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Information granulation and rough set approximation

Y. Y. Yao
2000 International Journal of Intelligent Systems  
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

Ahmad A. Allam, Mohammad Y. Bakeir, El-Sayed A. Abo-Tabl
2012 Journal of the Egyptian Mathematical Society  
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

Pei Wang, Qingguo Li
2017 Open Mathematics  
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

Yiyu Yao, Belur V. Dasarathy
2000 Data Mining and Knowledge Discovery: Theory, Tools, and Technology II  
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

Y.Y. Yao
1998 Information Sciences  
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

Guilong Liu, Ying Sai
2009 International Journal of Approximate Reasoning  
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

Shoubin Sun, Lingqiang Li, Kai Hu
2019 Mathematical Problems in Engineering  
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

Pankaj Kumar Singh, Surabhi Tiwari
2019 Hacettepe Journal of Mathematics and Statistics  
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

Jue Ma, Mohammed Atef, Ahmed Mostafa Khalil, Nasruddin Hassan, Gui-Xiu Chen
2020 IEEE Access  
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]

Yanfang Liu, William Zhu
2012 arXiv   pre-print
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

Zhi Kong, Liqun Gao, Qingli Wang, Lifu Wang, Yang Li
2008 2008 American Control Conference  
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

En-Bing Lin, Yu-Ru Syau
2014 International Journal of Machine Learning and Computing  
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]

Yanfang Liu, William Zhu
2012 arXiv   pre-print
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

Radwan Abu-Gdairi, Mostafa A. El-Gayar, Mostafa K. El-Bably, Kamel K. Fleifel
2021 Mathematics  
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

Yanfang Liu, William Zhu
2012 Journal of Applied Mathematics  
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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