Algebra and topology for dominance-based rough set approach

Salvatore Greco, B. Matarazzo, R. Slowinski

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


Dominance-based rough sets generalize classical indiscernibility based rough sets by handling ordered value sets of attributes and monotonic relationships between values of condition and decision attributes. Dominance based rough sets permit, in particular, a natural hybridization of fuzziness and roughness, which are complementary concepts of vagueness. In this article, we characterize the Dominance-based Rough Set Approach (DRSA) from the point of view of its mathematical foundations, taking into account algebraic structures and topological properties. We present algebraic representations of DRSA in terms of generalizations of several algebras already used to represent the classical rough set approach, namely: bipolar de Morgan Brouwer-Zadeh distributive lattice, bipolar Nelson algebra, bipolar Heyting algebra, bipolar double Stone algebra, bipolar three-valued Łukasiewicz algebra, bipolar Wajsberg algebra.We also present an algebraic model for ordinal classification. With respect to topological properties, using the concept of a bitopological space, we extend on DRSA the results obtained for classical rough sets.
Original languageEnglish
Title of host publicationAdvances in intelligent information systems
EditorsZ. Ras, L. Tsay
Place of PublicationBerlin
Number of pages36
ISBN (Print)9783642051821
Publication statusPublished - 2010

Publication series

NameStudies in computational intelligence
ISSN (Print)1860-949X


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