Higher order models for fuzzy random variables

Fuzzy Sets and Systems

Volumn 159, Issue 3, 2008, Pages 237-258

  Couso, Inés ^a   Sánchez, Luciano ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Fuzzy random variable; Imprecise probabilities; Random set; Second order possibility measure

Indexed keywords

FUZZY SETS; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

FUZZY RANDOM VARIABLES; IMPRECISE PROBABILITIES; RANDOM SETS; SECOND ORDER POSSIBILITY MEASURES;

RANDOM VARIABLES;

EID: 36048943078     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2007.09.004     Document Type: Article

References (47)

1. Aumann J. Integral of set valued functions. J. Math. Anal. Appl. 12 (1965) 1-12
2. Baudrit C., Couso I., and Dubois D. Probabilities of events induced by fuzzy random variables. Proc. Internat. Conf. in Fuzzy Logic and Technology (EUSFLAT 05) (2005), Barcelona, Spain
3. Baudrit C., Couso I., and Dubois D. Joint propagation of probability and possibility in risk analysis: towards a formal framework. Internat. J. Approx. Reasoning 45 (2007) 82-105
4. Boyen L., de Cooman G., and Kerre E.E. On the extension of P-consistent mappings. In: de Cooman G., Ruan D., and Kerre E.E. (Eds). Foundations and Applications of Possibility Theory-Proc. of FAPT'95 (1995), World Scientific, Singapore 88-98
5. Casillas J., and Sánchez L. Knowledge extraction from fuzzy data for estimating consumer behavior models. Proc. 2006 IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE'06) (2006), Vancouver, Canada 572-578
6. Couso I., Dubois D., Montes S., and Sánchez L. On various definitions of the variance of a fuzzy random variable. Proc. Fifth Internat. Symp. on Imprecise Probabilities: Theory and Applications (ISIPTA 07) (2007), Prague, Czech Republic 135-144
7. Couso I., Miranda E., and de Cooman G. A possibilistic interpretation of the expectation of a fuzzy random variable. In: López-Díaz M., Gil M.A., Grzegorzewski P., Hryniewicz O., and Lawry J. (Eds). Soft Methodology and Random Information Systems (2004), Springer, Berlin 133-140
8. I. Couso, S. Montes, P. Gil, Función de distribución y mediana de variables aleatorias difusas, in: Proc. VIII Congreso Español sobre Tecnologías y Lógica Fuzzy (ESTYLF'98), Pamplona, Spain, 1998, pp. 279-284 (in Spanish).
9. Couso I., Montes S., and Gil P. The necessity of the strong alpha-cuts of a fuzzy set. Internat. J. Uncertainly Fuzziness and Knowledge-Based Systems 9 (2001) 249-262
10. Couso I., Montes S., and Gil P. Second order possibility measure induced by a fuzzy random variable. In: Bertoluzza C., Gil M.A., and Ralescu D.A. (Eds). Statistical Modeling, Analysis and Management of Fuzzy Data (2002), Springer, Heidelberg 127-144
11. I. Couso, S. Montes, L. Sánchez, Varianza de una variable aleatoria difusa. Estudio de distintas definiciones, in: Proc. of XII Congreso Español de Tecnologías y Lógica Difusa (ESTYLF'04), Jaén, Spain, 2004. (in Spanish).
12. Couso I., Moral S., and Walley P. A survey of concepts of independence for imprecise probabilities. Risk, Decision and Policy 5 (2000) 165-181
13. Couso I., Sánchez L., and Gil P. Imprecise distribution function associated to a random set. Inform. Sci. 159 (2004) 109-123
14. de Cooman G. A behavioural model for vague probability assessments. Fuzzy Sets and Systems 154 (2005) 305-358
15. de Cooman G., and Aeyels D. Supremum preserving upper probabilities. Inform. Sci. 118 (1999) 173-212
16. de Cooman G., and Walley P. An imprecise hierarchical model for behaviour under uncertainty. Theory and Decision 52 (2002) 327-374
17. Diamond P., and Kloeden P. Metric Spaces of Fuzzy Sets (1994), World Scientific, Singapore
18. Dubois D., and Prade H. The mean value of a fuzzy number. Fuzzy Sets and Systems 24 (1987) 279-300
19. Dubois D., and Prade H. The three semantics of fuzzy sets. Fuzzy Sets and Systems 90 (1997) 141-150
20. Feng Y., Hu L., and Shu H. The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets and Systems 120 (2001) 487-497
21. Ferson S., Ginzburg L., Kreinovich V., Nguyen H.T., and Starks S.A. Uncertainty in risk analysis: towards a general second-order approach combining interval, probabilistic, and fuzzy techniques. Proc. 2002 IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE'02) (2002), Honolulu, Hawaii, USA 1342-1347
22. Ferson S., Kreinovich V., Ginzburg L., Sentz K., and Myers D.S. Constructing probability boxes and Dempster-Shafer structures, Sandia National Laboratories, SAND2002-4015 (2003), Albuquerque, NM, USA
23. Herencia J.A. Graded sets and points: a stratified approach to fuzzy sets and points. Fuzzy Sets and Systems 77 (1996) 191-202
24. Klement E.P., Puri M.L., and Ralescu D.A. Limit theorems for fuzzy random variables. Proc. Roy. Soc. London A 407 (1986) 171-182
25. Körner R. On the variance of fuzzy random variables. Fuzzy Sets and Systems 92 (1997) 83-93
26. Krätschmer V. A unified approach to fuzzy random variables. Fuzzy Sets and Systems 123 (2001) 1-9
27. Kruse R. On the variance of random sets. J. Math. Anal. Appl. 122 (1987) 469-473
28. Kruse R., and Meyer K.D. Statistics with Vague Data (1987), D. Reidel Publishing Company, Dordrecht
29. Kwakernaak H. Fuzzy random variables: definition and theorems. Inform. Sci. 15 (1978) 1-29
30. Kyburg Jr. H.E., and Pittarelli M. Set-based Bayesianism. IEEE Trans. Systems Man Cybernet. 26 (1996) 324-339
31. M.A. Lubiano, Variation measures for imprecise random elements, Ph.D. Thesis, Universidad de Oviedo, Spain, 1999 (in Spanish).
32. Miranda E., de Cooman G., and Couso I. Lower previsions induced by multi-valued mappings. J. Stat. Plann. Inference 133 (2005) 173-197
33. Miranda E., Couso I., and Gil P. Study of the probabilistic information of a random set. Proc. Third Internat. Symp. on Imprecise Probabilities and Their Applications (ISIPTA'03) (2003), Lugano, Switzerland
34. Miranda E., Couso I., and Gil P. Random intervals as a model for imprecise information. Fuzzy Sets and Systems 154 (2005) 386-412
35. Miranda E., Couso I., and Gil P. Random sets as imprecise random variables. J. Math. Anal. Appl. 307 (2005) 32-47
36. Nguyen H.T. On random sets and belief functions. J. Math. Anal. Appl. 65 (1978) 531-542
37. Otero A., Otero J., Sánchez L., and Villar J.R. Longest path estimation from inherently fuzzy data acquired with GPS using genetic algorithms. Second Internat. Symp. on Evolving Fuzzy Systems 2006 (EFS06) (2006), Ambleside Lake District, UK 300-306
38. Puri M., and Ralescu D. Fuzzy random variables. J. Math. Anal. Appl. 114 (1986) 409-422
39. Sánchez L., and Couso I. Advocating the use of imprecisely observed data in genetic fuzzy systems. IEEE Trans. Fuzzy Systems 15 (2007) 551-562
40. Sánchez L., Couso I., and Casillas J. A multiobjective genetic fuzzy system with imprecise probability fitness for vague data. Second Internat. Symp. on Evolving Fuzzy Systems 2006 (EFS06) (2006), Ambleside, Lake District, UK 131-136
41. L. Sanchez, I. Couso, J. Casillas. Knowledge extraction from vague data with genetic fuzzy systems under a combination of crisp and imprecise criteria, IEEE Trans. on Fuzzy Systems 2007, submitted for publication.
42. Sánchez L., Otero J., and Villar J.R. Boosting of fuzzy models for high-dimensional imprecise datasets. Proc. 11th Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference (IPMU) (2006), Paris, France
43. Sánchez L., Suárez M.R., and Couso I. A fuzzy definition of mutual information with application to the design of genetic fuzzy classifiers. Proc. Internat. Conf. on Machine Intelligence (ACIDCA-ICMI05) (2005), Tozeur, Tunisia 602-609
44. Sánchez L., Suárez M.R., Villar J.R., and Couso I. Some results about mutual information-based feature selection and fuzzy discretization of vague data. Proc. 16th IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE07) (2007), London, UK
45. L. Sánchez, M.R. Suárez, J.R. Villar, I. Couso, Mutual information-based feature selection and fuzzy discretization of vague data, Soft Comput. 2007, submitted for publication.
46. Walley P. Statistical Reasoning with Imprecise Probabilities (1991), Chapman & Hall, London
47. Walley P. Statistical inferences based on a second-order possibility distribution. Internat. J. General Systems 26 (1997) 337-384