American Journal of Applied Mathematics

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A New Fuzzy-Valued Additive Measure

Received: 16 September 2015    Accepted: 09 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.

DOI 10.11648/j.ajam.20150306.14
Published in American Journal of Applied Mathematics (Volume 3, Issue 6, December 2015)
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), 2024. Published by Science Publishing Group

Keywords

Gradual Number, Fuzzy Number, Fuzzy-Valued Measure

References
[1] D. Dubois and H. Prade, Gradual elements in a fuzzy set, Soft Computing, 12 (2008), 165 - 175.
[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.
Author Information
  • College of Mathematics and Information Science, Hebei University, Baoding, China

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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://download.sciencepg.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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