Geodesic
Converting a continuous fuzzy signal by a linear dynamic system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 34-48.

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

In this paper, we apply the method of Green's function to the search for bounded solutions of a high-order linear differential equation with constant coefficients and a fuzzy right-hand side. A class of equations with positive coefficients and a nonnegative Green's function is distinguished, for which the results on the existence and smoothness of a fuzzy solution bounded on the whole axis are established. We prove that in the case where the right-hand side has a triangular form, the solution has the same form. Examples of radio engineering circuits with fuzzy input signals are considered.
Keywords: fuzzy-valued functions, fuzzy dynamical systems with a constant coefficient, Green's function method. 
@article{INTO_2024_237_a3,
     author = {V. L. Khatskevich},
     title = {Converting a continuous fuzzy signal by a linear dynamic system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {34--48},
     publisher = {mathdoc},
     volume = {237},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_237_a3/}
}
TY  - JOUR
AU  - V. L. Khatskevich
TI  - Converting a continuous fuzzy signal by a linear dynamic system
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2024
SP  - 34
EP  - 48
VL  - 237
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2024_237_a3/
LA  - ru
ID  - INTO_2024_237_a3
ER  - 
%0 Journal Article
%A V. L. Khatskevich
%T Converting a continuous fuzzy signal by a linear dynamic system
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2024
%P 34-48
%V 237
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2024_237_a3/
%G ru
%F INTO_2024_237_a3
V. L. Khatskevich. Converting a continuous fuzzy signal by a linear dynamic system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 34-48. http://geodesic.mathdoc.fr/item/INTO_2024_237_a3/

[1] Averkin A. N., Nechetkie mnozhestva v modelyakh upravleniya i iskusstvennogo intellekta, Nauka, M., 1986

[2] Baskakov S. I., Radiotekhnicheskie tsepi i signaly, Vysshaya shkola, M., 1988

[3] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970

[4] Demenkov N. P., Mikrin E. A., Mochalov I. A., “Nechetkoe optimalnoe upravlenie lineinymi sistemami. Ch. 1. Pozitsionnoe upravlenie”, Inform. tekhnol., 25:5 (2019), 259–270

[5] Krasnoselskii M. A., Burd V. Sh., Kolesov Yu. S., Nelineinye pochti periodicheskie kolebaniya, Nauka, M., 1970

[6] Mochalov I. A., Khrisat M. S., Shikhab Eddin M. Ya., “Nechetkie differentsialnye uravneniya v zadachakh upravleniya. Ch. II”, Inform. tekhnol., 21:4 (2015), 243–250

[7] Pegat A., Nechetkoe modelirovanie i upravlenie, BINOM. Laboratoriya znanii, M., 2015

[8] Khatskevich V. L., “Nepreryvnye protsessy s nechetkimi sostoyaniyami i ikh prilozheniya”, Avtomat. telemekh., 8 (2023), 43–60

[9] Ahmad L., Farooq M., Abdullah S., Solving $n$th order fuzzy differential equation by fuzzy Laplace transform, arXiv: arXiv:1403.0242 [math.GM]

[10] Allahviranloo T., Abbasbandy S., Salahshour S., Hakimzadeh A., “A new method for solving fuzzy linear differential equations”, Soft Comput., 92 (2011), 181–197

[11] Aumann R. J., “Integrals of set-valued functions”, J. Math. Anal. Appl., 12 (1965), 1–12

[12] Bede B., Gal S. G. , “Almost periodic fuzzy-number-valued functions”, Fuzzy Sets Syst., 147:3 (2004), 385–403

[13] Bede B., Gal S. G. , “Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations”, Fuzzy Sets Syst., 151:3 (2005), 581–599

[14] Cao L., Yao D., Li H., Meng W., Lu R., “Fuzzy-based dynamic event triggering formation control for nonstrict-feedback nonlinear MASs”, Fuzzy Sets Syst., 452 (2023), 1–22

[15] Dai R., Chen M., “On the structural stability for two-point boundary value problems of undamped fuzzy differential equations”, Fuzzy Sets Syst., 453:95–114 (2023)

[16] ElJaoui E., Melliani S., Chadli L. S., “Solving second-order fuzzy differential equations by the fuzzy Laplace transform method”, Adv. Differ. Equations., 2015, 66

[17] Esmi E., Sanchez D. E., Wasques V. F., de Barros L. C., “Solutions of higher order linear fuzzy differential equations with interactive fuzzy values”, Fuzzy Sets Syst., 419 (2021), 122–140

[18] Hukuhara M., “Intégration des applications mesurables dont la valeur est un compact convexe”, Func. Ekvacioj., 11 (1967), 205–223

[19] Kaleva O., “Fuzzy differential equations”, Fuzzy Sets Syst., 24:3 (1987), 301–317

[20] Kaleva O., Seikkala S., “On fuzzy metric spaces”, Fuzzy Sets Syst., 12 (1984), 215–229.

[21] Khastan A., Bahrami F., Ivaz K., “New results on multiple solutions for $N$th order fuzzy differential equations under generalized differentiability”, Boundary Value Probl., 7 (2009), 1–13

[22] Liu H. K., “Comparison result of two-point fuzzy boundary value problems”, Int. J. Comput. Math. Sci., 5:1, 463–469

[23] Park J. Y., Han H. K., “Existence and uniqueness theorem for a solution of fuzzy differential equations”, Int. J. Math. Math. Sci., 22:2 (1996), 271–279

[24] Puri M. L., Ralescu D. A., “Differential of fuzzy functions”, J. Math. Anal. Appl., 91 (1983), 552–558

[25] Salahshour S., Allahviranloo T., “Applications of fuzzy Laplace transforms”, Soft Comput., 17 (2013), 145–158

[26] Seikkala S., “On the fuzzy initial value problem”, Fuzzy Sets Syst., 24:3 (1987), 319–330

[27] Wu H. C., “The fuzzy Riemann integral and its numerical integration”, Fuzzy Sets Syst., 110:1 (2000), 1–25

[28] Zhao R., Lu L., Feng G., “Asynchronous fault detection filtering design for continuous-time T-S fuzzy affine dynamic systems in finite-frequency domain”, Fuzzy Sets Syst., 452 (2023), 168–190