In this paper we review four fuzzy extensions of the socalled tight pair of covering based rough set approximation operators. Furthermore, we propose two new extensions of the tight pair: for the first model, we apply the technique of representation by levels to define the approximation operators, while the second model is an intuitive extension of the crisp operators. For the six models, we st...

Article history: Received 1 March 2011 Received in revised form 26 December 2011 Accepted 29 December 2011 Available online 10 January 2012

Article history: Received 2 February 2016 Received in revised form 13 May 2016 Accepted 27 June 2016 Available online 1 July 2016

The sample variation of indices for approximation of sets in the context of rough sets data analysis is considered. We consider the g and a indices and some other ones – lower and upper bound approximation of decision classes. We derive confidence bounds for these indices as well as a two group comparison procedure. Finally we present procedures to compare the approximation quality of two sets ...

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 ...