An optimal solution to multi-goal fuzzy linear programming problems using elementary transformations
-
Keywords:
Linear Programming Problem (LPP), Multi-goal, Elementary Transformation Method, Triangular Number.Abstract
This article explores how to solve multipurpose problems to obtain optimal solutions using fuzzy linear programming. Our goal is to minimize production and transportation costs by using the most basic transportation methods and comparing the results to conventional methods. We discuss the results of numerical examples and illustrate this method.
Downloads
References
Y. Tan and Y. Long, “Option-game approach to analyze technology innovation investment under fuzzy environment,” Journal of Applied Mathematics, vol. 2012, Article ID 830850, 9 pages, 2012.
L. Zhang, X. Xu, and L. Tao, “Some similarity measures for triangular fuzzy number and their applications in multiple criteria group decision-making,” Journal of Applied Mathematics, vol. 2013, Article ID 538261, 7 pages, 2013.
H. Tsai and T. Chen, “A fuzzy nonlinear programming approach for optimizing the performance of a four-objective fluctuation smoothing rule in a wafer fabrication factory,” Journal of Applied Mathematics, vol. 2013, Article ID 720607, 15 pages, 2013.
M. Delgado, J. L. Verdegay, and M. A. Vila, “A general model for fuzzy linear programming,” Fuzzy Sets and Systems, vol. 29, no. 1, pp. 21–29, 1989.
H. Rommelfanger, “Fuzzy linear programming and applications,” European Journal of Operational Research, vol. 92, no. 3, pp. 512–527, 1996.
N. van Hop, “Solving fuzzy (stochastic) linear programming problems using superiority and inferiority measures,” Information Sciences, vol. 177, no. 9, pp. 1977–1991, 2007.
M. Jiménez, M. Arenas, A. Bilbao, and M. V. Rodríguez, “Linear programming with fuzzy parameters: an interactive method resolution,” European Journal of Operational Research, vol. 177, no. 3, pp. 1599–1609, 2007.
H.-C. Wu, “Optimality conditions for linear programming problems with fuzzy coefficients,” Computers & Mathematics with Applications, vol. 55, no. 12, pp. 2807–2822, 2008.
X. Liu, “Measuring the satisfaction of constraints in fuzzy linear programming,” Fuzzy Sets and Systems, vol. 122, no. 2, pp. 263–275, 2001.
J. Chiang, “Fuzzy linear programming based on statistical confidence interval and interval-valued fuzzy set,” European Journal of Operational Research, vol. 129, no. 1, pp. 65–86, 2001.
K. D. Jamison and W. A. Lodwick, “Fuzzy linear programming using a penalty method,” Fuzzy Sets and Systems, vol. 119, no. 1, pp. 97–110, 2001.
T. León and E. Vercher, “Solving a class of fuzzy linear programs by using semi-infinite programming techniques,” Fuzzy Sets and Systems, vol. 146, no. 2, pp. 235–252, 2004.
N. Mahdavi-Amiri and S. H. Nasseri, “Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables,” Fuzzy Sets and Systems, vol. 158, no. 17, pp. 1961–1978, 2007.
K. Ganesan and P. Veeramani, “Fuzzy linear programs with trapezoidal fuzzy numbers,” Annals of Operations Research, vol. 143, no. 1, pp. 305–315, 2006.
H. R. Maleki, M. Tata, and M. Mashinchi, “Linear programming with fuzzy variables,” Fuzzy Sets and Systems, vol. 109, no. 1, pp. 21–33, 2000.
S. M. Hashemi, M. Modarres, E. Nasrabadi, and M. M. Nasrabadi, “Fully fuzzified linear programming, solution and duality,” Journal of Intelligent and Fuzzy Systems, vol. 17, no. 3, pp. 253–261, 2006.
T. Allahviranloo, F. H. Lotfi, M. K. Kiasary, N. A. Kiani, and L. Alizadeh, “Solving fully fuzzy linear programming problem by the ranking function,” Applied Mathematical Sciences, vol. 2, no. 1–4, pp. 19–32, 2008.
F. H. Lotfi, T. Allahviranloo, M. A. Jondabeh, and L. Alizadeh, “Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 3151–3156, 2009.
A. Kumar, J. Kaur, and P. Singh, “A new method for solving fully fuzzy linear programming problems,” Applied Mathematical Modelling, vol. 35, no. 2, pp. 817–823, 2011.
X. Guo and D. Shang, “Fuzzy approximate solution of positive fully fuzzy linear matrix equations,” Journal of Applied Mathematics, vol. 2013, Article ID 178209, 7 pages, 2013.
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.