Interactive decision making using possibility and necessity measures for a fuzzy random multiobjective 0-1 programming problem

Cybernetics and Systems

Volumn 37, Issue 1, 2006, Pages 59-74

  Katagiri, Hideki ^a   Sakawa, Masatoshi ^a   Nishizaki, Ichiro ^a,b  

^a HIROSHIMA UNIVERSITY   (Japan)

^b NONE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; FUZZY SETS; INTERACTIVE COMPUTER SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; STOCHASTIC PROGRAMMING;

FUZZINESS; POSSIBILISTIC PROGRAMMING; RANDOMNESS; REFERENCE POINT METHOD;

DECISION MAKING;

EID: 29044433092     PISSN: 01969722     EISSN: 10876553     Source Type: Journal    
DOI: 10.1080/01969720500320817     Document Type: Article

References (23)

1. Beak, E. M. L. 1955. On optimizing a convex function subject to linear inequalities. Journal of Royal Statistic Society, 17:173-184.
2. Charnes, A. and W. W. Cooper. 1963. Deterministic equivalents for optimizing and satisfying under chance constraints. Operations Research, 11:18-39.
3. Dantzig, G. B. 1955. Linear programming under uncertainty. Management Science, 1:197-206.
4. Geoffrion, A. M. 1978. Stochastic programming with aspiration or fractile criteria. Management Sciences, 13:672-679.
5. Dubois, D. and H. Prade. 1978. Operations on fuzzy numbers. International Journal of Systems Science, 9:613-626.
6. Dubois, D. and H. Prade. 1980. Fuzzy sets and systems. New York: Academic Press.
7. Inuiguchi, M. 1992. Relationships between modality constrained programming problems and various fuzzy mathematical programming problems. Fuzzy Sets and Systems, 49:243-259.
8. Inuiguchi, M., H. Ichihasi, and H. Tanaka. 1990. Fuzzy programming: A survey of recent developments. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, edited by R. Slowinski and J. Teghem. Dordrecht: Kluwer Academic Publishers, pp. 45-68.
9. Kataoka, S. 1963. A stochastic programming model. Econometrica, 31:181-196.
10. Katagiri, H. and H. Ishii. 2000a. Chance constrained bottleneck spanning tree problem with fuzzy random edge costs. Journal of the Operations Research Society of Japan, 43:128-137.
11. Katagiri, H. and H. Ishii. 2000b. Linear programming problem with fuzzy random constraint. Mathematica Japonica, 52:123-129.
12. Katagiri, H., M. Sakawa, and H. Ishii. 2004. Fuzzy random bottleneck spanning tree problems using possibility and necessity measures. European Journal of Operational Research, 152:88-95.
13. Kruse, R. and K. D. Meyer. 1987. Statistics with vague data d. Dordrecht: Reidel Publishing Company.
14. Kwakernaak, H. 1978. Fuzzy random variable-1. Information Sciences, 15:1-29.
15. Li, H.-L. 1994. A global approach for general 0-1 fractional programming. European Journal of Operational Research, 73:590-596.
16. Luhandjula, M. K. and M. M. Gupta. 1996. On fuzzy stochastic optimization. Fuzzy Sets and Systems, 81:47-55.
17. Puri, M. L. and D. A. Ralescu. 1986. Fuzzy random variables. Journal of Mathematical Analysis and Applications, 114:409-422.
18. Sakawa, M. 1993. Fuzzy sets and interactive multiobjective optimization. New York: Plenum Press.
19. Vajda, S. 1982. Probabilistic programming. New York: Academic Press.
20. Wang, G.-Y. and Z. Qiao. 1993. Linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems, 57:295-311.
21. Wierzbicki, A. P. 1980. The use of reference objectives in multiobjective optimization. In Multiple criteria decision making: Theory and application, edited by G. Frande and T. Gal. New York: Springer-Verlag, pp. 468-486.
22. Zadeh, L. A. 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1:3-28.
23. Zimmermann, H.-J. 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1:45-55.