A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method
Applied and Computational Mathematics
Volume 4, Issue 1-2, January 2015, Pages: 1-3
Received: Oct. 10, 2014;
Accepted: Oct. 20, 2014;
Published: Oct. 24, 2014
Views 3266 Downloads 269
Mohammad Mehdi Shamooshaki, Department of Mathematics, Comprehensive Imam Hossein University, Tehran, Iran
Ali Hosseinzadeh, Department of Mathematics, Comprehensive Imam Hossein University, Tehran, Iran
Seyyed Ahmad Edalatpanah, Department of Applied Mathematics, Tonekabon Branch, Islamic Azad University, Tonekabon, Iran
Follow on us
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.
Fully Fuzzy Linear Programming, LR-Type Fuzzy Numbers, Ranking Function, Lexicography
To cite this article
Mohammad Mehdi Shamooshaki,
Seyyed Ahmad Edalatpanah,
A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method, Applied and Computational Mathematics. Special Issue: New Advances in Fuzzy Mathematics: Theory, Algorithms, and Applications.
Vol. 4, No. 1-2,
2015, pp. 1-3.
H. Tanaka, T. Okuda and K. Asai, " On fuzzy mathematical programming", J.Cybernetics,3 (1974) 37–46.
R.E. Bellman and L.A. Zadeh, " Decision making in a fuzzy environment", Management Sci, 17 (1970) 141–164.
H.J. Zimmermann, " Fuzzy programming and linear programming with several objective functions", Fuzzy Sets and Systems, 1 (1978) 45–55.
H.R. Maleki, M. Tata and M. Mashinchi, " Linear Programming with fuzzy variables ", Fuzzy Sets and Systems, 109 (2002) 21-33.
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.
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.
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.
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.
A. Kumar, J. Kaur and P. Singh, "A new method for solving fully fuzzy linear programming problems", Appl. Math. Modell, 35 (2011) 817-823.
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.
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.