Topologies on                                                                            Z                                  n                                                 that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

Download Full-text

On Quasi Discrete Topological Spaces in Information Systems

International Journal of Artificial Life Research ◽

10.4018/jalr.2012040104 ◽

2012 ◽

Vol 3 (2) ◽

pp. 38-52 ◽

Cited By ~ 1

Author(s):

Tutut Herawan

Keyword(s):

Information System ◽

Information Systems ◽

Topological Space ◽

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Topological Spaces ◽

Discrete Topology

This paper presents an alternative way for constructing a topological space in an information system. Rough set theory for reasoning about data in information systems is used to construct the topology. Using the concept of an indiscernibility relation in rough set theory, it is shown that the topology constructed is a quasi-discrete topology. Furthermore, the dependency of attributes is applied for defining finer topology and further characterizing the roughness property of a set. Meanwhile, the notions of base and sub-base of the topology are applied to find attributes reduction and degree of rough membership, respectively.

Download Full-text

The Position of Rough Set in Soft Set

International Journal of Applied Metaheuristic Computing ◽

10.4018/jamc.2012070103 ◽

2012 ◽

Vol 3 (3) ◽

pp. 33-48

Author(s):

Tutut Herawan

Keyword(s):

Topological Space ◽

Set Theory ◽

Rough Set ◽

Equivalence Relation ◽

Rough Set Theory ◽

Soft Set ◽

General Topology ◽

Discrete Topology ◽

Special Case

In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete topology using indiscernibility (equivalence) relation in rough set theory is described. Secondly, the paper describes that a “general” topology is a special case of soft set. Hence, it is concluded that every rough set can be considered as a soft set.

Download Full-text

An Approach Based on Generic Label Correcting Algorithm for Supply Chain Modeling

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.411-414.2085 ◽

2013 ◽

Vol 411-414 ◽

pp. 2085-2088

Author(s):

Xiao Qing Geng ◽

Yu Wang

Keyword(s):

Supply Chain ◽

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Decision Rules ◽

Data Space ◽

Different Types ◽

Supply Chain Modeling

In this paper, the rough set theory is applied to reduce the complexity of data space and to induct decision rules. It proposes the generic label correcting (GLC) algorithm incorporated with the decision rules to solve supply chain modeling problems. This proposed approach is agile because by combining various operators and comparators, different types of paths in the reduced networks can be solved with one algorithm.

Download Full-text

A comparison of two types of rough approximations based on Nj-neighborhoods

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210272 ◽

2021 ◽

pp. 1-14

Author(s):

Tareq M. Al-Shami ◽

Ibtesam Alshammari ◽

Mohammed E. El-Shafei

Keyword(s):

Topological Space ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Mathematical Tool ◽

Approximation Spaces ◽

Uncertain Knowledge ◽

Accuracy Measures

In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of Nj-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.

Download Full-text

Bi-covering rough sets

Filomat ◽

10.2298/fil2107361a ◽

2021 ◽

Vol 35 (7) ◽

pp. 2361-2369

Author(s):

Mohamed Abo-Elhamayel

Keyword(s):

Data Mining ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Inclusion Relation ◽

Different Types ◽

Paper Construct ◽

Lower And Upper Approximations ◽

The Universe

Rough set theory is a useful tool for knowledge discovery and data mining. Covering-based rough sets are important generalizations of the classical rough sets. Recently, the concept of the neighborhood has been applied to define different types of covering rough sets. In this paper, based on the notion of bi-neighborhood, four types of bi-neighborhoods related bi-covering rough sets were defined with their properties being discussed. We first show some basic properties of the introduced bi-neighborhoods. We then explore the relationships between the considered bi-covering rough sets and investigate the properties of them. Also, we show that new notions may be viewed as a generalization of the previous studies covering rough sets. Finally, figures are presented to show that the collection of all lower and upper approximations (bi-neighborhoods of all elements in the universe) introduced in this paper construct a lattice in terms of the inclusion relation ?.

Download Full-text

The Role of Spatial Context Information in the Generalization of Geographic Information: Using Reducts to Indicate Relevant Attributes

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi9010037 ◽

2020 ◽

Vol 9 (1) ◽

pp. 37

Author(s):

Anna Fiedukowicz

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Geographic Information ◽

Spatial Context ◽

Common Elements ◽

Fuzzy Rough Set ◽

Different Types ◽

Selection Of

Generalization of geographic information enables cognition and understanding not only of objects and phenomena located in space but also the relations and processes between them. The automation of this process requires formalization of cartographic knowledge, including information on the spatial context of objects. However, the question remains which information is crucial to the decisions regarding the generalization (in this paper: selection) of objects. The article presents and compares the usability of three methods based on rough set theories (rough set theory, dominance-based rough set theory, fuzzy rough set theory) that facilitate the designation of the attributes relevant to a decision. The methods are using different types (levels of measurements) of attributes. The author determines reducts and their cores (common elements) that show the relevance of attributes stemming from the spatial context. The fuzzy rough set theory method proved the least useful, whereas the rough set theory and dominance-based rough set theory methods seem to be recommendable (depending on the governing level of measurement).

Download Full-text

Different Types of Search Algorithms for Rough Sets

Acta Cybernetica ◽

10.14232/actacyb.24.1.2019.8 ◽

2019 ◽

Vol 24 (1) ◽

pp. 105-120 ◽

Cited By ~ 1

Author(s):

Dávid Nagy ◽

Tamás Mihálydeák ◽

László Aszalos

Keyword(s):

Information System ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Search Algorithms ◽

Different Types ◽

Set Approximation ◽

Available Information ◽

The Given

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 settwo 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 bestated, then all the objects that are indiscernible from the given object must be taken into consideration. The indiscernibility relation is an equivalencerelation 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. In the authors’ previous research the possible usage of the correlation clusteringin rough set theory was investigated. In this paper the authors show how different types of search algorithms affect the set approximation.

Download Full-text