Computing Approximations of Dominance-Based Rough Sets by Bit-Vector Encodings

This paper introduces a mechanism for computing approximations of Dominance-Based Rough Sets (DBRS) by bit-vector encodings. DBRS was introduced by Greco et al. as an extension of Pawlak's classical rough sets theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes. Our formulation of dominance-based approximation spaces is based on the concept of indexed blocks introduced by Chan and Tzeng. Indexed blocks are sets of objects indexed by pairs of decision values where approximations of sets of decision classes are defined in terms of exclusive neighborhoods of indexed blocks. In this work, we introduced an algorithm for updating indexed blocks incrementally, and we show that the computing of dominance-based approximations can be accomplished more intuitively and efficiently by encoding indexed blocks as bit-vectors. In addition, bit-vector encodings can simplify the definitions of lower and upper approximations greatly. Examples are given to illustrate presented concepts.