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Generalized fuzzy rough approximation operators based on fuzzy coverings
2008
International Journal of Approximate Reasoning
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Based on a fuzzy covering of a universe of discourse, two pairs of generalized lower and upper fuzzy rough approximation operators are constructed by means of an implicator I and a triangular norm T. ...
Topological properties of the generalized fuzzy rough approximation operators and characterizations of the fuzzy T-partition by the generalized upper fuzzy rough approximation operators are further established ...
Acknowledgement This work was supported by the Hong Kong RGC Earmarked Research Grant CUHK4711/06H. ...
doi:10.1016/j.ijar.2008.01.006
fatcat:qnjcq5lewrh57ofncwdhumoccm
Fuzzy rough approximations of process data
2008
International Journal of Approximate Reasoning
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A new way of determining the upper variable precision fuzzy rough approximation is proposed. ...
As a new aspect, a unified form of expressing the lower and upper crisp approximations is considered. It can be applied to defining new fuzzy rough set models. ...
This is not only due to different forms of fuzzy operators (intersection, union, implication) that can be used in definitions of fuzzy rough approximations. ...
doi:10.1016/j.ijar.2007.03.016
fatcat:5e3jwx5kuzhrlckgq7ewoj4j2u
(𝓘, 𝓣) −Standard Neutrosophic Rough Set And Its Topologies Properties
2016
Zenodo
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In this paper, we defined (𝓘, 𝓣) − standard neutrosophic rough sets based on an implicator 𝓘 and a t-norm 𝓣 on 𝑫∗; lower and upper approximations of standard neutrosophic sets in a standard neutrosophic ...
approximation are defined. ...
[20] constructed ( , ) − intuitionistic fuzzy rough sets determined by an implicator and a t-norm on * . ...
doi:10.5281/zenodo.570892
fatcat:rcodsyjlsrchreu2dnzdjgciii
Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems
2006
Computers and Mathematics with Applications
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Then, based on the approximation operators above, we propose the fuzzy reasoning based on the new fuzzy rough set. ...
By means of the above fuzzy reasoning based on the new fuzzy rough set, for a given premise, we can obtain the fuzzy reasoning consequence expressed by the fuzzy interval constructed by the above two approximations ...
They defined a broad family of fuzzy rough sets, each of which is determined by a triangular norm and an implicator. ...
doi:10.1016/j.camwa.2005.12.003
fatcat:ilts6b53dbfj3fhcwrustezvtq
Survey of Rough and Fuzzy Hybridization
2007
IEEE International Fuzzy Systems conference proceedings
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This paper provides a broad overview of logical and black box approaches to fuzzy and rough hybridization. ...
Since both theories originated in the expert system domain, there are a number of research proposals that combine rough and fuzzy concepts in supervised learning. ...
ACKNOWLEDGMENTS This work is partly funded by the UK EPSRC grant GR/S98603/01. ...
doi:10.1109/fuzzy.2007.4295352
dblp:conf/fuzzIEEE/LingrasJ07
fatcat:vygojaq46zb6zej6q3jtlna5au
Rough set theory for the interval-valued fuzzy information systems
2008
Information Sciences
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Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2-3) (1990) 191-209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets. ...
Secondly several interesting properties of the approximation operators are examined, and the interrelationships of the interval-valued rough fuzzy set models in the classical Pawlak approximation space ...
On the one hand, they define a broad family of fuzzy rough sets by respecting the fuzzy similarity relation that is determined by an implicator and a t-norm. ...
doi:10.1016/j.ins.2007.12.005
fatcat:nf6j2axbbvbutno3q4fnj53pbi
A comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis
2015
Fuzzy sets and systems (Print)
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By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research. ...
Both implicator-conjunctor-based definitions and noise-tolerant models are studied. ...
Acknowledgements Lynn D'eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project ...
doi:10.1016/j.fss.2014.11.018
fatcat:ssi2rn3tazbvdfypgpup45azku
Further Study of MultigranulationT-Fuzzy Rough Sets
2014
The Scientific World Journal
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The optimistic multigranulationT-fuzzy rough set model was established based on multiple granulations underT-fuzzy approximation space by Xu et al., 2012. ...
The full important properties of multigranulationT-fuzzy lower and upper approximation operators are also presented. ...
Acknowledgments This work is supported by Natural Science Foundation of China (no. 61105041) and National Natural Science Foundation of CQ CSTC (no. cstc 2013jcyjA40051). ...
doi:10.1155/2014/927014
pmid:25215336
pmcid:PMC4156983
fatcat:wnzgosukxngupce4fjr5da7lqq
Fuzzy Relation-based Approximation Techniques in Supporting Medical Diagnosis
2017
Journal of Automation, Mobile Robotics & Intelligent Systems
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Assume that is a fuzzy relation on , for instance, a fuzzy similarity relation which re lects similarities of object determined (3) and (4) are fuzzy lower and fuzzy upper rough approximation operators ...
Radzikowska and Kerre [18] showed that these fuzzy connectives are the best ones for fuzzy generalization of traditional (crisp) rough sets. ...
doi:10.14313/jamris_1-2017/3
fatcat:aacgpp6qn5eevn7kn53ek6azky
An axiomatic approach of fuzzy rough sets based on residuated lattices
2009
Computers and Mathematics with Applications
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Rough set theory was developed by Pawlak as a formal tool for approximate reasoning about data. Various fuzzy generalizations of rough approximations have been proposed in the literature. ...
In this paper, we present an operator-oriented characterization of L-fuzzy rough sets, that is, L-fuzzy approximation operators are defined by axioms. ...
In [25] , based on a fuzzy similarity relation, Radzikowska and Kerre define a broad family of the so called (I, T )-fuzzy rough sets which is determined by an implicator I and a triangular norm T . ...
doi:10.1016/j.camwa.2009.03.100
fatcat:g2wal5giy5dhfjnxhptr7u7k5q
Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature
2017
Complexity
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Rough sets models, which have been recently proposed, are developed applying the different fuzzy generalisations. ...
Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies. ...
Zhao and Xiao [131] defined the general type-2 fuzzy-rough sets and discussed the basic properties of lower and upper approximation operators. ...
doi:10.1155/2017/1608147
fatcat:o6khgyofg5g55hwgdj2y6angii
A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators
2014
The Scientific World Journal
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These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed ...
In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. ...
Acknowledgments This work is supported by the National Natural Science ...
doi:10.1155/2014/783940
pmid:25162065
pmcid:PMC4138800
fatcat:vu7bffredzchpbja34oonrvak4
A New Approach to Fuzzy-Rough Nearest Neighbour Classification
[chapter]
2008
Lecture Notes in Computer Science
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In the experimental analysis, we evaluate our approach with both classical fuzzy-rough approximations (based on an implicator and a t-norm), as well as with the recently introduced vaguely quantified rough ...
By contrast to the latter, our method uses the nearest neighbours to construct lower and upper approximations of decision classes, and classifies test instances based on their membership to these approximations ...
The difference between them is in the definition of the approximations: while FRNN-FRS uses "traditional" operations based on a t-norm and an implicator, FRNN-VQRS uses a fuzzy quantifier-based approach ...
doi:10.1007/978-3-540-88425-5_32
fatcat:7qiiqibtonbyzefzuoqhpc7cf4
Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection
2014
International Journal of Approximate Reasoning
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This paper introduces a flexible extension of rough set theory: multi-adjoint fuzzy rough sets, in which a family of adjoint pairs are considered to compute the lower and upper approximations. ...
This new setting increases the number of applications in which rough set theory can be used. ...
This is similar to what happens in fuzzy rough set theory, where a t-norm and fuzzy implication are used in order to extend the classical rough lower and upper approximation operators. ...
doi:10.1016/j.ijar.2013.09.007
fatcat:2dnnbxf7vvgw5ncszue5qfhpr4
Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge
2003
Expert systems
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We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets. ...
Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. ...
Logical operators L-fuzzy set theoretical operations such as complement, intersection and union can be defined by means of suitable generalizations of the well-known connectives from Boolean logic. ...
doi:10.1111/1468-0394.00250
fatcat:d2nphurk3jhwlht7swj4z7weae
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