Revised simplex method and its application for solving fuzzy linear programming problems

European Journal of Industrial Engineering

Volumn 6, Issue 3, 2012, Pages 259-280

  Nasseri, S H ^a   Attari, H ^a   Ebrahimnejad, A ^b  

^a UNIVERSITY OF MAZANDARAN   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

DEA; Fuzzy data envelopment analysis; Fuzzy linear programming; Ranking of fuzzy numbers; Revised simplex method

Indexed keywords

DATA ENVELOPMENT ANALYSIS; FUZZY RULES; FUZZY SET THEORY; INDUSTRIAL RESEARCH;

FUZZY DATA ENVELOPMENT ANALYSIS; FUZZY LINEAR PROGRAMMING; FUZZY LINEAR PROGRAMMING PROBLEMS; FUZZY MATHEMATICAL PROGRAMMING; LINEAR PROGRAMMING MODELS; LINEAR PROGRAMMING PROBLEM; RANKING OF FUZZY NUMBERS; REVISED SIMPLEX METHODS;

LINEAR PROGRAMMING;

EID: 84860734000     PISSN: 17515254     EISSN: 17515262     Source Type: Journal    
DOI: 10.1504/EJIE.2012.046670     Document Type: Article

References (41)

1. Bass, S. and Kwakernaak, H. (1977) 'Rating and ranking of multiple-aspect alternatives using fuzzy sets', Automatica, Vol. 13, pp.47-58. (Pubitemid 8545609)
2. Bellman, R. and Zadeh, L.A. (1970) 'Decision-making in a fuzzy environment', Management Scie., Vol. 17 B, pp.141-164.
3. Benhamadou, M. (2002) 'On the simplex algorithm 'revised form', Advances in Engineering Software, Vol. 33, pp.769-777.
4. Buckley, J.J. (1988) 'Possibilistic linear programming with triangular fuzzy numbers', Fuzzy Sets and Systems, Vol. 26, pp.135-138.
5. Buckley, J.J. (1989) 'Solving possibilistic linear programming problems', Fuzzy Sets and Systems, Vol. 31, pp.329-341.
6. Buckley, J.J. and Feuring, T. (2000) 'Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming', Fuzzy Sets and Systems, Vol. 109, pp.35-53.
7. Cadenas, J.M. and Verdegay, J.L. (2000) 'Using ranking functions in multiobjective fuzzy linear programming', Fuzzy Sets and Systems, Vol. 111, pp.47-53.
8. Campos, L. and Verdegay, J.L. (1989) 'Linear programming problems and ranking of fuzzy numbers', Fuzzy Sets and Systems, Vol. 32, pp.1-11.
9. Chanas, S. (1983) 'The use of parametric programming in fuzzy linear programming', Fuzzy Sets and Systems, Vol. 11, pp.243-251. (Pubitemid 14507024)
10. Chang, W.K. (1981) 'Ranking of fuzzy utilities with triangular membership functions', in International Conference on Policy Analysis and Informations Systems, Tamkang University, ROC, pp.163-171.
11. Chen, S.J. and Hwang, C.L. (1991) Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, Heidelberg.
12. Delgado, M., Verdegay, J.L. and Vila, M.A. (1989) 'A general model for fuzzy linear programming', Fuzzy Sets and Systems, Vol. 29, pp.21-29.
13. Deng, Y. and Zhenfu, Z. (2006) 'Ranking fuzzy numbers with an area method using radius of gyration', Computers and Mathematics with Applications, Vol. 51, pp.1127-1136. (Pubitemid 44038196)
14. Dubios, D. and Prade, H. (1978) 'Operations on fuzzy numbers', J. System Sci., Vol. 9, pp.613-626.
15. Dubois, D. and Prade, H. (1980) 'Ranking fuzzy numbers in the setting of possibility theory', Information Sciences, Vol. 30, pp.183-224.
16. Ebrahimnejad, A. and Nasseri, S.H. (2009) 'Using complementary slackness property to solve linear programming with fuzzy parameters', Fuzzy Information and Engineering, Vol. 3, pp.233-245.
17. Ebrahimnejad, A. and Nasseri, S.H. (2010) 'A dual simplex method for bounded linear programs with fuzzy numbers', International Journal of Mathematics in Operational Research, Vol. 2, No. 6, pp.762-779.
18. Ebrahimnejad, A., Nasseri, S.H. and Hosseinzadeh Lotfi, F. (2010b) 'Bounded linear programs with trapezoidal fuzzy nymbers', International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 18, No. 3, pp.269-286.
19. Ebrahimnejad, A., Nasseri, S.H. and Mansourzadeh, S.M. (Forthcoming) 'Bounded primal simplex algorithm for bounded linear programming with fuzzy cost coefficients', International Journal of Operations Research and Information Systems.
20. Ebrahimnejad, A., Nasseri, S.H., Hosseinzadeh Lotfi, F. and Soltanifar, M. (2010a) 'A primal-dual method for linear programming problems with fuzzy variables', European Journal of Industrial Engineering, Vol. 4, No. 2, pp.189-209.
21. Efstathiou, J. and Tong, R.M. (1982) 'Ranking fuzzy sets: a decision theoretic approach', IEEE Trans. On Systems, Man, and Cybernetics, Vol. 12, No. 5, pp.655-659. (Pubitemid 13464289)
22. Herrera, F., Kovács, M. and Verdegay, J.L. (1993) 'Optimality for fuzzified mathematical programming problems: a parametric approach', Fuzzy Sets and Systems, Vol. 54, pp.279-285.
23. Inuiguchi, M., Ichihashi, H. and Kume, Y. (1993) 'Modality constrained programming problems: a unified approach to fuzzy mathematical programming problems in the setting of possibility theory', Information Sciences, Vol. 67, pp.93-126.
24. Julien, B. (1994) 'An extension to possibilistic linear programming', Fuzzy Sets and Systems, Vol. 64, pp.195-206.
25. Klir, G.J. and Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall PTR.
26. Lai, Y.J. and Hwang, C.L. (1992) Fuzzy Mathematical Programming Methods and Applications, Springer, Berlin.
27. Mahdavi-Amiri, N. and Nasseri, S.H. (2007) 'Duality results and a dual simplex method for linear programming with trapezoidal fuzzy variables', Fuzzy Sets and Systems, Vol. 158, pp.1961-1978. (Pubitemid 47001999)
28. Mahdavi-Amiri, N., Nasseri, S.H. and Yazdani Cherati, A. (2009) 'Fuzzy primal simplex algorithms for solving fuzzy linear programming problems', Iranian Journal of Operational Research, Vol. 2, pp.68-84.
29. Nasseri, S.H. and Ebrahimnejad, A. (2010a) 'A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems', European Journal of Industrial Engineering, Vol. 4, No. 3, pp.372-389.
30. Nasseri, S.H. and Ebrahimnejad, A. (2010b) 'A fuzzy dual simplex method for a fuzzy number linear programming problem', Advances in Fuzzy Sets and Systems, Vol. 5, No. 2, pp.81-95.
31. Nasseri, S.H. and Khabiri, B. (2010) 'A revised simplex algorithm for fuzzy number linear programming problems using linear ranking functions', International Journal of Mathematics and Computation, Vol. 8, No. 10, pp.114-126.
32. Nasseri, S.H. and Mahdavi-Amiri, N. (2009) 'Some duality results on linear programming problems with symmetric fuzzy numbers', Fuzzy Information and Engineering, Vol. 1, pp.59-66.
33. Orlovsky, S.A. (1980) 'On formalization of a general fuzzy mathematical problem', Fuzzy Sets and Systems, Vol. 3, pp.311-321.
34. Ramík, J. and Rímánek, J. (1985) 'Inequality relation between fuzzy numbers and its use in fuzzy optimization', Fuzzy Sets and Systems, Vol. 16, pp.123-138. (Pubitemid 15528219)
35. Tanaka, H., Ichihashi, H. and Asai, K. (1984) 'A formulation of fuzzy linear programming problems based on comparison of fuzzy numbers', Control and Cybernet, Vol. 13, pp.185-194.
36. Verdegay, J.L. (1984) 'A dual approach to solve the fuzzy linear programming problems', Fuzzy Sets and Systems, Vol. 14, pp.131-141.
37. Wanga, Z.X., Liu, Y.J., Fan, Z.P. and Feng, B. (2009) 'Ranking L-R fuzzy number based on deviation degree', Information Sciences, Vol. 179, pp.2070-2077.
38. Yager, R.R. (1981) 'A procedure for ordering fuzzy subsets of the unit interval', Information Sciences, Vol. 24, pp.143-161.
39. Zadeh, L.A. (1965) 'Fuzzy sets', Information and Control, Vol. 8, pp.338-353.
40. Zimmermann, H.J. (1978) 'Fuzzy programming and linear programming with several objective functions', Fuzzy Sets and Systems, Vol. 1, pp.45-55.
41. Zimmermann, H.J. (1985) 'Applications of fuzzy set theory to mathematical programming', Information Sciences, Vol. 36, pp.29-58.