We address in principle the notion of a boundary and we propose a version of mereology better adapted to rough set theory than the original version. We discuss the motivation and differences between the original and proposed now versions of rough mereology and we show that the Pawlak notion of a boundary in rough set theory is a particular case of the more general notion of a boundary in the ro...

The concept of approximation is one of the most fundamental in rough set theory. In this work we examine this basic notion as well as its extensions and modifications. The goal is to construct a parameterized approximation mechanism making it possible to develop multi–stage multi–level concept hierarchies that are capable of maintaining acceptable level of imprecision from input to output.

We investigate the operators associated with approximations in the rough set theory introduced by Pawlak in his [Paw82,MP84] and extensively studied by the Rough Set community [RS06]. We use universal algebra techniques to establish a natural characterization of operators associated with rough sets.

We prove the recent result of Liu and Zhu [2] and discuss some consequences of that and related facts for the development of rough set theory.

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

In this paper, we introduce the new definition of rough membership function using continues and discuss several concepts properties continuous set value functions as results on . Moreover, extend to topology spaces by substituted an equivalence class prove some theorems certain types more general fundamental generalized sets. Our result concept valued theory.

In this paper, we introduce soft sets over 2 where 2 is the power set of the universe U , propose some operations on soft sets over 2 and investigate some types of soft sets over 2 such as keeping intersection and keeping union. We obtain lattice and topological structures of soft sets over 2 . We consider soft rough approximations and soft rough sets, and obtain structures of soft rough sets. ...

Article history: Received 13 January 2012 Received in revised form 10 May 2012 Accepted 17 June 2012 Available online 29 June 2012

Article history: Received 23 October 2011 Received in revised form 20 February 2012 Accepted 20 February 2012 Available online 9 March 2012

Article history: Received 16 November 2010 Received in revised form 26 November 2011 Accepted 2 December 2011 Available online 9 December 2011