The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent’s view about crisp and non crisp objects over a set of objects has a rough evolution. In this research the nature of the problem is examined from number-theoretic and combinatorial perspectives under very few assumpt...

In Pawlak rough sets, the structure of the definable set families is simple and clear, but in generalizing rough sets, the structure of the definable set families is a bit more complex. There has been much research work focusing on this topic. However, as a fundamental issue in relation based rough sets, under what condition two relations induce the same definable set family has not been discus...

In this article we consider rough differential equations (RDEs) driven by non-geometric rough paths, using the concept of branched rough paths introduced in [Gub10]. We first show that branched rough paths can equivalently be defined as γ-Hölder continuous paths in some Lie group, akin to geometric rough paths. We then show that every branched rough path can be encoded in a geometric rough path...

Article history: Received 1 December 2012 Received in revised form 5 October 2013 Accepted 9 February 2014 Available online 20 February 2014

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...