Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...

Rough set theory uses the concept of upper and lower approximations to encapsulate inherent inconsistency in real-world objects. Information multisystems are represented using multisets instead of crisp sets. This paper begins with an overview of recent works on multisets and rough sets. Rough multiset is introduced in terms of lower and upper approximations and explores related properties. The...

The shortest path problem (SPP) is one of the most important combinatorial optimization problems in graph theory due to its various applications. The uncertainty existing in the real world problems makes it difficult to determine the arc lengths exactly. The fuzzy set is one of the popular tools to represent and handle uncertainty in information due to incompleteness or inexactness. In most cas...

In the paper, we present a integrated approach combined Rough Set theory and SVM algorithm. The approach udl be divided into two steps. The fust step is classified roughlv with Rough Set, rule should be induced in this step by infonilation system. The second step should ht: classified precisely based on SVM Algorithn~, in this step we present two new fiuidrunental principles to help us select b...

Although computers have come a long way since their invention, they are basically able to handle only crisp values at the hardware level. Unfortunately, the world we llve in consists of problems which fail to fall into this category, i.e. uncertainty is all too common. In this work, we look at a problem which involves uncertainty. To be specific we deal with attributes which are fuzzy sets. Und...

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...

One of the main concepts in grey system theory is how systems should be controlled under incomplete or lack of information situation. Grey number denoting an uncertain value is described in real interval from this concept. In this paper, we introduce the real formal concept analysis based on grey-rough set theory by using grey numbers, instead of binary values. We propose, to extend the notion ...

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