Measurability criteria for fuzzy random vectors

Fuzzy Optimization and Decision Making

Volumn 5, Issue 3, 2006, Pages 245-253

  Feng, Xueqin ^a   Liu, Yian Kui ^a  

^a HEBEI UNIVERSITY   (China)

Author keywords

Fuzzy random vector; Fuzzy vector; Measurability criteria

Indexed keywords

CONFORMAL MAPPING; MATHEMATICAL MODELS; MEASUREMENT THEORY; PROBLEM SOLVING; RANDOM PROCESSES; VECTORS;

EQUIVALENT FORMULATIONS; FUZZY RANDOM VECTORS; FUZZY VECTORS; MEASURABILITY CRITERIA;

FUZZY SETS;

EID: 33746033317     PISSN: 15684539     EISSN: 15732908     Source Type: Journal    
DOI: 10.1007/s10700-006-0013-0     Document Type: Article

References (26)

1. Dubois, D., & Prade, H. (1988). Possibility theory. New York: Plenum Press.
2. Dugundji, J. (1966). Topology. Boston: Allyn and Bacon Inc.
3. Klein, E., & Thompson, A.C. (1984). Theory of correspondences. New York: Wiley.
4. Klir, G. J. (1999). On fuzzy-set interpretation of possibility theory. Fuzzy Sets and Systems, 108, 263-273.
5. Krätschmer, V. (2001). A unified approach to fuzzy random variables. Fuzzy Sets and Systems, 123, 1-9.
6. Kruse, R., & Meyer, K.D. (1987). Statistics with vague data. Dordrecht: D. Reidel Publishing Company.
7. Kwakernaak, H. (1978). Fuzzy Random Variables - I. Information Sciences, 15, 1-29.
8. Kwakernaak, H. (1979). Fuzzy Random Variables - II. Information Sciences, 17, 253-278.
9. Liu, B. (2004). Uncertainty theory: an introduction to its axiomatic foundations. Berlin: Springer-Verlag.
10. Liu, B. (2001a). Fuzzy random chance-constrained programming. IEEE Transactions on Fuzzy Systems 9, 713-720.
11. Liu, B. (2001b). Fuzzy random dependent-chance programming. IEEE Transactions on Fuzzy Systems, 9, 721-726.
12. Liu, Y.-K. (2000). On the convergence of measurable set-valued function sequence on fuzzy measure space. Fuzzy Sets and Systems, 112, 241-249.
13. Liu, Y.-K., & Liu, B. (2003a). Fuzzy random variable: a scalar expected value operator. Fuzzy Optimization and Decision Making, 2, 143-160.
14. Liu, Y.-K., & Liu, B. (2003b). A class of fuzzy random optimization: expected value models. Information Sciences, 155, 89-102.
15. Liu, Y.-K., & Liu, B. (2005a). On minimum-risk problems in fuzzy random decision systems. Computers and Operations Research, 32, 257-283.
16. Liu, Y.-K., & Liu, B. (2005b). Fuzzy random programming with equilibrium chance constraints. Information Sciences, 170, 363-395.
17. López-Diaz, M., & Gil, M. A. (1997). Constructive Definitions of Fuzzy Random Variables. Statistics and Probability Letters, 36, 135-143.
18. Luhandjula, M. K. (1996). Fuzziness and randomness in an optimization framework. Fuzzy Sets and Systems, 77, 291-297.
19. Nahmias, S. (1978). Fuzzy variables. Fuzzy Sets and Systems, 1, 97-101.
20. Puri, M. L., & Ralescu, D. A. (1986). Fuzzy random variables. Journal of Mathematical Analaysis and Applications, 114, 409-422.
21. Rockafellar, R. T., & Wets, R. J-B. (1998). Variational analysis. Berlin: Spring-Verlag.
22. Wang, G., & Qiao, Z. (1993). Linear programming with fuzzy random variable coefficients. Fuzzy Sets and Systems, 57, 295-311.
23. Wang, P. (1982). Fuzzy contactability and fuzzy variables. Fuzzy Sets and Systems, 8, 81-92.
24. Yager, R. R. (1992). On the specificity of a possibility distribution. Fuzzy Sets and Systems, 50, 279-292.
25. Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3-28.
26. Zhang, W. (1989). Set-valued measures and random sets. china: Sian Jiaotong Univ. Press (in Chinese).