scholarly journals Use of Some Topological Concepts in the Study of Some COVID−19 Symptoms

2020 ◽  
Vol 13 (4) ◽  
pp. 852-860
Author(s):  
Samirah ALZahrani
Keyword(s):  
Information System ◽  
Similarity Relation ◽  
Topological Spaces ◽  
Upper Approximation

We apply some topological concepts on topological spaces generated from both equality and similarity relation for our information system, which examine 10 hypothetical patients who suffer from some COVID−19 symptoms. This is based on the degree of accuracy generated from the cardinality of the lower and upper approximation. This method is clarified by application.

On Quasi Discrete Topological Spaces in Information Systems

2012 ◽  
Vol 3 (2) ◽  
pp. 38-52 ◽  
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.

scholarly journals A New Approach to Rough Set Based on Remote Neighborhood Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Shoubin Sun ◽  
Lingqiang Li ◽  
Kai Hu
Keyword(s):  
Rough Set ◽  
Topological Spaces ◽  
New Approach ◽  
Upper Approximation ◽  
Basic Properties ◽  
Approximation Operators ◽  
Dual Notion

The notion of neighborhood systems is abstracted from the geometric notion of “near”, and it is primitive in the theory of topological spaces. Now, neighborhood systems have been applied in the study of rough set by many researches. The notion of remote neighborhood systems is initial in the theory of topological molecular lattice, and it is abstracted from the geometric notion of “remote”. Therefore, the notion of remote neighborhood systems can be considered as the dual notion of neighborhood systems. In this paper, we develop a theory of rough set based on remote neighborhood systems. Precisely, we construct a pair of lower and upper approximation operators and discuss their basic properties. Furthermore, we use a set of axioms to describe the lower and upper approximation operators constructed from remote neighborhood systems.

Topological structures of a type of granule based covering rough sets

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3129-3141
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Spaces ◽  
Topological Properties ◽  
Binary Relations ◽  
Upper Approximation ◽  
Approximation Operators

Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindel?f property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

Research on Knowledge Change Rate-Based Attribute Importance Measure Method

2015 ◽  
Vol 713-715 ◽  
pp. 628-632
Author(s):  
Fa Chao Li ◽  
Qi Hui Hu
Keyword(s):  
Information System ◽  
Information Fusion ◽  
Comprehensive Evaluation ◽  
Importance Measure ◽  
Fuzzy Decision ◽  
Attribute Importance ◽  
Change Rate ◽  
Broad Application ◽  
Upper Approximation ◽  
Knowledge Change

For the problem of attribute importance measure, basing on the decision information system, and according to the characteristics and shortcomings of the existing measure modes, we discussed the associated features between the lower and upper approximation of decision classes and the knowledge in system. Then, we constructed an attribute importance measure mode based on the knowledge change rate, and analyzed the features of the constructing measure mode from different angles. Theoretical analysis and example calculation show that the established mode is a supplement and perfect for the existing measure modes, and it not only can effectively use the existed information to reveal the associated features among each attribute, but also have a good structural characteristic and strong interpretability. It has a broad application prospect among information fusion, fuzzy decision, comprehensive evaluation and so on.

On Characterization of Relation Based Rough Set Algebras

2010 ◽  
pp. 69-91
Author(s):  
Wei-Zhi Wu ◽  
Wen-Xiu Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Axiomatic Approach ◽  
Topological Spaces ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Topological Spaces

Rough set theory is one of the most advanced areas popularizing GrC. The basic notions in rough set theory are the lower and upper approximation operators. A rough set algebra is a set algebra with two additional lower and upper approximation operators. In this chapter, we analyze relation based rough set algebras in both crisp and fuzzy environments. We first review the constructive definitions of generalized crisp rough approximation operators, rough fuzzy approximation operators, and fuzzy rough approximation operators. We then present the essential properties of the corresponding lower and upper approximation operators. We also characterize the approximation operators by using the axiomatic approach. Finally, the connection between fuzzy rough set algebras and fuzzy topological spaces is established.

scholarly journals Properties of nano Δ* open sets

2021 ◽  
Vol 2070 (1) ◽  
pp. 012100
Author(s):  
K Meena ◽  
J Dhivya ◽  
R Kalaiselvi
Keyword(s):  
Equivalence Relation ◽  
Topological Spaces ◽  
Lower Approximation ◽  
Upper Approximation

Abstract This article aims at introducing nano Δ* open sets in Nano Topological Spaces (NTS). The NTS are nothing but the spaces created in terms of equivalence relation which is derived from lower approximation, upper approximation and boundaries of a subset of a universal set. An elaborate study on various properties and characterizations of Nano Δ* open sets in relation with nano δ open sets and nano δg-kemel operator are explained in this article.

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