On minimum-risk problems in fuzzy random decision systems

Computers and Operations Research

Volumn 32, Issue 2, 2005, Pages 257-283

  Liu, Yian Kui ^a   Liu, Baoding ^b  

^a HEBEI UNIVERSITY   (China)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Fuzzy random programming; Fuzzy random variable; Genetic algorithm; Mean chances; Neural network

Indexed keywords

FUZZY CONTROL; MAPPING; NEURAL NETWORKS; OPTIMIZATION; PROBABILITY; PROBLEM SOLVING; RISK ASSESSMENT;

FUZZY RANDOM DECISION SYSTEMS; FUZZY RANDOM PROGRAMMING; MEAN CHANCES;

DECISION SUPPORT SYSTEMS;

EID: 4544296724     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(03)00235-1     Document Type: Article

References (34)

1. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. 1:1978;3-28.
2. Dubois D., Prade H. Possibility theory. 1988;Plenum Press, New York.
3. Klir G.J. On fuzzy-set interpretation of possibility theory. Fuzzy Sets and Systems. 108:1999;263-373.
4. Inuiguchi M., Ramík 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.
5. Lai Y.J., Hwang C.L. Fuzzy mathematical programming: methods and applications. 1992;Springer, Berlin.
6. Liu B. Toward fuzzy optimization without mathematical ambiguity. Fuzzy Optimization and Decision Making. 1(1):2002;43-63.
7. Liu B. Uncertain programming. 1999;Wiley, New York.
8. Liu B. Theory and practice of uncertain programming. 2002;Physica, Heidelberg.
9. Charnes A., Cooper W.W. Deterministic equivalents for optimizing and satisfying under chance constraints. Operations Research. 11:1963;18-39.
10. Liu B. Dependent-chance programming. a class of stochastic optimization Computers and Mathematics with Applications. 34:1997;89-104.
11. Liu B. Minimax chance constrained programming models for fuzzy decision systems. Information Sciences. 112:1998;25-38.
12. Liu B. Dependent-chance programming in fuzzy environments. Fuzzy Sets and Systems. 109(1):2000;97-106.
13. Inuiguchi M., Ichihashi H., Kume Y. Modality constrained programming problems. a unified approach to fuzzy mathematical programming problems in the setting of possibility theory Information Sciences. 67:1993;93-126.
14. Luhandjula M.K., Gupta M.M. On fuzzy stochastic optimization. Fuzzy Sets and Systems. 81:1996;47-55.
15. Wang G., Qiao Z. Linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems. 57:1993;295-311.
16. Qiao Z., Wang G. On solution and distribution problems of the linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems. 58:1993;155-170.
17. Luhandjula M.K. Fuzziness and randomness in an optimization framework. Fuzzy Sets and Systems. 77:1996;291-297.
18. Sugeno M. Theory of fuzzy integral and its applications. PhD thesis, Tokyo Institute of Technology, 1974.
19. Wang Z., Klir J. Fuzzy measure theory. 1992;Plenum Press, New York.
20. Liu B. Fuzzy random chance-constrained programming. IEEE Transactions on Fuzzy Systems. 9(5):2001;713-720.
21. Liu B. Fuzzy random dependent-chance programming. IEEE Transactions on Fuzzy Systems. 9(5):2001;721-726.
22. Liu Y.K., Liu B. Fuzzy random variable. a scalar expected value operator Fuzzy Optimization and Decision Making. 2(2):2003;143-160.
23. Liu B., Liu Y.K. Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems. 10(4):2002;445-450.
24. Kwakernaak H. Fuzzy random variables - I. Definitions and theorems. Information Sciences. 15:1978;1-29.
25. Colubi A., Dominguez-Menchero J.S., López-Diaz M., et al. On the formalization of fuzzy random variables. Information Sciences. 133:2001;3-6.
26. Kruse R., Meyer K.D. Statistics with vague data. 1987;Reidel Publishing Company, Dordrecht.
27. López-Diaz M., Gil M.A. Constructive definitions of fuzzy random variables. Statistics and Probability Letters. 36:1997;135-143.
28. Puri M.L., Ralescu D.A. Fuzzy random variables. Journal of Mathematical Analysis and Applications. 114:1986;409-422.
29. Dubois D., Prade H. Fuzzy sets and systems: theory and applications. 1980;Academic Press, New York.
30. Grabisch M., Murofushi T., Sugeno M. Fuzzy measure of fuzzy event defined by fuzzy integrals. Fuzzy Sets and Systems. 50:1992;293-313.
31. Inuiguchi M., Ichihashi H., Tanaka H. Possibilistic linear programming with measurable multiattribute value functions. ORSA Journal on Computing. 1:1989;146-158.
32. Scarselli F., Tsoi A.C. Universal approximation using feedforward neural networks. a survey of some existing methods, and some new results Neural Networks. 11:1998;15-37.
33. Nahmias S. Fuzzy variable. Fuzzy Sets and Systems. 1:1978;97-101.
34. Liu B. Inequalities and convergence concepts of fuzzy and rough variables. Fuzzy Optimization and Decision Making. 2(2):2003;87-100