On distance between fuzzy variables

Journal of Intelligent and Fuzzy Systems

Volumn 19, Issue 3, 2008, Pages 197-204

  Li, Xiang ^a   Liu, Baoding ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Distance; Fuzzy random variable; Fuzzy variable; Random fuzzy variable

Indexed keywords

SET THEORY; TOPOLOGY; VECTORS;

DISTANCE; EXPECTED VALUES; FUZZY RANDOM; FUZZY RANDOM VARIABLE; FUZZY VARIABLE; FUZZY VARIABLES; FUZZY VECTORS; HAUSDORFF; METRIC SPACES; RANDOM FUZZY VARIABLE;

FUZZY SETS;

EID: 50249157916     PISSN: 10641246     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. L. Boxer, On Hausdorff-like metrics for fuzzy sets, Pattern Recognition Letters 18 (1997), 115-118.
2. B.B. Chaudhuri and A. Rosenfeld, On a metric distance between fuzzy sets, Pattern Recognition Letters 17 (1996), 1157-1160.
3. B.B. Chaudhuri and A. Rosenfeld, A modified Hausdorff distance between fuzzy sets, Information Sciences 118 (1999), 159-171.
4. P. Diamond and K. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35 (1990), 241-249.
5. J. Fan, Note on Hausdorff-like metrics for fuzzy sets, Pattern Recognition Letters 19 (1998), 793-796.
6. J. Kacprzyk, Multistage Fuzzy Control, Wiley, Chichester, 1997.
7. E.P. Klement, M.L. Puri and D. Ralescu, Limit theorems for fuzzy random variables, Proc Roy Soc London Ser A 407 (1986), 171-182.
8. R. Kruse and K.D. Meyer, Statistics with Vague Data, D. Reidel Publishing Company, Dordrecht, 1987.
9. H. Kwakernaak, Fuzzy random variables-I. Definitions and theorems, Information Sciences 15 (1978), 1-29.
10. H. Kwakernaak, Fuzzy random variables-II. Algorithms and examples for the discrete case, Information Sciences 17 (1979), 253-278.
11. P. Li and B. Liu, Entropy of credibility distributions for fuzzy variables, IEEE Transactions on Fuzzy Systems 16(1) (2008), 123-129.
12. X. Li and B. Liu, A sufficient and necessary condition for credibility measures, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 14(5) (2006), 527-535.
13. X. Li and B. Liu, Maximum entropy principle for fuzzy variables, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 15(Supp 2) (2007), 40-48.
14. B. Liu, Theory and Practice of Uncertain Programming, Physica-Verlag, Heidelberg, 2002.
15. B. Liu, Uncertainty Theory, Springer-Verlag, Berlin, 2004.
16. B. Liu, Random fuzzy dependent-chance programming and its hybrid intelligent algorithm, Information Sciences 141(3-4) (2002), 259-271.
17. B. Liu, Fuzzy random chance-constrained programming, IEEE Transactions on Fuzzy Systems 9(5) (2001), 713-720.
18. B. Liu and Y.K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems 10(4) (2002), 445-450.
19. B. Liu, A survey of credibility theory, Fuzzy Optimization and Decision Making 5(4) (2006), 387-408.
20. B. Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
21. B. Liu, A survey of entropy of fuzzy variables, Journal of Uncertain Systems 1(1) (2007), 4-13.
22. Y.K. Liu and B. Liu, Fuzzy random variables: A scalar expected value operator, Fuzzy Optimization and Decision Making 2(2) (2003), 143-160.
23. Y.K. Liu and B. Liu, Expected value operator of random fuzzy variable and random fuzzy expected value models, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 11(2) (2003), 195-215.
24. C. Negoita and D. Ralescu, Simulation, Knowledge-Based Computing, and Fuzzy Statistcs, Van Nostrand Reinhold Company, New York, 1987.
25. M.L. Puri and D. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications 91 (1983), 552-558.
26. M.L. Puri and D. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis and Applications 114 (1986), 409-422.
27. A. Rosenfeld, Distances between fuzzy sets, Pattern Recognition Letters 3 (1985), 229-233.
28. L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
29. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978), 3-28.
30. R. Zhao and B. Liu, Redundancy optimization problems with uncertainty of combining randomness and fuzziness, European Journal of Operational Research 157(3) (2004), 716-735.
31. Y. Zhu and B. Liu, Continuity theorems and chance distribution of random fuzzy variable, Proceedings of the Royal Society of London Series A 460 (2004), 2505-2519.
32. Y. Zhu and B. Liu, Some inequalities of random fuzzy variables with application to moment convergence, Computers & Mathematics with Applications 50(5-6) (2005), 719-727.