An extension of the linear programming method with fuzzy parameters

International Journal of Mathematics in Operational Research

Volumn 3, Issue 1, 2011, Pages 44-55

  Hatami Marbini, Adel ^a   Tavana, Madjid ^b  

^a LOUVAIN SCHOOL OF MANAGEMENT   (Belgium)

^b LA SALLE UNIVERSITY   (United States)

Author keywords

Decision making; FLP; Fuzzy linear programming; Fuzzy sets

Indexed keywords

EID: 79960241061     PISSN: 17575850     EISSN: 17575869     Source Type: Journal    
DOI: 10.1504/IJMOR.2011.037312     Document Type: Article

References (26)

1. Amid, A., Ghodsypour, S.H. and O'Brien, C. (2006) 'Fuzzy multiobjective linear model for supplier selection in a supply chain', International Journal of Production Economics, Vol. 104, No. 2, pp.394-407. (Pubitemid 44403074)
2. Baykasoǧlu, A. and Göçken, T. (2008) 'A review and classification of fuzzy mathematical programs', Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology, Vol. 19, No. 3, pp.205-229.
3. Bellman, R.E. and Zadeh, L.A. (1970) 'Decision making in a fuzzy environment', Management Science, Vol. 17, No. 4, pp.141-164.
4. Chen, L.H. and Ko, W.C. (2010) 'Fuzzy linear programming models for NPD using a four-phase QFD activity process based on the means-end chain concept', European Journal of Operational Research, Vol. 201, No. 2, pp.619-632.
5. Dubois, D. and Prade, H. (1978) 'Operations on fuzzy numbers', International Journal of Systems, Vol. 9, No. 1, pp.613-626.
6. Ghodousian, A. and Khorram, E. (2008) 'Fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max-min composition', Information Sciences, Vol. 178, No. 2, pp.501-519. (Pubitemid 47600205)
7. Gupta, P. and Mehlawat, M.K. (2009) 'Bector-Chandra type duality in fuzzy linear programming with exponential membership functions', Fuzzy Sets and Systems, Vol. 160, No. 22, pp.3290-3308.
8. Hosseinzadeh Lotfi, F., Allahviranloo, T., Alimardani Jondabeh, M. and Alizadeh, L. (2009) 'Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Applied Mathematical Modelling, Vol. 33, No. 7, pp.3151-3156.
9. Inuiguchi, M. and Ramík, J. (2000) 'Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem', Fuzzy Sets and Systems, Vol. 111, No. 1, pp.3-28.
10. Inuiguchi, M., Ichihashi, H. and Tanaka, H. (1990) 'Fuzzy programming: a survey of recent developments', in Slowinski, R. and Teghem, J. (Eds.): Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, Kluwer Academic Publishers, Dordrecht, pp.45-68.
11. Jana, B. and Roy, T.K. (2005) 'Multi-objective fuzzy linear programming and its application in transportation model', Tamsui Oxford Journal of Mathematical Sciences, Vol. 21, No. 2, pp.243-268.
12. Jiménez, M. (1996) 'Ranking fuzzy numbers through the comparison of its expected intervals', International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 4, No. 4, pp.379-388. (Pubitemid 126545331)
13. Jiménez, M., Arenas, M., Bilbao, A. and Rodríguez, M.V. (2007) 'Linear programming with fuzzy parameters: an interactive method resolution', European Journal of Operational Research, Vol. 177, No. 3, pp.1599-1609. (Pubitemid 44709440)
14. Leung, Y. (1988) Spatial Analysis and Planning under Imprecision, North-Holland, Amsterdam.
15. Lodwick, W.A. and Jamison, K.D. (2007) 'Theoretical and semantic distinctions of fuzzy, possibilistic, and mixed fuzzy/possibilistic optimization', Fuzzy Sets and Systems, Vol. 158, pp.1861-1872. (Pubitemid 47001991)
16. Luhandjula, M.K. (1989) 'Fuzzy optimization: an appraisal', Fuzzy Sets and Systems, Vol. 30, No. 3, pp.257-282.
17. Mahdavi-Amiri, 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, Vol. 158, No. 17, pp.1961-1978. (Pubitemid 47001999)
18. Mula, J., Poler, R. and Garcia-Sabater, J.P. (2008) 'Capacity and material requirement planning modeling by comparing deterministic and fuzzy models', International Journal of Production Research, Vol. 46, No. 20, pp.5589-5606.
19. Peidro, D., Mula, J., Jiménez, M. and Botella, M.M. (2010) 'A fuzzy linear programming based approach f or tactical supply chain planning in an uncertainty environment', European Journal of Operational Research, Vol. 205, No. 1, pp.65-80.
20. Rommelfanger, H. (2007) 'A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values', Fuzzy Sets and Systems, Vol. 158, No. 17, pp.1892-1904. (Pubitemid 47001994)
21. Tan, R.R., Culaba, A.B. and Aviso, K.B. (2008) 'A fuzzy linear programming extension of the general matrix-based life cycle model', Journal of Cleaner Production, Vol. 16, No. 13, pp.1358-1367. (Pubitemid 351787860)
22. Van Hop, N. (2007) 'Solving linear programming problems under fuzziness and randomness environment using attainment values', Information Sciences, Vol. 177, No. 14, pp.2971-2984. (Pubitemid 46661939)
23. Vasant, P.M. (2003) 'Application of fuzzy linear programming in production planning', Fuzzy Optimization and Decision Making, Vol. 2, No. 3, pp.229-241.
24. Wu, H.C. (2008) 'Optimality conditions for linear programming problems with fuzzy coefficients', Computers and Mathematics with Applications, Vol. 55, No. 12, pp.2807-2822.
25. Yager, R.R. (1978) 'Ranking fuzzy subsets over the unit interval', Proceedings of 17th IEEE International Conference on Decision and Control, San Diego, CA, pp.1435-1437.
26. Zimmermann, H.J. (1987) Fuzzy Sets, Decision Making and Expert Systems, Kluwer Academic Publishers, Boston.