Geodesic
On a method of solving of possibilistic-probabilistic programming problems
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 1, pp. 21-33.

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

The paper studies possibilistic-probabilistic optimization problems, based on the principle of expected possibility, and a method for solving its stochastic analogue in the case of the weakest t-norm describing the interaction of fuzzy parameters. The conditions that are easier to verify and ensure the convergence of the method of stochastic quasigradients of the solution of an equivalent stochastic analog are obtained.
Keywords: possitbilistic-probabilistic optimization, stochastic quasi-gradient method, fuzzy random variable, the weakest t-norm. 
@article{FSSC_2021_16_1_a1,
     author = {Yu. E. Egorova},
     title = {On a method of solving of possibilistic-probabilistic programming problems},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {21--33},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a1/}
}
TY  - JOUR
AU  - Yu. E. Egorova
TI  - On a method of solving of possibilistic-probabilistic programming problems
JO  - Nečetkie sistemy i mâgkie vyčisleniâ
PY  - 2021
SP  - 21
EP  - 33
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a1/
LA  - ru
ID  - FSSC_2021_16_1_a1
ER  - 
%0 Journal Article
%A Yu. E. Egorova
%T On a method of solving of possibilistic-probabilistic programming problems
%J Nečetkie sistemy i mâgkie vyčisleniâ
%D 2021
%P 21-33
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a1/
%G ru
%F FSSC_2021_16_1_a1
Yu. E. Egorova. On a method of solving of possibilistic-probabilistic programming problems. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 1, pp. 21-33. http://geodesic.mathdoc.fr/item/FSSC_2021_16_1_a1/

[1] Yazenin A. V., “Linear programming with random fuzzy data”, Soviet Journal of Computer and Systems Sciences, 1991, no. 30, 86–93 | MR | Zbl

[2] “On a method of solving a problem of linear programming with random fuzzy data”, Journal of Computer and Systems Sciences International, 36:5 (1997), 737–741 | Zbl

[3] Egorova Yu. E., Yazenin A. V., “Stochastic quasi-gradient method for solving possibilistic-probabilistic optimization task of one class”, Herald of Tver State University. Series: Applied Mathematics, 2014, no. 4, 57–70 (in Russian)

[4] Egorova Y. E., Yazenin A. V., “The problem of possibilistic-probabilistic optimization”, Journal of Computer and Systems Sciences International, 56:4 (2017), 652–667 | DOI | MR | MR | Zbl

[5] Yazenin A., Soldatenko I., “On the Problem of Possibilistic-Probabilistic Optimization with Constraints on Possibility/Probability”, Advances in Intelligent Systems and Computing, Lecture Notes in Computer Science, 11291, eds. Giove S., Masulli F., Fuller R., Springer, Cham, 2019, 43–54 | DOI

[6] Yazenin A., Soldatenko I., “On the Problem of Possibilistic-Probabilistic Optimization with Constraints on Possibility/Probability”, Advances in Intelligent Systems and Computing, Lecture Notes in Computer Science, 11291, eds. Giove S., Masulli F., Fuller R., Springer, Cham, 2019, 43–54 | DOI

[7] Egorova Yu. E., “Stochastic penalty method in problems of probabilistic-probabilistic programming”, Fuzzy Systems and Soft Computing, 14:1 (2019), 64–74 (in Russian) | DOI | Zbl

[8] Yazenin A., Soldatenko I., “A portfolio of minimum risk in a hybrid uncertainty of a possibilistic-probabilistic type: comparative study”, Advances in Fuzzy Logic and Technology 2017, EUSFLAT 2017, IWIFSGN 2017, Advances in Intelligent Systems and Computing, 643, eds. Kacprzyk J., Szmidt E., Zadrożny S., Atanassov K., Krawczak M., 2018, 551–563 | DOI

[9] Egorova Yu. E., Yazenin A. V., “A method for minimum risk portfolio optimization under hybrid uncertainty”, Journal of Physics: Conference Series, 973 (2018), 012033 | DOI

[10] Nahmias S., “Fuzzy variables”, Fuzzy Sets and Systems, 1:2 (1978), 97–110 | DOI | MR | Zbl

[11] Nahmias S., “Fuzzy variables in a random environment”, Advances in Fuzzy Set Theory and Applications, eds. M.M. Gupta, R.K. Ragade, R.R. Yager, North-Holland, Amsterdam, 1979, 165–180 | MR

[12] Yazenin A., Wagenknecht M., Possibilistic Optimization. A Measure-Based Approach, Brandenburgische Technische Universitat, Cotbus, Germany, 1996, 133 pp.

[13] 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)

[14] Khokhlov M. Yu., Yazenin A. V., “Calculation of numerical characteristics of fuzzy random variables”, Herald of Tver State University. Series: Applied Mathematics, 2003, no. 1, 39–43 (in Russian) | MR

[15] Dubois D., Prade H., Theorie des Possibilites, Application a la Representation des Connaissances en Informatique, Masson, Paris, 1988 | MR | MR

[16] Nguyen H. T., Walker E. A., A First Course in Fuzzy Logic, CRC Press, Boca Raton, 1997 | MR | Zbl

[17] Hong D. H., “Parameter estimations of mutually t-related fuzzy variables”, Fuzzy Sets and Systems, 123:1 (2001), 63–71 | DOI | MR | Zbl

[18] Ermolev Yu. M., Stochastic programming methods, Nauka Publ., Moscow, 1976 (in Russian)