Affiliations: Department of Computer Science, University of Akron
Akron, OH, 44325-4003, USA and Department of Information Communications, Kainan
University No. 1 Kainan Road, Luchu, Taoyuan County 338, Taiwan.
E-mail: chan@uakron.edu | Department of Business and Entrepreneurial
Administration, Kainan University No. 1 Kainan Road, Luchu, Taoyuan County 338,
Taiwan and Institute of Management of Technology, National Chiao Tung
University 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan. E-mail: ghtzeng@mail.knu.edu.tw;
ghtzeng@cc.nctu.edu.tw
Abstract: Dominance-based rough set introduced by Greco et al. is an extension
of Pawlak¡¯s classical rough set theory by using dominance relations
in place of equivalence relations for approximating sets of preference ordered
decision classes satisfying upward and downward union properties. This paper
introduces the concept of indexed blocks for representing dominance-based
approximation spaces. Indexed blocks are sets of objects indexed by pairs of
decision values. In our study, inconsistent information is represented by
exclusive neighborhoods of indexed blocks. They are used to define
approximations of decision classes. It turns out that a set of indexed blocks
with exclusive neighborhoods forms a partition on the universe of objects.
Sequential rules for updating indexed blocks incrementally are considered and
illustrated with examples.
