A New Fuzzy-Valued Additive Measure

Cai-Li Zhou

doi:doi:10.11648/j.ajam.20150306.14

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A New Fuzzy-Valued Additive Measure

Cai-Li Zhou

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)

Received: 16 September 2015 Accepted: 9 October 2015 Published: 27 October 2015

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Abstract

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.ajam.20150306.14
Page(s)	259-264
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), 2015. Published by Science Publishing Group

Keywords

Gradual Number, Fuzzy Number, Fuzzy-Valued Measure

References

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[2]	D. Dubois, J. Fortin and P. Zielinnski, Interval PERT and its fuzzy extension, Studies in Fuzziness and Soft Computing, 252 (2010), 171 -199.
[3]	J. Fortin and D. Dubois, Solving fuzzy PERT using gradual real numbers, In L. Penserini, A. Perini, and P. Peppas, editors, STAIRS 2006: Proceedings of the Third Starting AI Researcher's Symposium, IOS Press, Fairfax, VA, 160 (2006), 196 - 207.
[4]	J. Fortin, D. Dubois and H. Fargier, Gradual numbers and their application to fuzzy interval analysis, IEEE Transactions on fuzzy systems, 16 (2008), 388 - 402.
[5]	A. Kasperski, P. Zielinski, Using gradual numbers for solving fuzzy-valued combinatorial optimization problems, Foundations of Fuzzy Logic and Soft Computing, (2007), 656 - 665.
[6]	E.A. Stock, Gradual numbers and fuzzy optimization, ph.D. Thesis, University of Colorado Denver, Denver, America. 2010.
[7]	M. Stojakovic, Fuzzy valued measure, Fuzzy Sets and Systems, 65 (1994), 95 - 104.
[8]	J. Wu, X. Xue and C. Wu, Radon–Nikodym theorem and Vitali–Hahn–Saks theorem on fuzzy number measures in Banach spacers, Fuzzy Sets and Systems, 117 (2001) 339 - 346.
[9]	X. Xue, M. Ha and C. Wu, On the extension of the fuzzy number measures in Banach spaces: Part I. Representation of the fuzzy number measures, Fuzzy Sets and Systems, 78 (1996) 347 - 354.
[10]	C. Zhou and P. Wang, New fuzzy probability spaces and fuzzy random variables based on gradual numbers, In: 2014 9th International Conference, BIC-TA 2014, (2014), 633 - 643.
[11]	C. Zhou and J. Li, New Fuzzy Measure Based on Gradual Numbers, International Journal of Mathematical Analysis, 9 (2015), 101 - 110.
[12]	C. Zhou and G. Zhang, A Fuzzy Metric on the Space of Fuzzy Sets, International Journal of Mathematical Analysis, 9 (2015), 237 - 247.

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Cai-Li Zhou. (2015). A New Fuzzy-Valued Additive Measure. American Journal of Applied Mathematics, 3(6), 259-264. https://doi.org/10.11648/j.ajam.20150306.14

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ACS Style

Cai-Li Zhou. A New Fuzzy-Valued Additive Measure. Am. J. Appl. Math. 2015, 3(6), 259-264. doi: 10.11648/j.ajam.20150306.14

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AMA Style

Cai-Li Zhou. A New Fuzzy-Valued Additive Measure. Am J Appl Math. 2015;3(6):259-264. doi: 10.11648/j.ajam.20150306.14

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@article{10.11648/j.ajam.20150306.14,
  author = {Cai-Li Zhou},
  title = {A New Fuzzy-Valued Additive Measure},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {259-264},
  doi = {10.11648/j.ajam.20150306.14},
  url = {https://doi.org/10.11648/j.ajam.20150306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.14},
  abstract = {In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.},
 year = {2015}
}

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TY  - JOUR
T1  - A New Fuzzy-Valued Additive Measure
AU  - Cai-Li Zhou
Y1  - 2015/10/27
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.14
DO  - 10.11648/j.ajam.20150306.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 259
EP  - 264
PB  - Science Publishing Group
SN  - 2330-006X
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AB  - In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.
VL  - 3
IS  - 6
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Author Information

Cai-Li Zhou

College of Mathematics and Information Science, Hebei University, Baoding, China

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APA Style

Cai-Li Zhou. (2015). A New Fuzzy-Valued Additive Measure. American Journal of Applied Mathematics, 3(6), 259-264. https://doi.org/10.11648/j.ajam.20150306.14

Copy | Download

ACS Style

Cai-Li Zhou. A New Fuzzy-Valued Additive Measure. Am. J. Appl. Math. 2015, 3(6), 259-264. doi: 10.11648/j.ajam.20150306.14

Copy | Download

AMA Style

Cai-Li Zhou. A New Fuzzy-Valued Additive Measure. Am J Appl Math. 2015;3(6):259-264. doi: 10.11648/j.ajam.20150306.14

Copy | Download

@article{10.11648/j.ajam.20150306.14,
  author = {Cai-Li Zhou},
  title = {A New Fuzzy-Valued Additive Measure},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {259-264},
  doi = {10.11648/j.ajam.20150306.14},
  url = {https://doi.org/10.11648/j.ajam.20150306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.14},
  abstract = {In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A New Fuzzy-Valued Additive Measure
AU  - Cai-Li Zhou
Y1  - 2015/10/27
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.14
DO  - 10.11648/j.ajam.20150306.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 259
EP  - 264
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.14
AB  - In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.
VL  - 3
IS  - 6
ER  -

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