Interactive multiobjective fuzzy random linear programming: Maximization of possibility and probability

European Journal of Operational Research

Volumn 188, Issue 2, 2008, Pages 530-539

  Katagiri, Hideki ^a   Sakawa, Masatoshi ^a   Kato, Kosuke ^a   Nishizaki, Ichiro ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Fuzzy random variable; Interactive algorithm; Multiobjective linear programming; Possibilistic programming; Probability maximization model; Stochastic programming

Indexed keywords

DECISION MAKING; LINEAR PROGRAMMING; RANDOM VARIABLES; STOCHASTIC PROGRAMMING;

FUZZY RANDOM VARIABLES; INTERACTIVE ALGORITHMS; MULTIOBJECTIVE LINEAR PROGRAMMING; POSSIBILISTIC PROGRAMMING; PROBABILITY MAXIMIZATION MODELS;

FUZZY SETS;

EID: 38149076033     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2007.02.050     Document Type: Article

References (46)

1. Beale E.M.L. On optimizing a convex function subject to linear inequalities. Journal of the Royal Statistical Society 17 (1955) 173-184
2. Charnes A., and Cooper W.W. Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Research 11 (1955) 18-39
3. Charnes A., and Cooper W.W. Goal programming and multiple objective functions. European Journal of Operational Research 1 (1977) 39-54
4. Dantzig G.B. Linear programming under uncertainty. Management Science 1 (1955) 197-206
5. Dutta P., Chakraborty D., and Roy A.R. A single-period inventory model with fuzzy random variable demand. Mathematical and Computer Modelling 41 (2005) 915-922
6. Dubois D., and Prade H. Fuzzy Sets and Systems (1980), Academic Press, New York
7. Geoffrion A.M. Stochastic programming with aspiration or fractile criteria. Management Science 13 (1967) 672-679
8. Gil M.A., Lopez-Diaz M., and Ralescu D.A. Overview on the development of fuzzy random variables. Fuzzy Sets and Systems 157 (2006) 2546-2557
9. Ignizio J.P. Generalized goal programming: Overview. Computer & Operations Research 10 (1983) 277-289
10. Inuiguchi M., and Ramik J. Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems 111 (2000) 3-28
11. H. Katagiri, H. Ishii, T. Itoh, Fuzzy random linear programming problem, in: Proceedings of Second European Workshop on Fuzzy Decision Analysis and Neural Networks for Management, Planning and Optimization, 1997, pp. 107-115.
12. H. Katagiri, H. Ishii, Linear programming problem under fuzziness and randomness, in: Proceedings of International Conference on Applied Stochastic System Modeling, 2000, pp. 97-106.
13. Katagiri H., and Ishii H. Chance constrained bottleneck spanning tree problem with fuzzy random edge costs. Journal of the Operations Research Society of Japan 43 (2000) 128-137
14. Katagiri H., and Sakawa M. An interactive fuzzy satisficing method for fuzzy random linear multiobjective 0-1 programming problems through the expectation optimization model. Mathematical and Computer Modelling 40 (2004) 411-421
15. H. Katagiri, M. Sakawa, H. Ishii, Multiobjective fuzzy random linear programming using E-model and possibility measure, in: Proceedings of Joint Ninth IFSA and World Congress and 20th NAFIPS International Conference, 2001, pp. 2295-2300.
16. Katagiri H., Sakawa M., and Ohsaki S. An interactive satisficing method through the variance minimization model for fuzzy random multiobjective linear programming problems. In: Tanino T., Tamaki T., and Inuiguchi M. (Eds). Multi-Objective Programming and Goal Programming: Theory and Applications (Advances in Soft Computing) (2003), Springer-Verlag 171-176
17. H. Katagiri, M. Sakawa, K. Kato, S. Ohsaki, An interactive satisficing method based on the fractile optimization model using possibility and necessity measure for fuzzy random multiobjective linear programming problem, in: Proceedings of the Asia Pacific Management Conference, 2003, pp. 795-802.
18. Katagiri H., and Sakawa M. A study on fuzzy random linear programming problems based on possibility and necessity measure. In: Bilgic T., Baets B.D., and Kaynak O. (Eds). Fuzzy Sets and Systems - IFSA 2003 (Lecture Notes in Computer Science) (2003), Springer 725-732
19. Katagiri H., Mermri E.B., Sakawa M., Kato K., and Nishizaki I. A possibilistic and stochastic programming approach to fuzzy random MST problems. IEICE Transaction on Information and Systems E88-D (2005) 1912-1919
20. Katagiri H., Sakawa M., and Ishii H. Fuzzy random bottleneck spanning tree problems. European Journal of Operational Research 152 (2004) 88-95
21. Kataoka S. A stochastic programming model. Econometrica 31 (1963) 181-196
22. Kaufman A., and Gupta M.M. Introduction to Fuzzy Arithmetic: Theory and Applications (1985), Van Nostrand Reinhold Company
23. Klir G.J., and Folger T.A. Fuzzy Sets, Uncertainty, and Information (1988), Prentice Hall
24. Korner R., and Nather W. Linear regression with random fuzzy variable: Extended classical estimates, best linear estimates, least squares estimates. Journal of Information Sciences 109 (1998) 95-118
25. Kruse R., and Meyer K.D. Statistics with Vague Data (1987), D. Riedel Publishing Company
26. Kuhn H.W., and Tucker A.W. Nonlinear programming. In: Neyman J. (Ed). Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (1951), University of California Press 481-492
27. Kwakernaak H. Fuzzy random variable-1. Information Sciences 15 (1978) 1-29
28. Li S., and Ogura Y. Fuzzy random variables, conditional expectations and fuzzy valued martingales. Journal of Fuzzy Mathematics 4 (1996) 905-927
29. Liu B. Fuzzy random chance-constrained programming. IEEE Transaction on Fuzzy Systems 9 (2001) 713-720
30. Liu B. Fuzzy random dependent-chance programming. IEEE Transaction on Fuzzy Systems 9 (2001) 721-726
31. Lopez D.M., and Gil M.A. Constructive definitions of fuzzy random variables. Statistics & Probability Letters 36 (1997) 135-143
32. Lopez D.M., and Gil M.A. An extension of Fubini's theorem for fuzzy random variables. Information Sciences 115 (1999) 29-41
33. Luhandjula M.K., and Gupta M.M. On fuzzy stochastic optimization. Fuzzy Sets and Systems 81 (1996) 47-55
34. Puri M.L., and Ralescu D.A. Fuzzy random variables. Journal of Mathematical Analysis and Applications 14 (1986) 409-422
35. Qiao Z., and Wang G. On solutions and distribution problems of the linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems 50 (1993) 120-155
36. Ramik J. New interpretation of the inequality relations in fuzzy goal programming problems. Central European Journal for Operations Research and Economics 4 (1996) 279-294
37. Ramik J., and Vlach M. Generalized Concavity in Optimization and Decision Making (2001), Kluwer Publ. Comp., Boston, Dordrecht, London
38. Wang G.-Y., and Qiao Z. Linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems 57 (1993) 295-311
39. A.P. Wierzbicki, The use of reference objectives in multiobjective optimization - Theoretical implications and practical experiences, WP-79-66, International Institute for Applied Systems Analysis, Laxenburg, Austria, 1979.
40. Wu H.-C. Pricing European options based on the fuzzy pattern of Black-Sholes formula. Computer & Operations Research 31 (2004) 1069-1081
41. Yoshida Y. A stopping game in a stochastic and fuzzy environment. Mathematical and Computer Modelling 30 (1999) 147-158
42. Yoshida Y., Yasuda M., Nakagami J., and Kurano M. A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty. Fuzzy Sets and Systems 157 (2006) 2614-2626
43. Zadeh L.A. Probability measure of fuzzy events. Journal of Mathematical Analysis and Applications 23 (1968) 421-427
44. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28
45. Zmeskal Z. Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach). International Review of Financial Analysis 14 (2005) 263-275
46. Zimmermann H.-J. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1 (1978) 45-55