Fuzzy linear programming with grades of satisfaction in constraints

Iranian Journal of Fuzzy Systems

Volumn 6, Issue 3, 2009, Pages 17-35

  Javadian, N ^a   Maali, Y ^a   Mahdavi Amiri, N ^b  

^a DEPARTMENT OF INDUSTRIAL ENGINEERING   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fuzzy constraints; Fuzzy linear programming; Multi objective linear programming

Indexed keywords

EID: 77953546964     PISSN: 17350654     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. R. E. Bellman and L. A. Zadeh, Decision making in fuzzy environment, Management Science. 17 (1970), 141-164.
2. V. J. Bowman, On the relationship of the Tchebycheff norm and the efficient frontier of mul-ticriteria objectives. In: H. Thiriez and S. Zionts (Eds.), Multiple Criteria Decision Making, Springer-Verlag, Berlin, 1976, 76-86.
3. J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods, Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-21.
4. M. Delgado, J. L. Verdegay and M. A. Vila, A general model for fuzzy linear programming. Fuzzy Sets and Systems, 29 (1989), 21-29.
5. S. C. Fang and C. F. Hu, Linear programming with fuzzy coefficients in constraints, Computers and Mathematics with Applications, 37 (1999), 63-76.
6. S. M. Guu and Y. K. Wu, Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets and Systems, 107 (1999), 191-195.
7. U. Keymak and J. M. Sousa, Weighting of constraint in fuzzy optimization. Proceedings of the 10th IEEE International Conference on Fuzzy Systems, 3 (2001), 1131-1134.
8. K. Kosaka, H. Nonaka, M. F. Kawaguchi and T. Datet, The application of fuzzy linear programming to flow control of crossing gate network. Proceeding of the 9th Fuzzy System Symposium: Sapporo, (1993), 189-1182
9. Y. J. Lai and C. L. Hwang, Fuzzy mathematical programming, Springer, Berlin, 1992.
10. F. Li, M. Liu, C. Wu and S. Lou, Fuzzy optimization problems based on inequality degree, Proceedings of the First International Conference on Machine Learning and Cybernetics: Beijing, (2002), 1566-1570.
11. X. Q. Li, B. Zhang and H. Li, Computing efficient solutions to fuzzy multiple objective linear programming problems, Fuzzy Sets and Systems, 157 (2006), 1328-1332.
12. N. Mahdavi-Amiri and S. H. Nasseri, Duality results and a dual simplex method for linear programming problems with trapezoidal variables, Fuzzy Sets and Systems, 158 (2007), 1961-1978.
13. H. R. Maleki, M. Tata, and M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Sets and Systems, 109 (2000), 21-33.
14. Y. Nakahara, User oriented ranking criteria and its application to fuzzy mathematical programming problems. Fuzzy Sets and Systems, 94 (1998), 275-286.
15. S. Nakamura, K. Kosakat, M. F. Kawaguchi, H. Nonaka and T. Datet, Fuzzy linear programming with grade of satisfaction in each constraint. Proceedings of the Joint Fourth IEEE International Conference on Fuzzy Systems and the Second International Fuzzy Engineering Symposium, (1995), 781-786.
16. J. R. Ramik and H. Rommelfanger, Fuzzy mathematical programming based on some new inequality relations, Fuzzy Sets and Systems, 81 (1996), 77-87.
17. H. Rommelfanger, Fuzzy linear programming and applications, European Journal of Operational Research, 92 (1996), 512-527.
18. M. Sakawa, Fuzzy sets and interactive multiobjeetive optimization, Plenum Press: New York and London, 1993.
19. H. Tanaka, T. Okuda and K. Asai, On fuzzy mathematical programming. Journal of Cybernetics, 3 (1974), 37-46.
20. J. L. Verdegay, Fuzzy mathematical programming. In : M. M. Gupta, and E. Sanchez (Eds.), Approximate Reasoning in Decision Analysis, North-Holland: Amsterdam, 1982, 231-236.
21. B. Werners, An interactive fuzzy programming system, Fuzzy Sets and Systems, 23 (1987), 131-147.
22. B. Werners, Interactive multiple objective programming subject to flexible constraints, European Journal of Operational Research, 31 (1987), 342-349.
23. B. Werners, Aggregation models in mathematical programmi?ig, In: G. Mitra (Ed.), Mathematical Models for Decision Support, Springer, Berlin, (1988), 295-305.
24. Y. K. Wu, On the manpower allocation within matrix organization: a fuzzy linear programming approach, European Journal of Operational Research, 183(1) (2007), 384-393.
25. L. Ximvang, Measuring the satisfaction of constraints in fuzzy linear programming. Fuzzy Sets and Systems, 122 (2001), 263-275.
26. L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
27. H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of General Systems, 2 (1976), 209-215.