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Generalized fuzzy rough approximation operators based on fuzzy coverings

Tong-Jun Li, Yee Leung, Wen-Xiu Zhang
2008 International Journal of Approximate Reasoning  
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

Alicja Mieszkowicz-Rolka, Leszek Rolka
2008 International Journal of Approximate Reasoning  
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

Nguyen Xuan Thao, Florentin Smarandache
2016 Zenodo  
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

Min Liu, Degang Chen, Cheng Wu, Hongxing Li
2006 Computers and Mathematics with Applications  
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

Pawan Lingras, Richard Jensen
2007 IEEE International Fuzzy Systems conference proceedings  
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

Zengtai Gong, Bingzhen Sun, Degang Chen
2008 Information Sciences  
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

Lynn D'eer, Nele Verbiest, Chris Cornelis, Lluís Godo
2015 Fuzzy sets and systems (Print)  
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

Wentao Li, Xiaoyan Zhang, Wenxin Sun
2014 The Scientific World Journal  
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

Anna M. Radzikowska
2017 Journal of Automation, Mobile Robotics & Intelligent Systems  
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

Yan-Hong She, Guo-Jun Wang
2009 Computers and Mathematics with Applications  
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

Abbas Mardani, Mehrbakhsh Nilashi, Jurgita Antucheviciene, Madjid Tavana, Romualdas Bausys, Othman Ibrahim
2017 Complexity  
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

Tianyu Xue, Zhan'ao Xue, Huiru Cheng, Jie Liu, Tailong Zhu
2014 The Scientific World Journal  
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]

Richard Jensen, Chris Cornelis
2008 Lecture Notes in Computer Science  
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

Chris Cornelis, Jesús Medina, Nele Verbiest
2014 International Journal of Approximate Reasoning  
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

Chris Cornelis, Martine De Cock, Etienne E. Kerre
2003 Expert systems  
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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