Different types of search algorithms for rough sets

Based on the available information in many cases it can happen that two objects cannot be distinguished. If a set of data is given and in this set two objects have the same attribute values, then these two objects are called indiscernible. This indiscernibility has an effect on the membership relation, because in some cases it makes our judgment uncertain about a given object. The uncertainty appears because if something about an object is needed to be stated, then all the objects that are indiscernible from the given object must be taken into consideration. The indiscernibility relation is an equivalence relation which represents background knowledge embedded in an information system. In a Pawlakian system this relation is used in set approximation. Correlation clustering is a clustering technique which generates a partition using search algorithms. In the authors’ previous research the possible usage of the correlation clustering in rough set theory was investigated. In this paper the authors show how different types of search algorithms affect the set approximation

Dealing with uncertainty: A rough-set-based approach with the background of classical logic

The representative-based approximation has been widely studied in rough set theory. Hence, rough set approximations can be defined by the system of representatives, which plays a crucial role in set approximation. In the authors’ previous research a possible use of the similarity-based rough set in first-order logic was investigated. Now our focus has changed to representative-based approximation systems. In this article, the authors show a logical system relying on representative-based set approximation. In our approach, a three-valued partial logic system is introduced. Based on the properties of the approximation space, our theorems prove that in some cases, there exists an efficient way to evaluate the first-order formulae

Dealing with uncertainty: A rough-set-based approach with the background of classical logic

The representative-based approximation has been widely studied in rough set theory. Hence, rough set approximations can be defined by the system of representatives, which plays a crucial role in set approximation. In the authors’ previous research a possible use of the similarity-based rough set in first-order logic was investigated. Now our focus has changed to representative-based approximation systems. In this article, the authors show a logical system relying on representative-based set approximation. In our approach, a three-valued partial logic system is introduced. Based on the properties of the approximation space, our theorems prove that in some cases, there exists an efficient way to evaluate the first-order formulae