On some optimisation models in a fuzzy-stochastic environment

European Journal of Operational Research

Volumn 207, Issue 3, 2010, Pages 1433-1441

  Luhandjula, M K ^a   Joubert, J W ^b,c  

^a UNIVERSITY OF SOUTH AFRICA   (South Africa)

^b UNIVERSITY OF PRETORIA   (South Africa)

^c DSI CSIR Nanotechnology Innovation Centre   (South Africa)

Author keywords

Fuzziness; Fuzzy random variable; Optimisation; Probabilistic set; Randomness; Uncertain probability

Indexed keywords

FUZZINESS; FUZZY RANDOM VARIABLE; OPTIMISATIONS; PROBABILISTIC SET; RANDOMNESS; UNCERTAIN PROBABILITY;

FUZZY SYSTEMS; MATHEMATICAL PROGRAMMING; RANDOM PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

RANDOM VARIABLES;

EID: 77957701887     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.07.016     Document Type: Article

References (56)

1. E.E. Ammar On fuzzy random multiobjective quadratic programming European Journal of Operational Research 193 2 2009 329 341
2. V. Arnuautu, J. Sprekels, and D. Tiba Optimization problems for curved mechanical structures SIAM Journal on Control and Optimization 44 2 2005 743 775
3. J. Bán Radon-Nikodyḿ theorem and conditional expectation of fuzzy-valued measures and variables Fuzzy Sets and Systems 34 3 1990 383 392
4. R. Bellman, and L.A. Zadeh Decision making in a fuzzy environment Management Science 17 4 1970 141 164
5. F. Ben Abdelaziz, L. Enneifar, and J. Martel A multiobjective fuzzy stochastic program for water resources optimization: The case of lake management Information System and Operational Research Journal 42 3 2004 201 215
6. T. Bhaskar, R. Sundararajan, and P.G. Krishnan A fuzzy mathematical programming approach for cross-sell optimization in retail banking Journal of the Operational Research Society 60 5 2004 717 727
7. J.J. Buckley Uncertain probabilities III: The continuous case Soft Computing 8 3 2004 200 206
8. J.J. Buckley, and E. Eslami Uncertain probabilities I: The discrete case Soft Computing 7 8 2003 500 505
9. J.J. Buckley, and E. Eslami Uncertain probabilities II: The continuous case Soft Computing 8 3 2004 193 199
10. A. Colubi, J.S. Domínguez-Menchero, M. Ló-Díz, and D.A. Ralescu On the formalization of fuzzy random variables Information Sciences 133 1-2 2001 3 6
11. D. Dubois, and H. Prade Fuzzy Sets and Systems: Theory and Applications 1980 Academic Press
12. T. Hasuike, and H. Ishii Probability maximization models for portfolio selection under ambiguity Central European Journal of Operations Research 17 2 2004 159 180
13. K. Hirota Concepts of probablistic sets Fuzzy Sets and Systems 5 1 1981 31 46
14. P. Kall Stochastic Linear Programming 1976 Springer-Verlag
15. P. Kall, and S. Wallace Stochastic Programming 1994 John Wiley
16. H. Katagiri, E.B. Mermri, M. Sakawa, K. Kato, and I. Nishizaki A possibilistic and stochastic programming approach to fuzzy random MST problems IEICE - Transactions on Information Systems E88-D 8 2008 1912 1919
17. H. Katagiri, M. Sakawa, K. Kato, and I. Nishizaki Interactive multiobjective fuzzy random linear programming: Maximization of possibility and probability European Journal of Operational Research 188 2 2008 530 539
18. V. Kratschmer A unified approach to fuzzy random variables Fuzzy Sets and Systems 123 2001 1 9
19. D.L. Kreider, R.G. Kuller, D.R. Ostberg, and F.W. Perkins An Introduction to Linear Analysis 1966 Addison-Wesley
20. R. Kruse, and K.D. Meyer Statistics with Vague Data 1987 Reidel Publishing Company Dordrecht
21. H. Kwakernaak Fuzzy random variables I: Definitions and theorems Information Sciences 15 1 1978 1 29
22. H. Kwakernaak Fuzzy random variables II: Algorithms and examples for the discrete case Information Sciences 17 3 1979 253 278
23. Y.J. Lai, and C.L. Hwang Interactive fuzzy linear programming Fuzzy Sets and Systems 45 2 1992 169 183
24. Y.J. Lai, and C.L. Hwang A stochastic possibilistic programming model for bank hedging decision problems Fuzzy Sets and Systems 57 3 1992 351 363
25. J. Li, J. Xu, and M. Gen A class of multiobjective next term linear programming model with fuzzy random coefficients Mathematical and Computer Modelling 44 11-12 1992 1097 1113
26. B. Liu Fuzzy random chance-constrained programming IEEE Transactions on Fuzzy Systems 9 5 2001 713 720
27. B. Liu Uncertain Theory second ed. 2007 Springer-Verlag Berlin
28. Y.K. Liu, and B. Liu A class of fuzzy random optimization: next term expected value models Information Sciences 155 1-2 1992 89 102
29. Y.K. Liu, and B. Liu Fuzzy random programming with equilibrium chance constraints Information Sciences 170 2-4 2005 363 395
30. M.K. Luhandjula Optimization under hybrid uncertainty Fuzzy Sets and Systems 146 2 2004 187 203
31. M.K. Luhandjula Linear programming under randomness and fuzziness Fuzzy Sets and Systems 10 1-3 1983 45 55
32. M.K. Luhandjula Fuzzy optimization: An appraisal Fuzzy Sets and Systems 30 3 1989 257 282
33. M.K. Luhandjula A Monte Carlo simulation based approach for stochastic semi-infinite mathematical programming problems International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 15 2 2007 139 157
34. M.K. Luhandjula Fuzzy stochastic linear programming: Survey and future research directions European Journal of Operational Research 174 3 2006 1353 1367
35. M.K. Luhandjula, and M.M. Gupta On fuzzy stochastic optimization Fuzzy Sets and Systems 81 1 1996 47 55
36. M.K. Luhandjula, H. Ichihashi, and M. Inuiguchi Fuzzy and semi-infinite mathematical programming Information Sciences 61 3 1992 233 250
37. C. Mohan, and H. Nguyen A fuzzifying approach to stochastic programming Operations Research 34 2 1997 73 96
38. S. Nanda, G. Panda, and J. Dash A new solution method for fuzzy chance constrained programming problem Fuzzy Optimization and Decision Making 5 4 2006 355 370
39. L. Pachter, and B. Sturmfels The mathematics of phylogenomics SIAM Review 49 1 2007 3 31
40. T. Peña, P. Lara, and C. Castrodeza Multiobjective stochastic programming for feed formulation The Journal of the Operational Research Society 60 12 2009 1738 1748
41. M. Sakawa Fuzzy sets and Interactive Optimization 1993 Plenum Press
42. R. Schultz, and S. Tiedemann Conditional value-at-risk in stochastic programs with mixed-integer recourse Mathematical Programming 105 2 2006 365 386
43. G. Shackle Decision, Order and Time in Human Affairs 1961 Cambridge University Press
44. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press
45. A. Shiryaer Probability second ed. 1996 Springer-Verlag
46. H. Simon Administration Behaviour 1945 Free Press
47. S. Vajda Probabilistic Programming 1972 Academic Press
48. N. Van Hop Solving fuzzy (stochastic) linear programming problems using superiority and inferiority measures Information Sciences 177 9 2007 1977 1991
49. N. Van Hop Solving linear programming problems under fuzziness and randomness environment using attainment values Information Sciences 177 14 2007 2971 2984
50. M.R. Wagner Stochastic 0-1 linear programming under limited distributional information Operations Research Letters 36 2 2008 150 156
51. K. Weber, and Z. Sun Fuzzy stochastic dynamic programming for marketing decision support International Journal of Intelligent Systems 15 8 2007 763 783
52. L.A. Zadeh Probability measures of fuzzy events Journal of Mathematical Analysis and Applications 23 2 1968 421 427
53. K. Zhou, J. Doyle, and K. Glover Robust and Optimal Control 1996 Prentice-Hall Englewood Cliffs
54. H.J. Zimmerman Description and optimization of fuzzy systems International Journal of General Systems 2 4 1976 209 215
55. Z. Zmekal Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option European Journal of Operational Research 135 2 2001 303 310
56. Z. Zmekal Value at risk methodology under soft conditions approach (fuzzy-stochastic approach) European Journal of Operational Research 161 2 2005 337 347