Fuzzy random variables

Insurance: Mathematics and Economics

Volumn 44, Issue 2, 2009, Pages 307-314

  Shapiro, Arnold F ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Fuzzy random variables; Insurance; Random fuzzy sets

Indexed keywords

EID: 63749130587     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2008.05.008     Document Type: Article

References (39)

1. Buckley J.J. Fuzzy Probabilities (2005), Physica-Verlag, Berlin Heidelberg
2. Chao, R.-J., Ayyub, B.M., 1995, Distributions with Fuzziness and Randomness, In: Proceedings of ISUMA-NAFIPS'95, 668-673
3. Colubi A., Dominguez-Menchero J.S., Lopez-Diaz M., and Ralescu D.A. On the formalization of fuzzy random variables. Information Sciences 133 (2001) 3-6
4. De Vylder F.E. Advanced Risk Theory: A Self-Contained Introduction. Actuariat (1996)
5. Diamond P., and Kloeden P. Metric Spaces of Fuzzy Sets: Theory and Applications (1994), World Scientific, Singapore
6. Dionne G., and Vanasse C. A generalization of automobile insurance rating models: The negative binomial distribution with a regression component. Astin Bulletin 19 2 (1989)
7. Dubois D., and Prade J. Fuzzy Sets and Systems: Theory and Applications. Mathematics in Science and Engineering vol. 144 (1980), Academic Press, New York
8. Feng Y., Hu L., and Shu H. The variance and covariance off fuzzy random variables and their applications. Fuzzy Sets and Systems 120 (2001) 487-497
9. Gil M.Á. Fuzzy random variables: Development and state of the art. Mathematics of Fuzzy Systems, Linz Seminar on Fuzzy Set Theory (2004), Linz, Austria
10. Gil M.Á., López-Díaz M., and Ralescu D.A. Overview on the development of fuzzy random variables. Fuzzy Sets and Systems 157 (2006) 2546-2557
11. Giles J.R. Introduction to the Analysis of Metric Spaces (1987), Cambridge University Press, Cambridge
12. González-Rodríguez G., Colubi A., and Gil M.Á. A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing. Comput. Statist. Data Anal. 51 (2006) 163-176
13. Goodman I.R. Fuzzy sets as equivalent classes of random sets. In: Yager R.R. (Ed). Fuzzy Sets and Possibility Theory (1982) 327-343
14. Hirota K. Concepts of probabilistic sets. Fuzzy Sets and Systems 5 (1981) 31-46
15. Kato, Y., Izuka, T., Ohtsuki, R., Yamaguchi, S., 1999. A proposal for a new fuzzy probability distribution function, 1999 IEEE International Fuzzy Systems Conference Proceedings, 1334-1339
16. Klement E.P., Puri M.L., and Ralescu D.A. Limit theorems for fuzzy random variables. Proceedings of The Royal Society of London A 407 (1986) 171-182
17. Koissi M.-C., and Shapiro A.F. Fuzzy formulation of Lee-Carter mortality model. Insurance: Mathematics & Economics 39 3 (2006) 287-309
18. Krätschmer V. A unified approach to fuzzy random variables. Fuzzy Sets and Systems 123 (2001) 1-9
19. Kruse R., and Meyer K.D. Statistics with Vague Data (1987), D. Reidel Pub. Co
20. Kwakernaak H. Fuzzy random variables-I. definitions and theorems. Information Sciences 15 1 (1978) 1-29
21. Kwakernaak H. Fuzzy random variables-II. Algorithms and examples for the discrete case. Information Sciences 17 3 (1979) 253-278
22. Liu B. Uncertainty Theory: An Introduction to its Axiomatic Foundations (2004), Springer-Verlag, Berlin Heidelberg
23. López-Díaz M., and Ralescu D.A. Tools for fuzzy random variables: Embeddings and measurabilities. Computational Statistics & Data Analysis 51 (2006) 109-114
24. Möller B. Fuzzy randomness - a contribution to imprecise probability. ZAMM 84 10-11 (2004) 754-764
25. Möller, B., Beer, M., Reuter, U., 2005. Theoretical basics of fuzzy randomness - application to time series with fuzzy data, In: ICOSSAR 2005, pp. 1701-1707
26. Näther W. Random fuzzy variables of second order and applications to statistical inference. Information Sciences 133 (2001) 69-88
27. Nguyen H.T., and Wu B. Fundamentals of Statistics with Fuzzy Data (2006), Springer, New York
28. Puri M.L., and Ralescu D.A. Fuzzy random variables. Journal of Mathematical Analysis and Applications 114 (1986) 409-422
29. Shapiro A.F. Fuzzy logic in insurance. Insurance: Math. Econom. 35 (2004) 399-424
30. In: Sinha N.K., and Gupta M.M. (Eds). Soft Computing and Intelligent Systems: Theory and Applications (2000), Academic Press, San Diego, CA
31. Taylor A.E. Introduction to Functional Analysis (1958), John Wiley & Sons, Inc., New York
32. Viertl R., and Hareter D. Generalized Bayes' theorem for non-precise a-priori distribution. Metrika 59 (2004) 263-273
33. Wong Y.-C. Introductory Theory of Topological Vector Spaces (1992), Dekker, New York
34. Zadeh L.A. Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23 (1968) 421-427
35. Zadeh, L.A., 1975, The concept of a linguistic variable and its application to approximate reasoning, Part 1. Inform. Sci. 8, 199-249; Part 2. Inform. Sci. 8, 301-353; Part 3, Inform. Sci. 9, 43-80
36. Zadeh L.A. Fuzzy set as the basis for the theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28
37. Zadeh L.A. Fuzzy Probabilities. Inf. Process. Manage. 20 3 (1984) 363-372
38. Zadeh L.A. In: Ross T., Booker J.M., and Parkinson W.J. (Eds). Fuzzy Logic and Probability Applications: Bridging the Gap (2002), ASA SIAM Foreword
39. Zhong, C., Zhou, C., 1987, The Equivalence of Two Definition of Fuzzy Random Variables, in: Preprints of 2nd IFSA Congress, 59-62