On the average values of fuzzy numbers and their systems
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 1, pp. 5-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the extreme properties of the mean values of fuzzy numbers, as well as their systems. Nonlinear means are introduced and their properties are observed.
Keywords: fuzzy numbers, mean values, extreme properties.
@article{FSSC_2021_16_1_a0,
     author = {V. L. Khatskevich},
     title = {On the average values of fuzzy numbers and their systems},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {5--20},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a0/}
}
TY  - JOUR
AU  - V. L. Khatskevich
TI  - On the average values of fuzzy numbers and their systems
JO  - Nečetkie sistemy i mâgkie vyčisleniâ
PY  - 2021
SP  - 5
EP  - 20
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a0/
LA  - ru
ID  - FSSC_2021_16_1_a0
ER  - 
%0 Journal Article
%A V. L. Khatskevich
%T On the average values of fuzzy numbers and their systems
%J Nečetkie sistemy i mâgkie vyčisleniâ
%D 2021
%P 5-20
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a0/
%G ru
%F FSSC_2021_16_1_a0
V. L. Khatskevich. On the average values of fuzzy numbers and their systems. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 1, pp. 5-20. http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a0/

[1] Piegat A., Fuzzy Modeling and Control, Springer-Verlag, Berlin, Heidelberg, 2001, 725 pp.

[2] Borisov V. V., Fedulov A. S., Zernov M. M., Basics of fuzzy arithmetic, Tutorial, Goryachaya liniya - Telekom, Moscow, 2019, 98 pp. (in Russian)

[3] Dzhini K., Average values, Statistika Publ., Moscow, 1970, 447 pp. (in Russian)

[4] Orlov A. I., Prikladnaya statistika, Ekzamen Publ., Moscow, 2006, 672 pp. (in Russian)

[5] Nguyen H. T., Wu B., Fundamentals of statistics with fuzzy data, Springer, Berlin, 2006, 204 pp. | Zbl

[6] Gnedenko B. V., The Theory of Probability, AMS Chelsea Publishing, Providence, Rhode Island, 2005, 529 pp. | MR | MR

[7] Khatskevich V. L., “On some class of nonlinear mean random values”, Journal of Physics: Conference Series, 1479 (2020), 012087 | DOI

[8] Khatskevich V. L., “On random properties of mean values of continuous random variables and relations between them”, Journal of Mathematical Sciences, 1:2 (2017), 304–312 | DOI | MR

[9] Yazenin A. V., Basic concepts of the theory of possibilities. Mathematical decision-making apparatus in a hybrid uncertainty, Fizmatlit Publ., Moscow, 2016, 144 pp. (in Russian)

[10] Hoffmann-Jorgensen J., Probability with a view toward statistics, Chapman and Hall, New York, 1998, 589 pp. | MR

[11] Bargiela A., Pedrycz W., Nakashima T., “Multiple Regression with fuzzy data”, Fuzzy Sets and Systems, 2007, 2169–2188 | DOI | MR | Zbl

[12] Veldyaksov V. N., Shvedov A. S., “On the least squares method for regression with fuzzy data”, HSE Economic Journal, 18:2 (2014), 328–344 (in Russian)

[13] Dubois D., Prade H., “The mean value of fuzzy number”, Fuzzy Sets and Systems, 1987, 279–300 | DOI | MR | Zbl

[14] Fuller R., Majlender P., “On weighted possibilistic mean value and variance of fuzzy numbers”, Fuzzy Sets and Systems, 2003, 363–374 | DOI | MR | Zbl

[15] Khatskevich V. L., “On some extreme properties of average values and mathematical expectations of random variables”, Bulletin of the Voronezh State Technical University, 9:1-3 (2013), 39–44 (in Russian)

[16] Calvo T., Mesiar R., “Generalized median”, Fuzzy Sets and Systems, 124 (2001), 59–61 | DOI | MR

[17] Khardi G., Poja D., Littlvud D., Inequalities, MTsNMO Publ., Moscow, 2008, 456 pp. (in Russian)