Browsing by Author "Amrahov, S. E."

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A New Approach to Fuzzy Initial Value Problem
(2014) Gasilov, N. A.; Fatullayev, A. G.; Amrahov, S. E.; Khastan, A.; https://orcid.org/0000-0002-9955-8439; AEN-1756-2022
In this paper, we consider a high-order linear differential equation with fuzzy initial values. We present solution as a fuzzy set of real functions such that each real function satisfies the initial value problem by some membership degree. Also we propose a method based on properties of linear transformations to find the fuzzy solution. We find out the solution determined by our method coincides with one of the solutions obtained by the extension principle method. Some examples are presented to illustrate applicability of the proposed method.
On the Numerical Solution of Linear Differential Equations with Interval Coefficients
(2017) Gasilov, N. A.; Amrahov, S. E.; https://orcid.org/0000-0001-7747-5467; AEN-1756-2022; AAF-3339-2020
In this study, we consider Initial Value Problem (IVP) for a linear differential equation with interval coefficients. The initial values of the problem are taken as intervals, too. We interpret the interval IVP as a set of classical IVPs, and we investigate the bunch (set) of their solutions. We define this bunch to be the solution of the interval IVP. We develop a numerical method to find the upper and lower bounds of the solution bunch. We apply the method to an example and illustrate the solution.
Solution Method for A Boundary Value Problem with Fuzzy Forcing Function
(2015) Gasilov, N. A.; Amrahov, S. E.; Fatullayev, A.G.; Hashimoglu, I. F.; 0000-0002-9955-8439; 0000-0001-7747-5467; AEN-1756-2022; AAF-3339-2020
In this paper, we present a new approach to a non-homogeneous fuzzy boundary value problem. We consider a linear differential equation with real coefficients but with a fuzzy forcing function and fuzzy boundary values. We assume that the forcing function is a triangular fuzzy function. Unlike previous studies, we look for a solution that is a fuzzy set of real functions (not a fuzzy-valued function). Each of these real functions satisfies the boundary value problem with some membership degree. We have developed a method that finds this solution, and demonstrated its effectiveness using a test example. To show that the approach can be extended to other types of fuzzy numbers, we extended it to the trapezoidal case. For a particular example, we used the product t-norm to demonstrate how a new solution type can be obtained. (C) 2015 Elsevier Inc. All rights reserved.