Article history: Available online 16 April 2013

The aim of this paper to construct a new rough set structure for a given ideal and to study many of their properties. 2010 AMS Classification: 54A05, 54H99

Article history: Received 1 March 2009 Received in revised form 24 June 2010 Accepted 14 December 2011 Available online 22 December 2011

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