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Information granulation and rough set approximation
2000
International Journal of Intelligent Systems
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A multi-level granulation, characterized by a special class of equivalence relations, leads to a more general approximation structure. The notion of neighborhood systems is also explored. ...
The granulation structures used by standard rough set theory and the corresponding approximation structures are reviewed. ...
More precisely, the neighborhood system of x is given by NS(x) = {(x) R }. If R is a reflexive relation, one obtains a reflexive neighborhood system which is the covering U/R. ...
doi:10.1002/1098-111x(200101)16:1<87::aid-int7>3.0.co;2-s
fatcat:owa3ehk5ubbppjyrhg7upi4ehm
Approximation Space on Novel Granulations
2012
Journal of the Egyptian Mathematical Society
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The granulation structures used by rough set theory, neighborhood systems and topological space and the corresponding approximation structures, are studied. ...
Acknowledgment The authors greatly appreciate the valuable comments and additions of Prof. Dr. A. Skowron. ...
There is no additional requirements on neighborhood systems. Neighborhood systems can be used to describe more general types of relationships between elements of a universe [5, 16] . ...
doi:10.1016/j.joems.2012.08.001
fatcat:hq5cqxfj4jdsxcjmbswpujuz5q
The characterizations of upper approximation operators based on special coverings
2017
Open Mathematics
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Zhang et al. discussed the relationships between generalized rough sets based on covering and reflexive neighborhood system [49] and proposed the operator apr S . ...
can be treated as the generalized rough sets based on neighborhood systems. ...
doi:10.1515/math-2017-0015
fatcat:zcl3hurycbesfkp2ze6hhh5q7m
Information tables with neighborhood semantics
2000
Data Mining and Knowledge Discovery: Theory, Tools, and Technology II
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The neighborhood systems represent the semantics relationships between, and knowledge about, attribute values. ...
Information tables provide a convenient and useful tool for representing a set of objects using a group of attributes. This notion is enriched by introducing neighborhood systems on attribute values. ...
One of the issues in the theory of rough sets deals with information granulation according to the knowledge provided by an information table. 16, 17 Relationships between objects are defined based on ...
doi:10.1117/12.381723
dblp:conf/dmkdttt/Yao00
fatcat:ktmpmyu64bbwxjusvzwrgvujxe
Relational interpretations of neighborhood operators and rough set approximation operators
1998
Information Sciences
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This paper presents a framework for the formulation, interpretation, and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations. ...
A special class of neighborhood systems, called 1-neighborhood systems, is introduced. Three extensions of Pawlak approximation operators are analyzed. ...
ACKNOWLEDGEMENTS The author is grateful for discussion with and suggestions from T.Y. Lin on neighborhood systems. ...
doi:10.1016/s0020-0255(98)10006-3
fatcat:s6lfth4j5rfmxpy7en6rkukapm
A comparison of two types of rough sets induced by coverings
2009
International Journal of Approximate Reasoning
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In this paper, we compare the covering-based rough sets defined by Zhu with ones defined by Xu and Zhang. We further explore the properties and structures of these types of rough set models. ...
Rough set theory is an important technique in knowledge discovery in databases. In covering-based rough sets, many types of rough set models were established in recent years. ...
Acknowledgement This work is partially supported by the Key Project of the Chinese Ministry of Education (No. 108133) and the Project of the Beijing Language and Culture University. ...
doi:10.1016/j.ijar.2008.11.001
fatcat:q2yacc3g25gb3cljex26ej346u
A New Approach to Rough Set Based on Remote Neighborhood Systems
2019
Mathematical Problems in Engineering
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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. ...
Now, neighborhood systems have been applied in the study of rough set by many researches. ...
Wang [48] , Syau [49] , and Zhang [50] investigated relationships between reflexive generalized neighborhood system-based rough sets and other rough sets. ...
doi:10.1155/2019/8712010
fatcat:rmqustm66fhcnhcwrtbou5ebgi
Topological structures in rough set theory: A survey
2019
Hacettepe Journal of Mathematics and Statistics
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The topological notions are closely related to the notions and results of rough set theory, so the conjoint study of rough set theory and topology becomes essential. ...
Rough set theory provides a mathematical tool to study vague, imprecise, inconsistent and uncertain knowledge. ...
One of the authors, Pankaj Kumar Singh, gratefully acknowledge the University Grants Commission, New Delhi, India, for providing Senior Research Fellowship, student ID. 201516NETJRF-10459-1, to pursue ...
doi:10.15672/hujms.662711
fatcat:zgorr646bzemfnsndxy5tsddru
Novel models of fuzzy rough coverings based on fuzzy α-neighborhood and its application to decision-making
2020
IEEE Access
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Many scholars work on this theory and applied it to various fields [3] - [12] . Covering based rough sets are arguably one of the most studied generalizations of rough sets. ...
Sections 3 describes the complementary fuzzy α-neighborhoods with reflexively and gives three new kinds of a fuzzy rough set covering based on the fuzzy α-neighborhood operator. ...
doi:10.1109/access.2020.3044213
fatcat:kjpeqdhfube6foapyxggwgeqkm
Relation matroid and its relationship with generalized rough set based on relation
[article]
2012
arXiv
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Recently, the relationship between matroids and generalized rough sets based on relations has been studied from the viewpoint of linear independence of matrices. ...
Moreover, the relationships between the upper approximation operator in generalized rough sets and the closure operator in matroids are investigated. ...
In this paper, we build the connection between generalized rough sets based on relations and matroids through the predecessor and successor neighborhoods. ...
arXiv:1209.5456v2
fatcat:cpat6uqsrngenpczqg36hlskwm
Uncertainty measurement based on general relation
2008
2008 American Control Conference
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In incomplete information system, new information entropy and conditional entropy based on general relation are proposed. ...
Then the conclusion that the conditional entropy based on general relation decreases monotonously as the neighbor operators become finer is obtained. ...
Huang et al. discussed rough entropy based on generalized covering [10] . He proposed a tolerance fuzzy-rough sets based on fuzzy tolerance relation. ...
doi:10.1109/acc.2008.4587060
dblp:conf/amcc/KongGWWL08
fatcat:orbogltmp5d2blwlkrxjbgktdm
Comparisons between Rough Set Based and Computational Applications in Data Mining
2014
International Journal of Machine Learning and Computing
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Index Terms-Information system, rough set theory, wavelet, denoising. En-Bing Lin received his Ph. D. in mathematics from Johns Hopkins University. ...
Rough set theory and wavelet theory are totally different areas of research in mathematics. ...
Total Pure Reflexive Neighborhood Systems As it is known that a covering C of U can be regarded as a special form of neighborhood system which we call a covering neighborhood system. ...
doi:10.7763/ijmlc.2014.v4.432
fatcat:vgmshs5hybh6tn2abgo6yityza
Matroidal structure of rough sets based on serial and transitive relations
[article]
2012
arXiv
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The relationships between the upper approximation operators of rough sets based on relations and the closure operators of matroids in the above two constructions are studied. ...
In order to take advantages of both rough sets and matroids, in this paper we propose a matroidal structure of rough sets based on a serial and transitive relation on a universe. ...
In order to meet many real applications, the rough sets have been extended to generalized rough sets based on relations [8, 13, 19, 21, 27, 28] , and covering-based rough sets [2, 32, 33] . ...
arXiv:1209.4976v2
fatcat:cr6olodvlbcffdek2qvb2drvaa
Two Different Views for Generalized Rough Sets with Applications
2021
Mathematics
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Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak's rough sets and some of their extensions as confirming in the present paper. ...
The proposed methods depend basically on a new neighborhood (called basic-neighborhood). ...
Besides, introducing and studying a novel approach to generalize rough sets of multi-information systems based on a finite number of binary relations. ...
doi:10.3390/math9182275
fatcat:gsor6h6wgvgp5nshr7dlv4cmjm
Matroidal Structure of Rough Sets Based on Serial and Transitive Relations
2012
Journal of Applied Mathematics
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The relationships between the upper approximation operators of rough sets based on relations and the closure operators of matroids in the above two constructions are studied. ...
In order to take advantages of both rough sets and matroids, in this paper we propose a matroidal structure of rough sets based on a serial and transitive relation on a universe. ...
2012J01294, and the Science and Technology Key Project of Fujian province, China, under Grant no. 2012H0043. ...
doi:10.1155/2012/429737
fatcat:cevi6iyonrhhbpbbqqhnes6aea
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