This article is cited in 6 papers

On some properties of fuzzy expectations and nonlinear fuzzy expectations of fuzzy-random variables

V. L. Khatskevich

Russian Air Force Military Educational and Scientific Center of the “N.E. Zhukovsky and Yu.A. Gagarin Air Force Academy”, 54 a Staryh Bolshevikov str., Voronezh, 394064 Russia

Abstract: For fuzzy expectations of fuzzy-random variables, the properties of idempotence, homoge-neity, additivity, monotonicity, extreme property, which are modifications of the properties of mathematical expectations of real random variables, are established. Nonlinear fuzzy expectations are introduced, which are analogs of nonlinear associative means. Their properties are established.

Keywords: fuzzy-random variable, fuzzy expectations of fuzzy-random variables, nonlinear fuzzy expectations.

UDC: 519.766

Received: 11.01.2022
Revised: 03.03.2022
Accepted: 08.04.2022

DOI: 10.26907/0021-3446-2022-11-97-109

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2022, 66:11, 86–96