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Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense

Received: 27 October 2017     Accepted: 14 November 2017     Published: 5 December 2017
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Abstract

Integral inequalities have important applications in propability and engineering field. Sugeno integral is an important fuzzy integral in fuzzy theory, which has many applications in various fields. The object of this paper is to develop some new integral inequalities for Sugeno integral. Based on classical Hermite-Hadamard type inequality, this paper intends to extend it for the Sugeno integral. Some new Hermite-Hadamard type inequalities are derived for Sugeno integral based on s-convex function in the second sense. An example is used to illustrate the effectiveness of the new inequalities.

Published in Mathematics Letters (Volume 3, Issue 6)
DOI 10.11648/j.ml.20170306.14
Page(s) 77-82
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 Integral, Sugeno Integral, Herimite-Hadamard Inequality, s-Convex Function

References
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Cite This Article
  • APA Style

    Lanping Li. (2017). Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense. Mathematics Letters, 3(6), 77-82. https://doi.org/10.11648/j.ml.20170306.14

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    ACS Style

    Lanping Li. Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense. Math. Lett. 2017, 3(6), 77-82. doi: 10.11648/j.ml.20170306.14

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    AMA Style

    Lanping Li. Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense. Math Lett. 2017;3(6):77-82. doi: 10.11648/j.ml.20170306.14

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  • @article{10.11648/j.ml.20170306.14,
      author = {Lanping Li},
      title = {Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense},
      journal = {Mathematics Letters},
      volume = {3},
      number = {6},
      pages = {77-82},
      doi = {10.11648/j.ml.20170306.14},
      url = {https://doi.org/10.11648/j.ml.20170306.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20170306.14},
      abstract = {Integral inequalities have important applications in propability and engineering field. Sugeno integral is an important fuzzy integral in fuzzy theory, which has many applications in various fields. The object of this paper is to develop some new integral inequalities for Sugeno integral. Based on classical Hermite-Hadamard type inequality, this paper intends to extend it for the Sugeno integral. Some new Hermite-Hadamard type inequalities are derived for Sugeno integral based on s-convex function in the second sense. An example is used to illustrate the effectiveness of the new inequalities.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense
    AU  - Lanping Li
    Y1  - 2017/12/05
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ml.20170306.14
    DO  - 10.11648/j.ml.20170306.14
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
    SP  - 77
    EP  - 82
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20170306.14
    AB  - Integral inequalities have important applications in propability and engineering field. Sugeno integral is an important fuzzy integral in fuzzy theory, which has many applications in various fields. The object of this paper is to develop some new integral inequalities for Sugeno integral. Based on classical Hermite-Hadamard type inequality, this paper intends to extend it for the Sugeno integral. Some new Hermite-Hadamard type inequalities are derived for Sugeno integral based on s-convex function in the second sense. An example is used to illustrate the effectiveness of the new inequalities.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • School of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha, China

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