A New Approach to Establish Variable Consistency Dominance-Based Rough Sets Based on Dominance Matrices

Rough set theory is an effective mathematical tool for dealing with inconsistencies in information systems. Dominance based rough set (DBRS) is an extension to the original rough set, in which the equivalence relation is replaced by a dominance relation. However, in some condition, the lower approximation of DBRS can be emptied by only one "malicious" object. The variable consistency dominance based rough set (VC-DBRS) is proposed to avoid situations like this. The core conception of VC-DBRS is introducing parameters to control the consistency of objects including in lower approximations. There are several kinds of consistency measures have been proposed, but it is difficult to compute them by manual, especially for a large data set. It is necessary to find out an approach to calculate these measures automatically. This paper proposes a new algorithm based on dominance matrices to calculate the rough membership for VC-DBRS, and then presents how to use this measure to get the lower and upper approximation.