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

Finding the representative in a cluster using correlation clustering

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General set approximation and its logical applications *

Abstract To approximate sets a number of theories have appeared for the last decades. Starting up from some general theoretical pre-conditions the authors give a set of minimum requirements for the lower and upper approximations and define general partial approximation spaces. Then, these spaces are applied in logical investigations. The main question is what happens in the semantics of the first-order logic when the approximations of sets as semantic values of predicate parameters are used instead of sets as their total interpretations. On the basis of defined partial interpretations, logical laws relying on the defined general set-theoretical framework of set approximation are investigated

Finding the representative in a cluster using correlation clustering

Correlation clustering is a widely used technique in data mining. The clusters contain objects, which are typically similar to each other and different from objects from other groups. It can be an interesting task to find the member, which is the most similar to the others for each group. These objects can be called representatives. In this paper, a possible way to find these representatives are shown and software to test the method is also provided

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

Boundaries of membrane in P systems relying on multiset approximation spaces in language R

Membrane computing is an area within computer science which aims to develop a new computational model through the study of the characteristics of biological cells. It is a distributed and parallel computing model. Communication between regions through membranes, as well as membrane system and its environment, plays an important role in the process. Combination of P system with multiset approximation space leads to the abstract concept of ‘to be close enough to a membrane’. The designated goal is to perform calculations in this two-fold system by the help of language R. Some packages can perform calculations with multisets in R (such as ‘sets’ package), but they are more closely linked to fuzzy systems. In this paper a new program library in language R is initiated which had been created to encourage some fundamental calculations in membrane systems combined with multiset approximation spaces. Data structures and functions are illustrated by examples. Keywords: multiset approximation spaces, membrane computing, R languag