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A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method

Received: 10 October 2014    Accepted: 20 October 2014    Published: 24 October 2014
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Abstract

In this paper by using the lexicography method, we proposed a new model to solve fully fuzzy linear programming problem with L-R fuzzy number and find the fuzzy optimal solution of it. Our method has graceful structure and is easy to implement compared with some existing methods. To illustrate our method, a numerical example is solved.

Published in Applied and Computational Mathematics (Volume 4, Issue 1-2)

This article belongs to the Special Issue New Advances in Fuzzy Mathematics: Theory, Algorithms, and Applications

DOI 10.11648/j.acm.s.2015040102.11
Page(s) 1-3
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

Fully Fuzzy Linear Programming, LR-Type Fuzzy Numbers, Ranking Function, Lexicography

References
[1] H. Tanaka, T. Okuda and K. Asai, " On fuzzy mathematical programming", J.Cybernetics,3 (1974) 37–46.
[2] R.E. Bellman and L.A. Zadeh, " Decision making in a fuzzy environment", Management Sci, 17 (1970) 141–164.
[3] H.J. Zimmermann, " Fuzzy programming and linear programming with several objective functions", Fuzzy Sets and Systems, 1 (1978) 45–55.
[4] H.R. Maleki, M. Tata and M. Mashinchi, " Linear Programming with fuzzy variables ", Fuzzy Sets and Systems, 109 (2002) 21-33.
[5] F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha and L. Alizadeh, " Solving a fully fuzzylinear programming using lexicography method and fuzzy approximate solution", Appl. Math. Modell, 33 (2009) 3151-3156.
[6] H. MishmastNehi, H.R. Maleki, and M. Mashinchi, "Solving fuzzy number linear programming problem by lexicographic ranking function", Italian Journal of Pure and Applied Mathematics, 15 (2004) 9-20.
[7] S.H. Nasseri and E. Ardil, "Simplex Method for Fuzzy Variables Linear Programming Problems", World Academy of Science-Engineering and Technology, 8 (2005) 198-202.
[8] S.H. Nasseri , E. Ardil , A. Yazdani and R. Zaefarian, "Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers", World Academy of Science-Engineering and Technology, 10 (2005) 284-288.
[9] A. Kumar, J. Kaur and P. Singh, "A new method for solving fully fuzzy linear programming problems", Appl. Math. Modell, 35 (2011) 817-823.
[10] Saberi Najafi, H., and S. A. Edalatpanah, "A Note on A new method for solving fully fuzzy linear programming problems", Appl. Math. Modell,37 (2013)7865–7867.
[11] R. Ezzati,E. Khorram,R. Enayati," A New Algorithm to Solve Fully Fuzzy Linear Programming Problems Using the MOLP Problem ", Appl. Math. Modelling, (2013) http://dx.doi.org/10.1016/j.apm.2013.03.014.
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  • APA Style

    Mohammad Mehdi Shamooshaki, Ali Hosseinzadeh, Seyyed Ahmad Edalatpanah. (2014). A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method. Applied and Computational Mathematics, 4(1-2), 1-3. https://doi.org/10.11648/j.acm.s.2015040102.11

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    ACS Style

    Mohammad Mehdi Shamooshaki; Ali Hosseinzadeh; Seyyed Ahmad Edalatpanah. A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method. Appl. Comput. Math. 2014, 4(1-2), 1-3. doi: 10.11648/j.acm.s.2015040102.11

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    AMA Style

    Mohammad Mehdi Shamooshaki, Ali Hosseinzadeh, Seyyed Ahmad Edalatpanah. A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method. Appl Comput Math. 2014;4(1-2):1-3. doi: 10.11648/j.acm.s.2015040102.11

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  • @article{10.11648/j.acm.s.2015040102.11,
      author = {Mohammad Mehdi Shamooshaki and Ali Hosseinzadeh and Seyyed Ahmad Edalatpanah},
      title = {A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {1-2},
      pages = {1-3},
      doi = {10.11648/j.acm.s.2015040102.11},
      url = {https://doi.org/10.11648/j.acm.s.2015040102.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040102.11},
      abstract = {In this paper by using the lexicography method, we proposed a new model to solve fully fuzzy linear programming problem with L-R fuzzy number and find the fuzzy optimal solution of it. Our method has graceful structure and is easy to implement compared with some existing methods. To illustrate our method, a numerical example is solved.},
     year = {2014}
    }
    

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    AU  - Mohammad Mehdi Shamooshaki
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    AB  - In this paper by using the lexicography method, we proposed a new model to solve fully fuzzy linear programming problem with L-R fuzzy number and find the fuzzy optimal solution of it. Our method has graceful structure and is easy to implement compared with some existing methods. To illustrate our method, a numerical example is solved.
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Author Information
  • Department of Mathematics, Comprehensive Imam Hossein University, Tehran, Iran

  • Department of Mathematics, Comprehensive Imam Hossein University, Tehran, Iran

  • Department of Applied Mathematics, Tonekabon Branch, Islamic Azad University, Tonekabon, Iran

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