Abstract
We study the integration of fuzzy level sets associated with a fuzzy random variable when the underlying space is a separable Banach space or a weak star dual of a separable Banach space. In particular, the expectation and the conditional expectation of fuzzy level sets in this setting are presented. We prove the SLLN for pairwise independent identically distributed fuzzy convex compact valued level sets through the SLLN for pairwise independent identically distributed convex compact valued random set in separable Banach space. Some convergence results for a class of integrand martingale are also presented.
JEL Classification: C01, C02.
Mathematics Subject Classification (2010): 28B20, 60G42, 46A17, 54A20.
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Castaing, C., Godet-Thobie, C., Hoang, T.D., de Fitte, P.R. (2015). On the Integration of Fuzzy Level Sets. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics Volume 19. Advances in Mathematical Economics, vol 19. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55489-9_1
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DOI: https://doi.org/10.1007/978-4-431-55489-9_1
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