Change your habit to hang or waste the time to only chat with your friends. It is done by your everyday, don't you feel bored? Now, we will show you the new habit that, actually it's a very old habit to do that can make your life more qualified. When feeling bored of always chatting with your friends all free time, you can find the book enPDF rough sets and intelligent systems professor zdzisla...

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.

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.