Monotonic Variable Consistency Rough Set Approaches

  • Authors:

  • Jerzy Błaszczyński;Salvatore Greco;Roman Słowiński;Marcin Szelg

  • Affiliations:

  • Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland;Faculty of Economics, University of Catania, Corso Italia, 55, 95129 Catania, Italy;Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland and Systems Research Institute, Polish Academy of Sciences, 01-447 Warsaw, Poland;Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2009

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Abstract

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.