Monotonic variable consistency rough set approaches

J. Blaszczynski, Salvatore Greco, R. Slowinski, M. Szelag

    Research output: Contribution to journalArticlepeer-review


    We consider probabilistic rough set approaches based on different versions of the definition of rough approximation of a set. In these versions, consistency measures are used to control assignment of objects to lower and upper approximations. Inspired by some basic properties of rough sets, we find it reasonable to require from these measures several properties of monotonicity. We consider three types of monotonicity properties: monotonicity with respect to the set of attributes, monotonicity with respect to the set of objects, and monotonicity with respect to the dominance relation. We show that consistency measures used so far in the definition of rough approximation lack some of these monotonicity properties. This observation led us to propose new measures within two kinds of rough set approaches: Variable Consistency Indiscernibility-based Rough Set Approaches (VC-IRSA) and Variable Consistency Dominance-based Rough Set Approaches (VC-DRSA). We investigate properties of these approaches and compare them to previously proposed Variable Precision Rough Set (VPRS) model, Rough Bayesian (RB) model, and previous versions of VC-DRSA.
    Original languageEnglish
    Pages (from-to)979-999
    Number of pages21
    JournalInternational Journal of Approximate Reasoning
    Issue number7
    Publication statusPublished - Jul 2009


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