The solution and duality of imprecise network problems

Computers and Mathematics with Applications

Volumn 55, Issue 12, 2008, Pages 2767-2790

  Ghatee, Mehdi ^a   Hashemi, S Mehdi ^a   Hashemi, Behnam ^a   Dehghan, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Discrete optimization; Duality theorems; Fuzzy cost; Fuzzy supply demand; Optimality conditions; Risk taking

Indexed keywords

DECISION MAKING; FUZZY RULES; MATHEMATICAL MODELS; NETWORK ARCHITECTURE; NUMERICAL METHODS; SUPPLY CHAIN MANAGEMENT;

DISCRETE OPTIMIZATION; DUALITY THEOREMS; FUZZY COST; FUZZY SUPPLY-DEMAND; OPTIMALITY CONDITIONS; RISK TAKING;

PROBLEM SOLVING;

EID: 43049140493     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.10.023     Document Type: Article

References (51)

1. Montemanni R., Gambardella L.M., and Donati A.V. A branch and bound algorithm for the robust shortest path problem with interval data. Operation Research Letters 32 (2004) 225-232
2. Sengupta A., and Pal T.K. Solving the shortest path problem with interval arcs. Fuzzy Optimization and Decision Making 5 (2006) 79-99
3. Hashemi S.M., Ghatee M., and Nasrabadi E. Combinatorial algorithms for minimal interval cost flow problem. Applied Mathematics and Computation 175 (2006) 1200-1216
4. Sengupta A., and Pal T.K. Theory and methodology on comparing interval numbers. European Journal of Operational Research 127 (2000) 28-43
5. Wang X., and Kerre E. Reasonalble properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118 (2001) 375-385
6. Wang X., and Kerre E. Reasonalble properties for the ordering of fuzzy quantities (II). Fuzzy Sets and Systems 118 (2001) 387-405
7. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press, New York
8. Tanaka H., and Asai K. Fuzzy solution in fuzzy linear programming problems. IEEE Transactions on Systems Man and Cybernetics 14 (1984) 325-328
9. Inuiguchi M., and Sakawa M. Possible and necessary optimality tests in possibilistic linear programming problems. Fuzzy Sets and Systems 67 (1994) 29-46
10. Wu H.-C. Evaluate fuzzy optimization problems based on biobjective programming problems. Computers and Mathematics with Applications 47 (2004) 893-902
11. Wu H.-C. Fuzzy optimization problems based on the embedding theorem and possibility and necessity measures. Mathematical and Computer Modelling 40 (2004) 329-336
12. Maleki H.R. Ranking functions and their applications to fuzzy linear programming. Far East Journal of Mathematical Sciences 4 (2002) 283-301
13. Mahdavi-Amiri N., and Nasseri S.H. Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets and Systems 158 (2007) 1961-1978
14. Ramik J. Duality in fuzzy linear programming: Some new concepts and results. Fuzzy Optimization and Decision Making 4 (2005) 25-39
15. Wu H.C. An (α, β)-optimal solution concept in fuzzy optimization problems. Optimization 53 (2004) 203-221
16. Kuk H., and Tanino T. Optimality and duality in nonsmooth multiobjective optimization involving generalized type I functions. Computers and Mathematics with Applications 45 (2003) 1497-1506
17. 2 linear programming: A constructive approach. Journal of Mathematical Analysis and Applications 194 (1995) 389-413
18. W. Rodder, H.J. Zimmermann, Duality in fuzzy linear programming, in: A.V. Fiacco, K.O. Kortanek (Eds.), Extremal Methods and System Analysis, Berlin, New York, 1980, pp. 415-429
19. Hamacher H., Liberling H., and Zimmermann H.J. Sensitivity analysis in fuzzy linear programming. Fuzzy Sets and Systems 1 (1978) 269-281
20. Bector C.R., and Chandra S. On duality in linear programming under fuzzy environment. Fuzzy Sets and Systems 125 (2002) 317-325
21. Verdegay J.L. A dual approach to solve the fuzzy linear programming problems. Fuzzy Sets and Systems 14 (1984) 131-141
22. Hashemi S.M., Modarres M., Nasrabadi E., and Nasrabadi M.M. Fully fuzzified linear programming, solution and duality. Journal of Intelligent & Fuzzy Systems 17 (2006) 253-261
23. Inuiguchi M., Ramik J., Tanio T., and Vlach M. Satisficing solutions and duality in interval and fuzzy linear programming. Fuzzy Sets and Systems 135 (2003) 151-177
24. Hashemi S.M., Ghatee M., and Hashemi B. Fuzzy goal programming: Complementary slackness conditions and computational schemes. Applied Mathematics and Computation 179 (2006) 506-522
25. Ramik J. Duality in fuzzy linear programming with possibility and necessity relations. Fuzzy Sets and Systems 157 (2006) 1283-1302
26. Zhong Y., and Shi Y. Duality in fuzzy multi-criteria and multi-constraint level linear programming: A parametric approach. Fuzzy Sets and Systems 132 (2002) 335-346
27. Lee B.I., Chung N.K., and Tcha D.W. A parallel algorithm and duality for a fuzzy multiobjective linear fractional programming problem. Computers & Industrial Engineering 20 (1991) 367-372
28. Sakawa M., and Yano H. A fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems. Fuzzy Sets and Systems 67 (1994) 1927
29. Zhang C., Yuan X.H., and Lee E.S. Duality theory in fuzzy mathematical programming problems with fuzzy coefficients. Computers and Mathematics with Applications 49 (2005) 1709-1730
30. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353
31. Wu H.-C. Duality theory in fuzzy linear programming problems with fuzzy coefficients. Fuzzy Optimization and Decision Making 2 (2003) 6173
32. Wu H.-C. Duality theory in fuzzy optimization problems. Fuzzy Optimization and Decision Making 3 (2004) 345-365
33. Okada S., and Soper T. A shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets and Systems 109 (2000) 129-140
34. Lin C.J., and Wen U.P. A labeling algorithm for the fuzzy assignment problem. Fuzzy Sets and Systems 142 (2004) 373-391
35. Shih H.S., and Lee E.S. Fuzzy multi-level minimum cost flow problems. Fuzzy Sets and Systems 107 (1999) 159-176
36. Sakawa M. Fuzzy Sets and Interactive Multiobjective Optimization (1993), Plenum Press, New York, London
37. Sakawa M., Nishizaki I., and Uemura Y. Interactive fuzzy programming for multilevel linear programming problems. Computers and Mathematics with Applications 36 (1998) 71-86
38. Sakawa M., Nishizaki I., and Uemura Y. Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Fuzzy Sets and Systems 115 (2000) 93-103
39. Noda A.S., and Mortin C.G. An algorithm for the biobjective integer minimum cost flow problem. Computers & Operation Research 28 (2001) 139-156
40. Perny P., and Spanjaard O. A preference-based approach to spanning trees and shortest paths problems. European Journal of Operational Research 162 (2005) 584-601
41. Hukuhara M. Intégration des applications measurable dont la valeur est un compact convexe. Funkcialaj Ekvacioj 10 (1967) 205-223
42. Wu H.-C. Duality theorems in fuzzy mathematical programming problems based on the concept of necessity. Fuzzy Sets and Systems 139 (2003) 363-377
43. Giachetti R.E., and Young R.E. A parametric representation of fuzzy numbers and their arithmetic operators. Fuzzy Sets and Systems 91 (1997) 185-202
44. Wagenknecht M., Hampel R., and Schneider V. Computational aspects of fuzzy arithmetics based on Archimedean t-norms. Fuzzy Sets and Systems 123 (2001) 49-62
45. Diamond P., and Korner R. Extended fuzzy linear models and least squares estimates. Computers and Mathematics with Applications 33 (1997) 15-32
46. Diamond P., and Kloeden P. Metric Spaces of Fuzzy Sets (1995), World Scientiffc, Singapore
47. Hansen E. Global Optimization Using Interval Analysis (1992), Marcel Dekker Inc., USA
48. Chang P.T., and Lee E.S. Fuzzy linear regression with spreads unrestricted in sign. Computers and Mathematics with Applications 28 (1994) 61-70
49. M. Filaseta, Algebric number theory, Instructor notes, University of South Carolina, 1999
50. Ahuja R.K., Magnanti T.L., and Orlin J.B. Network Flows (1993), Prentice-Hall, Englewood Cliffs
51. Bector C.R., Chandra S., and Vijay V. Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs. Fuzzy Sets and Systems 146 (2004) 253-269