<i>I</i>-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers

Sangita Saha; Bijan Nath; Santanu Roy

doi:doi:10.11648/j.ijmfs.20160202.12

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I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers

Sangita Saha, Bijan Nath, Santanu Roy

Published in International Journal of Management and Fuzzy Systems (Volume 2, Issue 2)

Received: 18 August 2016 Accepted: 29 August 2016 Published: 11 October 2016

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Abstract

In this article, the notion of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. We establish the criterion for any arbitrary triple sequence of fuzzy numbers to be I-statistically pre-Cauchy. It is shown that an I-statistically convergent sequence of fuzzy numbers is I-statistically pre-Cauchy. Moreover a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-pre-Cauchy is established.

Published in	International Journal of Management and Fuzzy Systems (Volume 2, Issue 2)
DOI	10.11648/j.ijmfs.20160202.12
Page(s)	15-21
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), 2016. Published by Science Publishing Group

Keywords

Ideal, Filter, Statistical Convergence, Ideal Convergence, I-Statistical Convergence, Triple Sequence of Fuzzy Numbers, I-statistical Pre-Cauchy, Orlicz Function

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APA Style

Sangita Saha, Bijan Nath, Santanu Roy. (2016). I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers. International Journal of Management and Fuzzy Systems, 2(2), 15-21. https://doi.org/10.11648/j.ijmfs.20160202.12

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ACS Style

Sangita Saha; Bijan Nath; Santanu Roy. I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers. Int. J. Manag. Fuzzy Syst. 2016, 2(2), 15-21. doi: 10.11648/j.ijmfs.20160202.12

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AMA Style

Sangita Saha, Bijan Nath, Santanu Roy. I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers. Int J Manag Fuzzy Syst. 2016;2(2):15-21. doi: 10.11648/j.ijmfs.20160202.12

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@article{10.11648/j.ijmfs.20160202.12,
  author = {Sangita Saha and Bijan Nath and Santanu Roy},
  title = {I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {2},
  number = {2},
  pages = {15-21},
  doi = {10.11648/j.ijmfs.20160202.12},
  url = {https://doi.org/10.11648/j.ijmfs.20160202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20160202.12},
  abstract = {In this article, the notion of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. We establish the criterion for any arbitrary triple sequence of fuzzy numbers to be I-statistically pre-Cauchy. It is shown that an I-statistically convergent sequence of fuzzy numbers is I-statistically pre-Cauchy. Moreover a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-pre-Cauchy is established.},
 year = {2016}
}

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TY  - JOUR
T1  - I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers
AU  - Sangita Saha
AU  - Bijan Nath
AU  - Santanu Roy
Y1  - 2016/10/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ijmfs.20160202.12
DO  - 10.11648/j.ijmfs.20160202.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 15
EP  - 21
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20160202.12
AB  - In this article, the notion of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. We establish the criterion for any arbitrary triple sequence of fuzzy numbers to be I-statistically pre-Cauchy. It is shown that an I-statistically convergent sequence of fuzzy numbers is I-statistically pre-Cauchy. Moreover a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-pre-Cauchy is established.
VL  - 2
IS  - 2
ER  -

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Author Information

Sangita Saha

Department of Mathematics, National Institute of Technology Silchar, Assam, India
Bijan Nath

Department of Mathematics, National Institute of Technology Silchar, Assam, India
Santanu Roy

Department of Mathematics, National Institute of Technology Silchar, Assam, India

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APA Style

Sangita Saha, Bijan Nath, Santanu Roy. (2016). I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers. International Journal of Management and Fuzzy Systems, 2(2), 15-21. https://doi.org/10.11648/j.ijmfs.20160202.12

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ACS Style

Sangita Saha; Bijan Nath; Santanu Roy. I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers. Int. J. Manag. Fuzzy Syst. 2016, 2(2), 15-21. doi: 10.11648/j.ijmfs.20160202.12

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AMA Style

Sangita Saha, Bijan Nath, Santanu Roy. I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers. Int J Manag Fuzzy Syst. 2016;2(2):15-21. doi: 10.11648/j.ijmfs.20160202.12

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@article{10.11648/j.ijmfs.20160202.12,
  author = {Sangita Saha and Bijan Nath and Santanu Roy},
  title = {I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {2},
  number = {2},
  pages = {15-21},
  doi = {10.11648/j.ijmfs.20160202.12},
  url = {https://doi.org/10.11648/j.ijmfs.20160202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20160202.12},
  abstract = {In this article, the notion of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. We establish the criterion for any arbitrary triple sequence of fuzzy numbers to be I-statistically pre-Cauchy. It is shown that an I-statistically convergent sequence of fuzzy numbers is I-statistically pre-Cauchy. Moreover a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-pre-Cauchy is established.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - I-Statistically Pre-Cauchy Triple Sequences of Fuzzy Real Numbers
AU  - Sangita Saha
AU  - Bijan Nath
AU  - Santanu Roy
Y1  - 2016/10/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ijmfs.20160202.12
DO  - 10.11648/j.ijmfs.20160202.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 15
EP  - 21
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20160202.12
AB  - In this article, the notion of I-statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two is introduced. We establish the criterion for any arbitrary triple sequence of fuzzy numbers to be I-statistically pre-Cauchy. It is shown that an I-statistically convergent sequence of fuzzy numbers is I-statistically pre-Cauchy. Moreover a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be I-pre-Cauchy is established.
VL  - 2
IS  - 2
ER  -

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