A Novel Technique for Solving Multiobjective Fuzzy Linear Programming Problems
Abstract
This study considers multiobjective fuzzy linear programming (MFLP) problems in which the coefficients in the objective functions are triangular fuzzy numbers. The study proposing a new technique to transform MFLP problems into the equivalent single fuzzy linear programming problem and then solving it via linear ranking function using the simplex method, supported by numerical example.
Downloads
References
Allahviranloo, T., Hosseinzadeh, L.F., Kiasary, M.K., Kiani, N.A. and
Alizadeh, L., 2008. Solving full fuzzy linear programming problem by the
ranking function. Applied Mathematical Sciences, 2(1), pp.1932.
Amid, A., Ghodsypour, S.H. and Obrien, C., 2006. Fuzzy multiobjective
linear model for supplier selection in a supply chain. International journal of Production Economics, 104, pp.394407.
Amid, A., Ghodsypour, S.H. and Obrien, C., 2011. A weighted maxmin model for fuzzy multio´ bjective supplier selection in a supply chain. International Journal of Production Economics, 131, pp.139145.
Baky, I A., 2009. Fuzzy goal programming algorithm for solving decentralized bilevel multiobjective programming problems. Fuzzy Sets and Systems, 160, pp.27012713.
Baky, I.A., 2010. Solving multilevel multiobjective linear programming
problems through fuzzy goal programming approach. Applied Mathematical Modelling, 34, pp.23772387.
Bellman, R.F. and Zadeh, L.A., 1970. Decision making in fuzzy environment. Management Science, 17(4), pp.141146.
Buckley, J.J. and Feuring, T., 2000. Evolutionary algorithm solution to fuzzy problems. Fuzzy Sets and Systems, 109, pp.3553.
Cadenas, J.M. and Verdegay, J.L., 2000. Using ranking functions in multiobjective fuzzy linear programming. FuzzySets and Systems, 111, pp.4753.
Chen, L.H. and Ko, W.C., 2009. Fuzzy linear programming models for new product design using QFD with FMEA. Applied Mathematical Modelling, 33(2), pp.633647.
Chiang, J., 2005. The OS of the transportation problem with fuzzy demand and fuzzy product. Journal of Information Science and Engineering, 21, pp.439451.
Dantzig, G.B., 1963. Linear programming and extensions. University Press, Princeton.
Dehghan, M., Hashemi, B. and Ghatee, M., 2006. Computational methods for solving fully fuzzy linear system. Applied Mathematics and Computation, 179, pp.328343.
Dubois, D. and Prade, H., 1978. Operations on fuzzy numbers. International Journal of Systems Science, 9(6), pp.613626.
Ebrahimnejad, A., 2011. Sensitivity analysis in fuzzy number linear programming problems. Mathematical and Computer Modelling, 53(910), pp.18781888.
Ebrahimnejad, A. and Tavana, M., 2014. A novel method for solving linear programming problems with symmetrictrapezoidal fuzzy numbers. Applied Mathematical Modelling. Availale from: http://www.dx.doi.org/10.1016/j.apm.2014.02.024.13.
Fang, S.C. and Hu, C.F., 1996. Linear programming with fuzzy coefficients in constraints. Computers and Mathematics with Applications, 37(10), pp.6376.
Fortemps, P. and Roubens, M., 1996. Ranking and defuzzification methods based on area compensation. Fuzzy Sets Systems, 82(3), pp.319330.
Ganesan, K. and Veeramani, P., 2006. Fuzzy linear programming with trapezoidal fuzzy numbers. Annals of Operations Research, 143, pp.305315.
GarciaAguado, C. and Verdegay, J.L., 1993. On the sensitivity of membership functions for fuzzy linear programming problems. Fuzzy Sets Systems, 56(1), pp.4749.
Gupta, A. and Kumar, A., 2012. A new method for solving linear multiobjective transportation problems with fuzzy parameters. Applied Mathematical Modelling, 36, pp.14211430.
Hamadameen, A.O. and Zainuddin, Z.M., 2013. Multiobjective fuzzy stochastic linear programming problems in the 21st century. Life Science Journal, 10(4), pp.616647.
Hashemi, S., Nasrabadi, M.M.E. and Nasrabadi, M., 2006. Fully fuzzified linear programming, solution and duality. Journal of Intelligent and Fuzzy Systems, 17(3), pp.253261.
Hassanzadeh, A.S., Razmi, J. and Zhang, G., 2011. Supplier selection and order allocation based on fuzzy SWOT analysis and fuzzy linear programming. Expert Systems with Applications, 38(1), pp.334342.
Hosseinzadeh Lotfi, F., Allahviranloo, T., Alimardani, J.M. and Alizadeh, L., 2009. Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied Mathematical Modelling, 33(7), pp.31513156.
Inuiguchi, M., Ichihashi, H. and Tanaka, H., 1990. Fuzzy programming: A survey of recent developments. In: Slowinski, R. and Teghem, J., editors. Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Underuncertainty. Kluwer Academic Publishers, Dordrecht.
Iskander, M.G., 2002. Comparison of fuzzy numbers using possibility
programming: Comments and new concepts. Computers and Mathematics with Applications, 43, pp.833840.
Iskander, M.G., 2008. A computational comparison between two evaluation criteria in fuzzy multiobjective linear programs using possibility programming. Computers and Mathematics with Applications, 55, pp.25062511.
Kumar, A., Kaur, J. and Singh, P., 2011. A new method for solving fully fuzzy linear programming problems. Applied Mathematical Modelling, 35, pp.817823.
Lai, Y.J. and Hwaang, C.L., 1992. Fuzzy Mathematical Programming Methods and Applications. Springer, Berlin. Luhandjula, M.K., 1989. Fuzzy optimization: An appraisal. Fuzzy Sets and System, 30(3), pp.257282.
Luhandjula, M.K. and Rangoaga, M.J., 2014. An approach for solving a fuzzy multiobjective programming problem. European Journal of Operational Research, 232, pp.249255.
MahdaviAmiri, N. and Nasseri, S.H., 2006. Duality in fuzzy number linear programming by use of a certain linear ranking function. Applied Mathematics and Computation, 180(1), pp.206216.
MahdaviAmiri, N. and Nasseri, S.H., 2007. Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets and Systems, 158(17), pp.19611978.
Maleki, H.R., 2003. Ranking functions and their applications to fuzzy linear programming. Far East Journal of Mathematical Sciences, 4(3), pp.283301.
Maleki, H.R., Tata, M. and Mashinchi, M., 2000. Linear programming with
fuzzy variables. Fuzzy Sets and Systems, 109(1), pp.2133.
Nasseri, S.H., Ardil, E., Yazdani, A. and Zaefarian, R., 2005. Simplex method for solving linear programming problem with fuzzy number. World Academy of Science, Engineering and Technology, 10, pp.284288.
Negi, D.S. and Lee, E.S., 1993. Possibility programming by the comparison of fuzzy numbers. Computers and Mathematics with Application, 25, pp.4350.
Peidro, D., Mula, J., Jimenez, M. and Botella, M., 2010. A fuzzy linear
programming based approach for tactical supply chain planning in an uncertainty environment. European Journal of Operational Research, 205(1), pp.6580.
Rong, A. and Lahdelma, R., 2008. Fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production. European Journal of Operational Research, 186(3), pp.953964.
Roubens, M. and Jacques, T.J., 1991. Comparison of methodologies for fuzzy and stochastic multiobjective programming. Fuzzy Sets and Systems, 42(1), pp.119132.
Sakawa, M., 1993. Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press, New York.
Sakawa, M., Nishizaki, I. and Uemura, Y., 2000. Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters. Fuzzy Sets and Systems, 109, pp.319.
Sharma, S.D., 2012. Operations Research. Kedar Nath Ram Nath, Meerut, New Delhi, India.
Shoacheng, T., 1994. Interval number and fuzzy number linear programming. Fuzzy Sets and Systems, 66(3), pp.301306.
Stanciulescu, C., Fortemps, P., Installe, M. and Wertz, V., 2003. Multiobjective fuzzy linear programming problems with fuzzy decision variables. European Journal of Operational Research, 149, pp.654672.
Tanaka, H., Okuda, T. and Asai, K., 1974a. On fuzzy mathematical programming. Journal of Cybernetics, 3(4),pp.3746.
Tanaka, H., Okuda, T. and Asai, K., 1974b. On fuzzy mathematical programming. Journal of Cybernetics, 3(4), pp.131141.
Ullah Khan, I., Ahmad, T. and Maan, N., 2013. A simplified novel Technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), pp.536546.
Wang, L.X., 1997. A Course in Fuzzy Systems and Control. PrenticeHall, Inc., USA.
Wang, X. and Kerre, E., 2001. Reasonable properties for the ordinary of fuzzy quantities (part II). Fuzzy Sets and Systems, 118(3), pp.375405.
Wu, H., 2008a. Optimality conditions for linear programming problems with fuzzy coefficients. Computers and Mathematics with Applications, 55, pp.28072822.
Wu, H.C., 2008b. Using the technique of scalarization to solve the multiobjective programming problems with fuzzy coefficients. Mathematical and Computer Modelling, 48, pp.232248.
Yager, R.R., 1981. A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24(2), pp.143161.
Yager, R.R. and Filev, D.P., 1994. Essentials of Fuzzy Modeling and Control. John Wiley and Sons, Inc., USA.
Zadeh, L.A., 1965. Fuzzy Sets. Information and Control, 8, pp.338353.
Zhang, C., Yuan, X.H. and Lee, E.S., 2005. Duality theory in fuzzy mathematical programming problems with fuzzy coefficients. Computers and Mathematics with Applications, 49(11), pp.17091730.
Zimmermann, H.J., 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, pp.4555.
Zimmermann, H.J., 1987. Fuzzy Sets, Decision Making and Expert Systems. Kluwer Academic Publishers, Boston.
Copyright (c) 2017 Abdulqader O. Hamadameen
This work is licensed under a Creative Commons AttributionNonCommercialShareAlike 4.0 International License.
Authors who choose to publish their work with Aro agree to the following terms:

Authors retain the copyright to their work and grant the journal the right of first publication. The work is simultaneously licensed under a Creative Commons Attribution License [CC BYNCSA 4.0]. This license allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

Authors have the freedom to enter into separate agreements for the nonexclusive distribution of the journal's published version of the work. This includes options such as posting it to an institutional repository or publishing it in a book, as long as proper acknowledgement is given to its initial publication in this journal.

Authors are encouraged to share and post their work online, including in institutional repositories or on their personal websites, both prior to and during the submission process. This practice can lead to productive exchanges and increase the visibility and citation of the published work.
By agreeing to these terms, authors acknowledge the importance of open access and the benefits it brings to the scholarly community.