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Variational Principles of Fuzzy Mappings and Its Applications

Received: 19 July 2017     Published: 19 July 2017
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Abstract

In this paper, we firstly discuss the basic properties of the sub differential of fuzzy mapping and get some related conclusions. Secondly, we establish a variational principle of fuzzy mapping by establishing the concept of gauge fuzzy mapping. Then we prove the approximation sun rule of fuzzy mapping in sub-differential as the application of that principles.

Published in Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 4)
DOI 10.11648/j.sjams.20170504.13
Page(s) 139-146
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), 2017. Published by Science Publishing Group

Keywords

Fuzzy Mapping, Sub-differential, Gauge Mapping, Variational Principle, Approximation Sun Rule

References
[1] S. S. L. Chang, L. A. Zadeh, On fuzzy mappings and control, IEEE Trans. Syst. Man Cybernet. 2 (1972), 30-34.
[2] M. L. Puri, D. A. Ralescu, Differentials for fuzzy functions, J. Math. Anal. Appl. 91 (1983), 552-558.
[3] M. Panigrahi, G. Panda, S. Nanda, Convex fuzzy mapping with differentiability and its application in fuzzy optimization, European J. Oper. Res., 185 (2008), 47-62.
[4] B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets Syst. 230 (2013), 119-141.
[5] C. Zang, X, H. Yuan, E. S. Lee, Duality theory in fuzzy mathematical programming problems with fuzzy coefficients. Comput. Math. Appl., 49 (2005), 1709-1730.
[6] G. X. Wang, C. X. Wu. Directional derivatives and subsifferential of convex fuzzy mappings and application in convex fuzzy programming. Fuzzy Sets and Systems. 138 (2003), 559-591.
[7] Y. E. Bao, B. Dai, Researches on convex extension problems of fuzzy valued functions, J. Math. Comput. Sci., 16 (2015), 239-247.
[8] Y. E. Bao, J. J. Li, A study on the differential and subdifferential of fuzzy mapping and its application problem, J. Nonl. Sci. Appl., 16 (2015), 239-247.
[9] J. M. Borwein, Q. J. Zhu. Techniques of variation analysis. Springer-Verilog, New York, 2005.
[10] F. H. Clarke, Y. S. Ledyaev. Non smooth analysis and control theory. Springer-Verilog, New York, 1998.
[11] T. X. D. Ha. Some variants of the ekeland variational principle for a set-valued mappings. J. Optim. Theory. Appl. 124 (2005), 187-206.
[12] C. X. Wu, C. Wu, The supremum and infimum of the set of fuzzy numbers and its application. J. Math. Anal. Appl. 210 (1997), 499-511.
[13] Y. E. Bao, C. X. Wu. Convexity and semi-continuity of fuzzy mappings. Comput. Math. Appl. 51 (2006), 1809-1816.
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  • APA Style

    Yu-E Bao, Ying-Chun Niu, Yuan Li. (2017). Variational Principles of Fuzzy Mappings and Its Applications. Science Journal of Applied Mathematics and Statistics, 5(4), 139-146. https://doi.org/10.11648/j.sjams.20170504.13

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    ACS Style

    Yu-E Bao; Ying-Chun Niu; Yuan Li. Variational Principles of Fuzzy Mappings and Its Applications. Sci. J. Appl. Math. Stat. 2017, 5(4), 139-146. doi: 10.11648/j.sjams.20170504.13

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    AMA Style

    Yu-E Bao, Ying-Chun Niu, Yuan Li. Variational Principles of Fuzzy Mappings and Its Applications. Sci J Appl Math Stat. 2017;5(4):139-146. doi: 10.11648/j.sjams.20170504.13

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  • @article{10.11648/j.sjams.20170504.13,
      author = {Yu-E Bao and Ying-Chun Niu and Yuan Li},
      title = {Variational Principles of Fuzzy Mappings and Its Applications},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {5},
      number = {4},
      pages = {139-146},
      doi = {10.11648/j.sjams.20170504.13},
      url = {https://doi.org/10.11648/j.sjams.20170504.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170504.13},
      abstract = {In this paper, we firstly discuss the basic properties of the sub differential of fuzzy mapping and get some related conclusions. Secondly, we establish a variational principle of fuzzy mapping by establishing the concept of gauge fuzzy mapping. Then we prove the approximation sun rule of fuzzy mapping in sub-differential as the application of that principles.},
     year = {2017}
    }
    

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    T1  - Variational Principles of Fuzzy Mappings and Its Applications
    AU  - Yu-E Bao
    AU  - Ying-Chun Niu
    AU  - Yuan Li
    Y1  - 2017/07/19
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    DO  - 10.11648/j.sjams.20170504.13
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    UR  - https://doi.org/10.11648/j.sjams.20170504.13
    AB  - In this paper, we firstly discuss the basic properties of the sub differential of fuzzy mapping and get some related conclusions. Secondly, we establish a variational principle of fuzzy mapping by establishing the concept of gauge fuzzy mapping. Then we prove the approximation sun rule of fuzzy mapping in sub-differential as the application of that principles.
    VL  - 5
    IS  - 4
    ER  - 

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Author Information
  • College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao, P. R. China

  • College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao, P. R. China

  • College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao, P. R. China

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