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), 2014. Published by Science Publishing Group |
Fully Fuzzy Linear Programming, LR-Type Fuzzy Numbers, Ranking Function, Lexicography
[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. |
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
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
@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} }
TY - JOUR T1 - A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method AU - Mohammad Mehdi Shamooshaki AU - Ali Hosseinzadeh AU - Seyyed Ahmad Edalatpanah Y1 - 2014/10/24 PY - 2014 N1 - https://doi.org/10.11648/j.acm.s.2015040102.11 DO - 10.11648/j.acm.s.2015040102.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 1 EP - 3 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2015040102.11 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. VL - 4 IS - 1-2 ER -