**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30455

##### Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables

**Authors:**
Mahnaz Hosseinzadeh,
Aliyeh Kazemi

**Abstract:**

**Keywords:**
triangular fuzzy numbers,
fuzzy multi-objective linear programming problems,
fuzzy ranking,
supplier selection problem

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1126223

**References:**

[1] Gu Zhang, Y.H. Wu, M. Remias, J. Lu,0020 Formulation of fuzzy linear programming problems as four-objective constrained optimization problems, Applied Mathematics and Computation 139 (2003) 383–399.

[2] F. Arıkan, Z. lal Gungor, A two-phase approach for multi-objective programming problems with fuzzy coefficients, Information Sciences 177 (2007) 5191–5202.

[3] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353.

[4] H. Tanaka, T. Okuda, K. Asai, On fuzzy mathematical programming, J. Cybernetics Syst. 3 (1973) 37–46.

[5] H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1 (1978) 45–55. S

[6] J. L., Verdegay, Fuzzy mathematical programming, in (BM15), (1982)231-236

[7] B., Warners, Interactive Multiple Objective Programming subject to flexible constraint, European Journal of Operational Research, 31 (1987) 342-349.

[8] B., Warners, An Interactive Fuzzy Programming system, Fuzzy Sets and Systems, 23 (1987) 131-147.

[9] H. J., Zimmerman, Describing an optimization of fuzzy systems, international Journal of General System2 (1976)209-216.

[10] S., Chanas, te use of parametric programming in FLP, Fuzzy sets and Systems, 11 (1983) 243-251.

[11] J. L., Verdegay, A dual approach to solve the fuzzy Linear Programming Problem, Fuzzy Sets and Systems, 14 (1984) 131-141.

[12] J. L., Verdegay, Application of fuzzy optimization in operational research, Control and Sybernetics, 13 (1984) 229-239.

[13] C., Carlsson and P. Corhonen, A parametric approach to fuzzy linear programming, Fuzzy Sets and Systems, 20 (1986) 17-30.

[14] J., Ramik and J., Rimanek, Inequality relation between fuzzy numbers and its use in fuzzy otimization, fuzzy Sets and Systems, 16 (1985) 123-138.

[15] H., Tanaka, H. Ichihashi and K. Asai, A formulation of fuzzy Linear Programming Problems based on comparison of fuzzy numbers, Control and cybernetics, 13 (1984) 186- 194.

[16] Y.J., Lai and C.L. Hwang, A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems 49 (1992).

[17] H. Rommelfanger, R. Hanuscheck and J. Wolf, Linear programming with fuzzy objectives, Fuzzy Sets and Systems 29 (1989) 31- 48.

[18] J.J. Buckley, Possibilistic Linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26 (1988) 159- 174.

[19] C. Stanciulescu, Ph. Fortemps, M. Install, V. Wertz, Multiobjective fuzzy linear programming problems with fuzzy decision variables, European Journal of Operational Research 149 (2003) 654–675.

[20] H. Tanaka, P. Guo, H.J. Zimmermann, Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems, Fuzzy Sets and Systems 113 (2000) 323-332.

[21] H.R. Maleki, M. Tata, M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Set. Syst. 109 (2000) 21–33.

[22] J. Buckley, T. Feuring, Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming, Fuzzy Set. Syst. 109 (2000) 35–53.

[23] S.M. Hashemi, M. Modarres, E. Nasrabadi, M.M. Nasrabadi, Fully fuzzified linear programming, solution and duality, J. Intell. Fuzzy Syst. 17 (2006) 253–261.

[24] T. Allahviranloo, F.H. Lotfi, M.K. Kiasary, N.A. Kiani, L. Alizadeh, Solving full fuzzy linear programming problem by the ranking function, Appl. Math. Sci.2 (2008) 19–32.

[25] A Kumar, J Kaur, P Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35 (2011) 817–823.

[26] M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput. 179 (2006) 328–343.

[27] F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Modell. 33 (2009) 3151–3156.