FFLP problem with symmetric trapezoidal fuzzy numbers

Abstract: The most popular approach for solving fully fuzzy linear programming (FFLP) problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013) [Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), 536-546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013) had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014) [Ezzati, R., Khorram, E., & Enayati, R. (2014). A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5), 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014)’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method.

How to cite this paper

 Daneshrad, R & Jafari, D. (2015). FFLP problem with symmetric trapezoidal fuzzy numbers.Decision Science Letters , 4(2), 117-124.

Refrences

Allahviranloo, T., Lotfi, F. H., Kiasary, M. K., Kiani, N. A., & Alizadeh, L. (2008). Solving fully fuzzy linear programming problem by the ranking function. Applied Mathematical Sciences, 2(1), 19-32.

Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141.

Bhardwaj, B., & Kumar, A. (2013). A Note on the Paper “A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems”. Journal of Optimization Theory and Applications, 163, 1-12.

Buckley, J. J., & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets and Systems, 109(1), 35-53.

Dehghan, M., Hashemi, B., & Ghatee, M. (2006). Computational methods for solving fully fuzzy linear systems. Applied Mathematics and Computation,179(1), 328-343.

Ezzati, R., Khorram, E., & Enayati, R. (2014). A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5), 2333-2358.

Ganesan, K., & Veeramani, P. (2006). Fuzzy linear programs with trapezoidal fuzzy numbers. Annals of Operations Research, 143(1), 305-315.

Hashemi, S. M., Modarres, M., Naserabadi, E. & Naserabadi, M. M. (2006). Fully fuzzied linear programming, Solution and duality. Journal of Intelligence Fuzzy Systems, 17, 253-261.

Hatami, A., & Kazemipoor, H. (2014). Solving fully fuzzy linear programming with symmetric trapezoidal fuzzy numbers using Mehar’s method. Journal of Mathematical and Computational Science, 4(2), 463-470.

Hosseinzadeh Lotfi, F., Allahviranloo, T., Alimardani Jondabeh, M., & Alizadeh, L. (2009). Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied Mathematical Modelling, 33(7), 3151-3156.

Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), 536-546.

Kumar, A., Kaur, J., & Singh, P. (2010). Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Inequality Constraints. International Journal of Applied Mathematics & Computer Sciences, 6(1), 37-41.

Nasseri, S. H., Behmanesh, E., Taleshian, F., Abdolalipoor, M., & TaghiNezhad, N. A. (2013). Fully fuzzy linear programming with inequality constraints. International Journal of Industrial Mathematics, 5(4), 309-316.

Tanaka, H., Okuda, T., & Asai, K. (1974).On fuzzy mathematical programing. The Journal of
Cybernetics, 3, 37-46.

Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, 45-55.

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Decision Science Letters

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