@article{VTPMK_2023_3_a2,
author = {I. S. Soldatenko and I. B. Bresler and S. A. Rogonov and A. V. Yazenin},
title = {Mathematical models of a fuzzy random variable: a comparative study},
journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
pages = {41--63},
year = {2023},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTPMK_2023_3_a2/}
}
TY - JOUR AU - I. S. Soldatenko AU - I. B. Bresler AU - S. A. Rogonov AU - A. V. Yazenin TI - Mathematical models of a fuzzy random variable: a comparative study JO - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika PY - 2023 SP - 41 EP - 63 IS - 3 UR - http://geodesic.mathdoc.fr/item/VTPMK_2023_3_a2/ LA - ru ID - VTPMK_2023_3_a2 ER -
%0 Journal Article %A I. S. Soldatenko %A I. B. Bresler %A S. A. Rogonov %A A. V. Yazenin %T Mathematical models of a fuzzy random variable: a comparative study %J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika %D 2023 %P 41-63 %N 3 %U http://geodesic.mathdoc.fr/item/VTPMK_2023_3_a2/ %G ru %F VTPMK_2023_3_a2
I. S. Soldatenko; I. B. Bresler; S. A. Rogonov; A. V. Yazenin. Mathematical models of a fuzzy random variable: a comparative study. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2023), pp. 41-63. http://geodesic.mathdoc.fr/item/VTPMK_2023_3_a2/
[1] Féron R., “Ensembles aléatoires flous”, Comptes rendus de l'Académie des Sciences, 282 (1976), 903–906 | MR | Zbl
[2] Féron R., “Ensembles flous attachés à un ensemble aléatoire flou”, Publications Econométriques, 9 (1976), 51–66 | MR | Zbl
[3] Kwakernaak H., “Fuzzy random variables - I. Definitions and theorems”, Information Sciences, 15:1 (1978), 1–29 | DOI | MR | Zbl
[4] Kwakernaak H., “Fuzzy Random Variables - II. Algorithms and Examples for Discrete Case”, Information Sciences, 17 (1979), 253–278 | DOI | MR | Zbl
[5] Kruse R., Meyer K. D., Statistics with Vague Data, Springer, Dordrecht, 1987 | DOI | MR
[6] Nahmias S., “Fuzzy variables in a random environment”, Advances in Fuzzy Set Theory and Applications, eds. M.M. Gupta, R.K. Ragade, R.R. Yager, North-Holland, Amsterdam, 1979, 165–180 | MR
[7] Puri M. L., Ralescu D. A., “Fuzzy random variables”, Journal of Mathematical Analysis and Applications, 114:2 (1986), 409–422 | DOI | MR | Zbl
[8] Chachi J., “On Distribution Characteristics of a Fuzzy Random Variable”, Austrian Journal of Statistics, 47 (2018), 53–67 | DOI
[9] Zadeh L. A., “Fuzzy sets”, Information and Control, 8:3 (1965), 338–353 | DOI | MR | Zbl
[10] Zadeh L. A., “Fuzzy sets as a basis for a theory of possibility”, Fuzzy Sets and Systems, 1 (1978), 3–28 | DOI | MR | Zbl
[11] Nahmias S., “Fuzzy variables”, Fuzzy Sets and Systems, 1:2 (1978), 97–110 | DOI | MR | Zbl
[12] Dubois D., Prade H., “Fuzzy numbers: an overview”, Analysis of Fuzzy Information, v. 2, ed. J. Bezdek, CRC-Press, Boca Raton, 1988, 3–39 | MR
[13] Dubois D., Prade H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980 | MR | Zbl
[14] Liu B., Liu Y. K., “Expected Value of Fuzzy Variable and Fuzzy Expected Value Models”, IEEE Transactions on Fuzzy Systems, 10 (2002), 445–450 | DOI | MR
[15] Liu Y. K., Liu B., “Fuzzy Random Variables: A Scalar Expected Value Operator”, Fuzzy Optimization and Decision Making, 2 (2003), 143–160 | DOI | MR | Zbl
[16] Liu B., Uncertainty Theory, Springer-Verlag, Berlin, 2016 | MR
[17] Klement E. P., Puri M. L., Ralescu D. A., “Limit theorems for fuzzy random variables”, Proceedings of the Royal Society, 407 (1986), 171–182 | MR | Zbl
[18] Diamond P., Kloeden P., Metric Spaces of Fuzzy Sets, World Scientific, Singapore, 1994 | MR | Zbl
[19] Kratschmer V., “A unified approach to fuzzy random variables”, Fuzzy Sets and Systems, 123 (2001), 1–9 | DOI | MR | Zbl
[20] Couso I., Sánchez L., “Higher order models for fuzzy random variables”, Fuzzy Sets and Systems, 159 (2008), 237–258 | DOI | MR | Zbl
[21] Miyakoshi M., Shimbo M., Set representations of a fuzzy set and its application to Jensen’s inequality, Preprint
[22] Aumann R. J., “Integrals of Set-Valued Functions”, Journal of Mathematical Analysis and Applications, 12 (1965), 1–12 | DOI | MR | Zbl
[23] Yazenin A., Wagenknecht M., Possibilistic Optimization. A Measure-Based Approach, Brandenburgische Technische Universitat, Cotbus, Germany, 1996, 133 pp.
[24] Liu B., Theory and Practice of Uncertain Programming, Verlag, Heidelberg, Physica, 2002 | Zbl
[25] Peng J., Liu B., “Some Properties of Optimistic and Pessimistic Values of Fuzzy”, IEEE International Conference on Fuzzy Systems, 2 (2004), 745–750 | MR
[26] Shapiro A. F., “Fuzzy random variables”, Insurance: Mathematics and Economics, 44:2 (2009), 307–314 | DOI | MR | Zbl
[27] Khokhlov M. Yu., Yazenin A. V., “Calculation of numerical characteristics of fuzzy random variables”, Herald of Tver State University. Series: Applied Mathematics, 2003, no. 1, 39–43 (in Russian) | MR
[28] Khokhlov M. Yu., “Fuzzy random variables and their numerical characteristics”, Methods and algorithms for the study of optimal control problems, Tver, 2000 (in Russian)
[29] Shiryaev A. N., Veroyatnost, Moscow, 2007, 552 pp. (in Russian)