Incremental Approach Of Variable Precision Rough Set Based On Extended Dominance Relations

Dominance relation-based rough sets(DRS) extend the equivalence relations in classical rough set theory, and therefore can deal with preference-ordered information. In the definition of dominance relation, one object x is said to dominate another object y, only when all the attribute values of x dominate those of y. This requirement of dominance relation can hardly be satisfied when there are many attributes contained in given information systems. To address this problem, we introduce a parameter in the original definition and then defined a type of extended dominance relations, in which one object is said to dominate another object as long as the majority of the attribute values of this object are superior to those of another object. In addition, we combine the extended dominance relation with the Variable Precision Rough Set model(VPRS) which allows a certain degree of error classification rate, and then form the extended dominance relation-based VPRS model. Based on this type of rough set model, finally, our most important work in this thesis is considering dynamic information systems and developing efficient updating method for computation of approximation sets. Notice that the collected data in real problems are often updated from time to time, and the re-computing of approximation sets is very time costly using traditional method. In this thesis, we have proposed the updating method to fast compute approximation sets of VPRS model based on extended dominance relations. The updating principles according to different conditions are given, along with detailed theoretical proofs and the corresponding algorithms. We use a numerical example to show the effectiveness of the concept of extended dominance relation; and use the experimental results on 11 UCI data sets to show the advantages of the proposed updating method in running time, scalability and parameter sensitivity.