mathematical approach to uncertain and vague data analysis. It is,no doubt,one of the most challenging areas of modern computer applications. Rough set theory has led to many interesting applications and extensions. It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences,especially in research areas such as machine learning,intelligent systems,pattern recognition,knowledge discovery,decision analysis and expert systems.In this paper, after discussing classical rough set theory based on Indiscernibility Relation and its reduction algorithms, the extended model of rough set theory for based on dominance relation is studied, including a reduction algorithm related to this model. It turns out that the reduction algorithm leaves something to be desired. To show this, a counter example is thus presented to make clear the faults of this algorithm. To solve this problem, a new definition of dominance variable precision discernibility matrix is given by taking advantage of the unique characteristic of the extended model. The corresponding core and reduction algorithms are accordingly presented and proved correct by example.