In this article, we present some extensions of the rough set approach and we outline a challenge for the rough set based research. 2006 Elsevier Inc. All rights reserved.

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The articles [2], [3], [1], [4], and [5] provide the terminology and notation for this paper. For simplicity, we adopt the following rules: G denotes a group, A, B denote non empty subsets of G, N , H, H1, H2 denote subgroups of G, and x, a, b denote elements of G. Next we state a number of propositions: (1) For every normal subgroup N of G and for all elements x1, x2 of G holds x1 ·N · (x2 ·N)...

Article history: Available online 23 March 2013

We prove that the operators in a class of rough fractional integral operators and the related maximal operators are bounded from L p (v p) to L q (u q) with weight pair (u,v).

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.