Geodesic
Extremal properties of means of fuzzy random variables
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 160-169.

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In this paper, we examine extremal properties of fuzzy expectations and expectations of fuzzy random variables. We introduce a new mean characteristic—a scalar random variable that characterizes a given fuzzy random variable—and prove its extremal properties. Also, we study linear regressions of fuzzy random variables, obtain a formula for the optimal linear fuzzy regression, and prove that its correlation with the predicted value is maximal.
Keywords: fuzzy random variable, mean value, extremal property. 
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V. L. Khatskevich. Extremal properties of means of fuzzy random variables. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 160-169. http://geodesic.mathdoc.fr/item/INTO_2022_204_a15/

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