Modified Method for Solving Fully Fuzzy Linear Programming Problem with Triangular Fuzzy Numbers

Document Type: Research Paper

Author

Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand 831014,India.

Abstract

The Fuzzy Linear Programming problem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, we proposed a modified algorithm to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints. Recently, Ezzati et al. (Applied Mathematical Modelling, 39 (2015) 3183-3193) suggested a new algorithm to solve fully fuzzy linear programming problems. In this paper, we modified this algorithm and compare it with other existing methods. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method.

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Main Subjects


[1]      Zimmermann, H. J. (2011). Fuzzy set theory—and its applications. Springer Science & Business Media.

[2]     Baykaso─člu, A., & Subulan, K. (2015). An analysis of fully fuzzy linear programming with fuzzy decision variables through logistics network design problem. Knowledge-Based systems90, 165-184.

[3]     Dehghan, M., Hashemi, B., & Ghatee, M. (2006). Computational methods for solving fully fuzzy linear systems. Applied mathematics and computation179(1), 328-343.

[4]     Ebrahimnejad, A., & Tavana, M. (2014). A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers. Applied mathematical modelling38(17), 4388-4395.

[5]     Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of optimization theory and applications159(2), 536-546.

[6]     Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of optimization theory and applications159(2), 536-546.

[7]     Lotfi, F. H., Allahviranloo, T., Jondabeh, M. A., & Alizadeh, L. (2009). Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied mathematical modelling33(7), 3151-3156.

[8]     Kumar, A., Kaur, J., & Singh, P. (2011). A new method for solving fully fuzzy linear programming problems. Applied mathematical modelling35(2), 817-823.

[9]     Shamooshaki, M. M., Hosseinzadeh, A., & Edalatpanah, S. A. (2014). A new method for solving fully fuzzy linear programming with lr-type fuzzy numbers. International journal of data envelopment analysis and* Operations Research*1(3), 53-55.

[10] Veeramani, C., & Duraisamy, C. (2012). Solving fuzzy linear programming problem using symmetric fuzzy number approximation. International journal of operational research15(3), 321-336.

[11] Wu, H. C. (2008). Using the technique of scalarization to solve the multiobjective programming problems with fuzzy coefficients. Mathematical and computer modelling48(1), 232-248.

[12] Iskander, M. G. (2003). Using different dominance criteria in stochastic fuzzy linear multiobjective programming: A case of fuzzy weighted objective function. Mathematical and computer modelling37(1-2), 167-176.

[13] Mahdavi-Amiri, N., & Nasseri, S. H. (2006). Duality in fuzzy number linear programming by use of a certain linear ranking function. Applied mathematics and computation180(1), 206-216.

[14] Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied mathematical modelling39(12), 3183-3193.

[15] Dubois, D. J. (1980). Fuzzy sets and systems: theory and applications (Vol. 144). Academic press.

[16] Kauffman, A., & Gupta, M. M. (1991). Introduction to fuzzy arithmetic: Theory and application. Mathematics of Computation.

[17] Liou, T. S., & Wang, M. J. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy sets and systems50(3), 247-255.

[18] Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-operations research51(1), 285-297.

[19]  Das, S. K., Mandal, T., & Edalatpanah, S. A. (2017). A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied intelligence46(3), 509-519.

[20] Das, S. K., & Mandal, T. (2015). A single stage single constraints linear fractional programming problem: An approach. Operations research and applications: An international journal (ORAJ)2(1), 9-14.