Bounded linear programs with trapezoidal fuzzy numbers

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 18, Issue 3, 2010, Pages 269-286

  Ebrahimnejad, Ali ^a   Nasseri, Seyed Hadi ^b   Lotfi, Farhad Hosseinzadeh ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

Bounded linear programming; Fuzzy arithmetic; Fuzzy linear programming; Fuzzy ordering; Trapezoidal fuzzy numbers

Indexed keywords

FUZZY RULES;

BOUNDED LINEAR PROGRAMMING; FUZZY ARITHMETICS; FUZZY LINEAR PROGRAMMING; FUZZY ORDER; LINEAR PROGRAMMING PROBLEM; LINEAR PROGRAMS; LINEAR-PROGRAMMING; NEW APPROACHES; SYMMETRICS; TRAPEZOIDAL FUZZY NUMBERS;

LINEAR PROGRAMMING;

EID: 77952283338     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488510006532     Document Type: Article

References (37)

1. A. Zadeh, On fuzzy mathematical programming, Information and Control 8 (1965) 338-353.
2. H. Tanaka, T. Okuda and K. Asai, On fuzzy mathematical programming, The Journal of Cybernetics 13 (1974) 37-46.
3. H. Tanaka and K. Asai, Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems 13 (1984) 1-10. (Pubitemid 14604937)
4. H. J. Zimmermann, Optimization in fuzzy environment, presented at XXI International TIMES and 46th ORSA Conference (San Juan, Puerto Rioco 1974).
5. D. Dubois and H. Prade,Fuzzy Sets and Systems: Theory and Applications (Academic Press, New York, 1980).
6. H. Tanaka and K. Asai, Fuzzy solution in fuzzy linear programming problems, IEEE Transactions on Systems Man and Cybernetics 14 (1984) 325-328. (Pubitemid 14604164)
7. M. Inuiguchi and M. Sakawa, Possible and necessary optimality tests in possibilistic linear programming problems, Fuzzy Sets and Systems 67 (1994) 29-46.
8. H.-C. Wu, Evaluate fuzzy optimization problems based on biobjective programming problems, Computers and Mathematics with Applications 47 (2004) 893-902.
9. H.-C. Wu, Fuzzy optimization problems based on the embedding theorem and pos-sibility and necessity measures, Mathematical and Computer Modelling 48 (2008) 232-248.
10. H.-C. Wu, Using the technique of scalarization to solve the multiobjective program-ming problems with fuzzy coefficients, Mathematical and Computer Modelling 40 (2004) 329-336.
11. H. R. Maleki, Ranking functions and their applications to fuzzy linear programming, Far East J. Mathematical Sciences 4 (2002) 283-301.
12. N. Mahdavi-Amiri and S. H. Nasseri, Duality in fuzzy number linear programming by use of a certain linear ranking function, Applied Mathematics and Computation 180 (2006) 206-216.
13. N. Mahdavi-Amiri and S. H. Nasseri, Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables, Fuzzy Sets and Systems 158 (2007) 1961-1978.
14. N. Mahdavi-Amiri, S. H. Nasseri and A. Yazadi, Fuzzy primal simplex algorithms for solving fuzzy linear programming problems, Iranian J. Operational Research 1 (2009) 68-84.
15. A. Ebrahimnejad, S. H. Nasseri, F. Hosseinzadeh Lotfi and M. Soltanifar, A primal-dual method for linear programming problems with fuzzy variables, European J. Industrial Engineering 4(2) (2010)189-209.
16. A. Ebrahimnejad and S. H. Nasseri, Using complementary slackness property to solve linear programming with fuzzy parameters, Fuzzy Information and Engineering 3 (2009) 233-245.
17. S. H. Nasseri and A. Ebrahimnejad, A fuzzy primal simplex algorithm and its ap-plication for solving flexible linear programming problems, European J. Industrial Engineering 4(3) (2010) 372-389.
18. S. H. Nasseri and A. Ebrahimnejad, A fuzzy dual simplex method for fuzzy number linear programming problem, Advances in Fuzzy Sets and Systems 5(2) (2010) 81-95.
19. A. Ebrahimnejad and S. H. Nasseri, A dual simplex method for bounded linear pro-grammes with fuzzy numbers, Int. J. Mathematics in Operational Research (in press).
20. J. Ramik, Duality in fuzzy linear programming: Some new concepts and results, Fuzzy Optimization and Decision Making 4 (2005) 25-39.
21. H. C. Wu, An (αβ)-optimal solution concept in fuzzy optimization problems, Optimization 53 (2004) 203-221.
22. S. M. Hashemi, M. Ghatee and B. Hashemi, Fuzzy goal programming: Complementary slackness conditions and computational schemes, Applied Mathematics and Computation 179 (2006) 506-522.
23. J. Ramik, Duality in fuzzy linear programming with possibility and necessity relations, Fuzzy Sets and Systems 157 (2006) 1283-1302.
24. M. Ghatee, S. M. Hashemi, B. Hashemi and Mehdi Dehghan, The solution and duality of imprecise network problems, Computers and Mathematics with Applications 55 (2008) 2767-2790.
25. M. Ghatee and S. M. Hashemi, Ranking function-based solutions of fully fuzzified minimal cost flow problem, Information Sciences 177 (2007) 4271-4294.
26. M. Ghatee and S. M. Hashemi, Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design, Mathematical and Computer Modelling 49 (2009), 1030-1043.
27. S. Chen, Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method, European J. Operational Research 177 (2007) 445-457.
28. S. Muzzioli and H. Reynaerts, The solution of fuzzy linear systems by non-linear programming: a financial application, European J. Operational Research 177 (2007) 1218-1231.
29. M. Jiménez, M. Arenas, A. Bilbao and M. V. Rodríguez, Linear programming with fuzzy parameters: An interactive method resolution, European J. Operational Research 177 (2007) 1599-1609.
30. S. Li and C. Hu, Satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem, European J. Operational Research 197 (2009) 675-684.
31. W. Y. Liu, J. Li, K. Yue, N. Song and H. Yao, An approach for solving fuzzy games, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 14 (2006) 277-292.
32. J. R. Yu and G. H. Tzeng, Fuzzy multiple objective programming in an interval piece-wise regression model, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 17 (2009) 365-376.
33. F. Herrera, J. L. Verdegay and M. Kovacs, Homogeneous linear fuzzy functions and ranking methods in fuzzy linear programming problems, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 2 (1994) 25-35.
34. J. J. Buckley, T. Feuring and Y. Hayashi, Multi-objective fully fuzzified linear programming, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 9 (2001) 605-621.
35. P. M. Vasnat, Solving fuzzy linear programming problems with modified S-Curve membership function, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 13 (2005) 97-109.
36. K. Ganesan and P. Veeramani, Fuzzy linear programming with trapezoidal fuzzy numbers, Ann. Oper. Res. 143 (2006) 305-315.
37. S. H. Nasseri and N. Mahdavi-Amiri, Some duality results on linear programming problems with symmetric fuzzy numbers, Fuzzy Information and Engineering 1 (2009) 59-66.