This paper proposes new deenitions of lower and upper approximations which are basic concepts of rough set theory. These deenitions follow naturally from the concepts of ambiguity and deenability introduced in this paper. The new deenitions are compared to the classical deenitions and are shown to be more general in the sense that they are the only ones which can be used for any type of indisce...

The roughness of a rough set arises from the existence of its boundary region. In such a boundary region, each object has a non-zero rough membership degree. When an object’s rough membership degree is regarded as its fuzzy membership degree, a rough set can induce a fuzzy set. This relationship motivates us to assert that there may exist some inherent relations between the roughness of a rough...

This paper concerns some aspects of rough set based data analysis. In particular rough set look on Bayes’ formula leads to new methodology of reasoning from data and shows interesting relationship between Bayes’ theorem, rough sets and flow graphs. Three methods of flow graphs application in drawing conclusions from data are presented and examined. MOTTO: “It is a capital mistake to theorise be...

Article history: Received 18 September 2012 Received in revised form 13 July 2013 Accepted 1 September 2013 Available online 20 September 2013

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)...