Simulation of fuzzy random variables

Information Sciences

Volumn 179, Issue 5, 2009, Pages 642-653

  González Rodríguez, Gil ^a   Colubi, Ana ^b   Trutschnig, Wolfgang ^c  

^a EUROPEAN CENTRE FOR SOFT COMPUTING   (Spain)

^b UNIVERSITY OF OVIEDO   (Spain)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Fuzzy random variables; Hilbert spaces; Imprecise data; Simulation; Support functions

Indexed keywords

CLUSTER ANALYSIS; FUNCTIONS; FUZZY SETS; HILBERT SPACES; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

CONICAL STRUCTURES; EMPIRICAL RESULTS; FUNCTIONAL DATUMS; FUZZY RANDOM VARIABLES; IMPRECISE DATA; ORTHONORMAL BASES; RANDOM ELEMENTS; SIMULATION; SIMULATION TECHNIQUES; SUPPORT FUNCTIONS;

RANDOM VARIABLES;

EID: 57649240421     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.10.018     Document Type: Article

References (40)

1. Alonso M.C., Brezmes T., Lubiano M.A., and Bertoluzza C. A generalized real-valued measure of the inequality associated with a fuzzy random variable. International Journal of Approximate Reasoning 26 (2001) 47-66
2. Ayala G., León T., and Zapater V. Different averages of a fuzzy set with an application to vessel segmentation. IEEE Transactions on Fuzzy Systems 13 (2005) 384-393
3. Baudrit C., Guyonnet D., and Dubois D. Joint propagation of variability and imprecision in assessing the risk of groundwater contamination. Journal of Contaminant Hydrology 93 (2007) 72-84
4. Chalco-Cano Y., Roman-Flores H., and Gomide F. A new type of approximation for fuzzy intervals. Fuzzy Sets and Systems 159 (2008) 1376-1383
5. Colubi A. Statistical inference about the means of fuzzy random variables: applications to the analysis of fuzzy- and real-valued data. Fuzzy Sets and Systems (2008) 10.1016/j.fss.2007.12.019
6. Colubi A., Domínguez-Menchero J.S., and Gil M.A. A generalized strong law of large numbers. Probability Theory and Related Fields 114 (1999) 401-417
7. Colubi A., Domínguez-Menchero J.S., López-Díaz M., and Ralescu D.A. On the formalization of fuzzy random variables. Information Sciences 133 (2001) 3-6
8. Colubi A., Fernández-García C., and Gil M.A. Simulation of random fuzzy variables: an empirical approach to statistical/probabilistic studies with fuzzy experimental data. IEEE Transactions on Fuzzy Systems 10 (2002) 384-390
9. Coppi R., D'Urso P., and Giordani P. Component models for fuzzy data. Psychometrika 71 (2006) 733-761
10. Coppi R., Gil M.A., and Kiers H.A.L. The fuzzy approach to statistical analysis. Computational Statistics Data Analysis 51 (2006) 1-451 (special issue)
11. Diamond P., and Kloeden P. Metric Spaces of Fuzzy Sets: Theory and Applications (1994), World Scientific, Singapore
12. Diamond P., and Körner R. Extended fuzzy linear models and least squares estimates. Computers & Mathematics with Applications 33 (1997) 15-32
13. Domínguez-Menchero J.S., and González-Rodríguez G. Analyzing an extension of the isotonic regression problem. Metrika 66 (2007) 19-30
14. D'Urso P., and Giordani P. A weighted fuzzy c-means clustering model for fuzzy data. Computational Statistics Data Analysis 50 (2006) 1496-1523
15. Elstrodt J. Maß- und Integrationstheorie (1999), Springer, Berlin, Heidelberg, New York
16. Gil M.A. Fuzzy random variables. Information Sciences 133 (2001) 1-2
17. M.A. Gil, M. López-Díaz, D.A. Ralescu, Fuzzy sets and probability/statistics theories, Fuzzy Sets and Systems, special issue, 157 (2006) 2545-2682.
18. Gil M., Montenegro M., González-Rodríguez G., Colubi A., and Casals M. Bootstrap approach to the multi-sample test of means with imprecise data. Computational Statistics Data Analysis 51 (2006) 148-162
19. González-Rodríguez G., Montenegro M., Colubi A., and Gil M.A. Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data. Fuzzy Sets and Systems 157 (2006) 2608-2613
20. Hukuhara M. Integration des applications mesurables dont la valeur est un compact convexe. Funkcialaj Ekvacioj 10 (1967) 205-223
21. Klement E.P., Puri M.L., and Ralescu D.A. Limit Theorems for fuzzy random variables. Proceedings of the Royal Society of London. Series A 407 (1986) 171-182
22. Krätschmer V. Some complete metrics on spaces of fuzzy subsets. Fuzzy Sets and Systems 130 (2002) 357-365
23. Kwakernaak H. Fuzzy random variables-I. Definitions and theorems. Information Sciences 15 (1978) 1-29
24. Li S., and Guan L. Fuzzy set-valued Gaussian processes and Brownian motions. Information Sciences 177 (2007) 3251-3259
25. Narukawa Y., and Torra V. Fuzzy measures and integrals in evaluation of strategies. Information Sciences 177 (2007) 4686-4695
26. Nasibov E.N., and Peker S. On the nearest parametric approximation of a fuzzy number. Fuzzy Sets and Systems 159 (2008) 1365-1375
27. Montenegro M., Casals M.R., Lubiano M.A., and Gil M.A. Two-sample hypothesis tests of means of a fuzzy random variable. Information Sciences 133 (2001) 89-100
28. Montenegro M., Colubi A., Casals M.R., and Gil M.A. Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59 (2004) 31-49
29. Möller B., Graf W., and Beer M. Safety assessment of structures in view of fuzzy randomness. Computers and Structures 81 (2003) 1567-1582
30. Näther W. Random fuzzy variables of second order and applications to statistical inference. Information Sciences 133 (2001) 69-88
31. Parkash O., Sharma P.K., and Mahajan R. New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Information Sciences 178 (2008) 2389-2395
32. Puri M.L., and Ralescu D.A. Fuzzy random variables. Journal of Mathematical Analysis and Applications 114 (1986) 409-422
33. Ranilla J., and Rodríguez-Muñiz L.J. A heuristic approach to learning rules from fuzzy databases. IEEE Intelligent Systems 22 (2007) 62-68
34. Stefanini L., Sorini L., and Guerra M.L. Parametric representation of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets and Systems 157 (2006) 2423-2455
35. Trutschnig W. A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability. Fuzzy Sets and Systems 159 (2008) 259-269
36. Wang F.-H. On discovery of soft associations with most fuzzy quantifier for item promotion applications. Information Sciences 178 (2008) 1848-1876
37. Yager R.R. Using trapezoids for representing granular objects: applications to learning and OWA aggregation. Information Sciences 178 (2008) 363-380
38. Zadeh L. The concept of a linguistic variable and its application to approximate reasoning, I. Information Sciences 8 (1975) 199-249
39. Zadeh L. Toward a generalized theory of uncertainty -an outline. Information Sciences 172 (2005) 1-40
40. Zadeh L. Is there a need for fuzzy logic?. Information Sciences 178 (2008) 2751-2779