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Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables
Abstract:In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1126223Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 915
 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.
 F. Arıkan, Z. lal Gungor, A two-phase approach for multi-objective programming problems with fuzzy coefficients, Information Sciences 177 (2007) 5191–5202.
 L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353.
 H. Tanaka, T. Okuda, K. Asai, On fuzzy mathematical programming, J. Cybernetics Syst. 3 (1973) 37–46.
 H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1 (1978) 45–55. S
 J. L., Verdegay, Fuzzy mathematical programming, in (BM15), (1982)231-236
 B., Warners, Interactive Multiple Objective Programming subject to flexible constraint, European Journal of Operational Research, 31 (1987) 342-349.
 B., Warners, An Interactive Fuzzy Programming system, Fuzzy Sets and Systems, 23 (1987) 131-147.
 H. J., Zimmerman, Describing an optimization of fuzzy systems, international Journal of General System2 (1976)209-216.
 S., Chanas, te use of parametric programming in FLP, Fuzzy sets and Systems, 11 (1983) 243-251.
 J. L., Verdegay, A dual approach to solve the fuzzy Linear Programming Problem, Fuzzy Sets and Systems, 14 (1984) 131-141.
 J. L., Verdegay, Application of fuzzy optimization in operational research, Control and Sybernetics, 13 (1984) 229-239.
 C., Carlsson and P. Corhonen, A parametric approach to fuzzy linear programming, Fuzzy Sets and Systems, 20 (1986) 17-30.
 J., Ramik and J., Rimanek, Inequality relation between fuzzy numbers and its use in fuzzy otimization, fuzzy Sets and Systems, 16 (1985) 123-138.
 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.
 Y.J., Lai and C.L. Hwang, A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems 49 (1992).
 H. Rommelfanger, R. Hanuscheck and J. Wolf, Linear programming with fuzzy objectives, Fuzzy Sets and Systems 29 (1989) 31- 48.
 J.J. Buckley, Possibilistic Linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26 (1988) 159- 174.
 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.
 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.
 H.R. Maleki, M. Tata, M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Set. Syst. 109 (2000) 21–33.
 J. Buckley, T. Feuring, Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming, Fuzzy Set. Syst. 109 (2000) 35–53.
 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.
 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.
 A Kumar, J Kaur, P Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35 (2011) 817–823.
 M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput. 179 (2006) 328–343.
 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.