Notes on “Some Properties of <i>L</i>-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”

Yuan Wang; Keming Tang; Zhudeng Wang

doi:doi:10.11648/j.acis.20160402.11

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Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”

Yuan Wang, Keming Tang, Zhudeng Wang

Published in Automation, Control and Intelligent Systems (Volume 4, Issue 2)

Received: 29 February 2016 Accepted: 9 March 2016 Published: 23 March 2016

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Abstract

In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) _L or (TC) _R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.

Published in	Automation, Control and Intelligent Systems (Volume 4, Issue 2)
DOI	10.11648/j.acis.20160402.11
Page(s)	10-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Involutive Residuated Lattice, L-relation, L-fuzzy Topology, L-fuzzy Approximation Space

References

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APA Style

Yuan Wang, Keming Tang, Zhudeng Wang. (2016). Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Automation, Control and Intelligent Systems, 4(2), 10-14. https://doi.org/10.11648/j.acis.20160402.11

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ACS Style

Yuan Wang; Keming Tang; Zhudeng Wang. Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Autom. Control Intell. Syst. 2016, 4(2), 10-14. doi: 10.11648/j.acis.20160402.11

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AMA Style

Yuan Wang, Keming Tang, Zhudeng Wang. Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Autom Control Intell Syst. 2016;4(2):10-14. doi: 10.11648/j.acis.20160402.11

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@article{10.11648/j.acis.20160402.11,
  author = {Yuan Wang and Keming Tang and Zhudeng Wang},
  title = {Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”},
  journal = {Automation, Control and Intelligent Systems},
  volume = {4},
  number = {2},
  pages = {10-14},
  doi = {10.11648/j.acis.20160402.11},
  url = {https://doi.org/10.11648/j.acis.20160402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20160402.11},
  abstract = {In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.},
 year = {2016}
}

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TY  - JOUR
T1  - Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”
AU  - Yuan Wang
AU  - Keming Tang
AU  - Zhudeng Wang
Y1  - 2016/03/23
PY  - 2016
N1  - https://doi.org/10.11648/j.acis.20160402.11
DO  - 10.11648/j.acis.20160402.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 10
EP  - 14
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20160402.11
AB  - In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.
VL  - 4
IS  - 2
ER  -

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Author Information

Yuan Wang

College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China
Keming Tang

College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China
Zhudeng Wang

School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu, People's Republic of China

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Plain Text BibTeX RIS

APA Style

Yuan Wang, Keming Tang, Zhudeng Wang. (2016). Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Automation, Control and Intelligent Systems, 4(2), 10-14. https://doi.org/10.11648/j.acis.20160402.11

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ACS Style

Yuan Wang; Keming Tang; Zhudeng Wang. Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Autom. Control Intell. Syst. 2016, 4(2), 10-14. doi: 10.11648/j.acis.20160402.11

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AMA Style

Yuan Wang, Keming Tang, Zhudeng Wang. Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”. Autom Control Intell Syst. 2016;4(2):10-14. doi: 10.11648/j.acis.20160402.11

Copy | Download

@article{10.11648/j.acis.20160402.11,
  author = {Yuan Wang and Keming Tang and Zhudeng Wang},
  title = {Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”},
  journal = {Automation, Control and Intelligent Systems},
  volume = {4},
  number = {2},
  pages = {10-14},
  doi = {10.11648/j.acis.20160402.11},
  url = {https://doi.org/10.11648/j.acis.20160402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20160402.11},
  abstract = {In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Notes on “Some Properties of L-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”
AU  - Yuan Wang
AU  - Keming Tang
AU  - Zhudeng Wang
Y1  - 2016/03/23
PY  - 2016
N1  - https://doi.org/10.11648/j.acis.20160402.11
DO  - 10.11648/j.acis.20160402.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 10
EP  - 14
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20160402.11
AB  - In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.
VL  - 4
IS  - 2
ER  -

Copy | Download