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Fuzzy random variables

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  • Shapiro, Arnold F.

Abstract

There are two important sources of uncertainty: randomness and fuzziness. Randomness models the stochastic variability of all possible outcomes of a situation, and fuzziness relates to the unsharp boundaries of the parameters of the model. In this sense, randomness is largely an instrument of a normative analysis that focuses on the future, while fuzziness is more an instrument of a descriptive analysis reflecting the past and its implications. Clearly, randomness and fuzziness are complementary, and so a natural question is how fuzzy variables could interact with the type of random variables found in actuarial science. This article focuses on one important dimension of this issue, fuzzy random variables (FRVs). The goal is to introduce IME readers to FRVs and to illustrate how naturally compatible and complementary randomness and fuzziness are.

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  • Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:307-314
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    Cited by:

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    3. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    4. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    5. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    6. J. Le-Rademacher & L. Billard, 2017. "Principal component analysis for histogram-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 327-351, June.
    7. Alexey Shvedov, 2016. "Estimating the means and the covariances of fuzzy random variables," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 121-138.
    8. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.
    9. Shapiro, Arnold F., 2013. "Modeling future lifetime as a fuzzy random variable," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 864-870.
    10. Xianfei Hui & Baiqing Sun & Hui Jiang & Yan Zhou, 2022. "Modeling dynamic volatility under uncertain environment with fuzziness and randomness," Papers 2204.12657, arXiv.org, revised Oct 2022.
    11. Ravi Shankar Kumar & M. K. Tiwari & A. Goswami, 2016. "Two-echelon fuzzy stochastic supply chain for the manufacturer–buyer integrated production–inventory system," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 875-888, August.
    12. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem & Arnold F. Shapiro & Michel Terraza, 2012. "Capital asset pricing model with fuzzy returns and hypothesis testing," Working Papers 12-33, LAMETA, Universtiy of Montpellier, revised Sep 2012.
    13. Rachida Hennani & Michel Terraza, 2012. "Value-at-Risk stressée chaotique d’un portefeuille bancaire," Working Papers 12-23, LAMETA, Universtiy of Montpellier, revised Sep 2012.
    14. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    15. Arnold Shapiro, 2013. "Fuzzy post-retirement financial concepts: an exploratory study," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 261-278, November.
    16. Vahid Ranjbar & Gholamreza Hesamian, 2020. "Copula function for fuzzy random variables: applications in measuring association between two fuzzy random variables," Statistical Papers, Springer, vol. 61(1), pages 503-522, February.
    17. Sadefo Kamdem, J. & Mbairadjim Moussa, A. & Terraza, M., 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 702-712.
    18. Allahviranloo, Mahdieh & Chow, Joseph Y.J. & Recker, Will W., 2014. "Selective vehicle routing problems under uncertainty without recourse," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 62(C), pages 68-88.
    19. Lu Gan & Li Wang & Lin Hu, 2017. "Gathered Village Location Optimization for Chinese Sustainable Urbanization Using an Integrated MODM Approach under Bi-Uncertain Environment," Sustainability, MDPI, vol. 9(10), pages 1-25, October.
    20. Gholamreza Hesamian & Jalal Chachi, 2015. "Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables," Statistical Papers, Springer, vol. 56(1), pages 61-82, February.
    21. de Andrés-Sánchez, Jorge & González-Vila Puchades, Laura, 2017. "The valuation of life contingencies: A symmetrical triangular fuzzy approximation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 83-94.
    22. A. Shibu & M. Reddy, 2014. "Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 4075-4094, September.

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