Solutions of higher order linear fuzzy differential equations with interactive fuzzy values

Esmi, Estevão; Sánchez, Daniel Eduardo; Wasques, Vinícius Francisco; Barros, Laécio Carvalho de

doi:10.1016/j.fss.2020.07.019

Cited by 26 publications

(6 citation statements)

References 20 publications

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“…Other type of interactivity, which is not based on t-norm, is the one obtained by the concept of linearly interactivity, or also called completely correlation. This concept was introduced by Fullér et al [9], and subsequently, generalized by the authors of [10]. This type of interactivity can be used to study fuzzy differential equations [10,11] and optimization problems [4].…”

Section: Definition 2 (Sup-j Extension Principle)mentioning

confidence: 99%

“…This concept was introduced by Fullér et al [9], and subsequently, generalized by the authors of [10]. This type of interactivity can be used to study fuzzy differential equations [10,11] and optimization problems [4]. However this approach can only be applied to fuzzy numbers that have a co-linear relationship among their membership functions Alternatively, Esmi et al [12] employed a parametrized family of joint possibility distributions that has no restrictions, such as the linear correlation.…”

Section: Definition 2 (Sup-j Extension Principle)mentioning

confidence: 99%

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Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions

Wasques

2021

Explainable AI and Other Applications of Fuzzy Techniques

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This paper presents a numerical method to solve fuzzy partial differential equations, where the initial and boundary conditions are given by interactive fuzzy numbers. Interactivity is a relationship between fuzzy numbers that is associated with the notion of joint possibility distribution. From this approach, different solutions are presented to the fuzzy partial differential equation. In addition to the method, an algorithm is proposed to determine which of these solutions is most suitable for a given problem. The numerical solution is given by the finite difference method, adapted for the arithmetic operations of interactive fuzzy numbers. The method is applied to the heat equation, in order to illustrate the results.

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Section: Definition 2 (Sup-j Extension Principle)mentioning

confidence: 99%

Section: Definition 2 (Sup-j Extension Principle)mentioning

confidence: 99%

Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions

Wasques

2021

Explainable AI and Other Applications of Fuzzy Techniques

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“…This leads many researchers towards the study of fuzzy differential equations. Esmi et al [3] analyzed higher order interactive fuzzy differential equations. Comparison of fuzzy pre-diabetes and diabetes differential model is performed by Roy et al [4].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy-fractional modeling and simulation of electric circuits using extended He-Laplace-Carson algorithm

Qayyum,

Ahmad

2024

Phys. Scr.

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In literature, most of the electric circuits are found to be at integer order, which are unable to capture the involved uncertainties and memory effects. To understand these effects, the current study is focused on modeling and analysis of fuzzy-fractional LC circuit, RC circuit, RL circuit, and RLC circuit. Triangular fuzzy numbers are utilized to introduce uncertainties in circuits. The memory effects are considered through fractional derivative in Caputo sense. A hybrid homotopy perturbation method (HPM) is established for solution purpose, in which standard HPM is combined with Laplace-Carson transformation in fuzzy-Caputo sense. This leads to an excellent and well-organized approach to calculate numerical solutions in the aspect of fuzzy logic and fractional calculus. The results obtainedthrough proposed approach are validated by comparing them with already existing results in literature. Residual errors are also calculated across the domain of r at fractional order to determine the convergence and stability of electric circuit models. To study the dynamics of inductor, resistor, and capacitor on current along with fractional and fuzzy parameters involved in the electric circuits, contour and three-dimensional plots are constructed. Several plots specifying the fuzzy membership function of models across various parameter values are also demonstrated. The results achieved through this study indicate that He-Laplace-Carson method can assist engineers and researchers when dealing with electric circuits characterized by fuzzy and fractional dynamics.

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“…To approximate the solution of a FDE according to the generalized Hukuhara derivative, Esmi et al [6] proposed a numerical method based on a fuzzy arithmetic called J γ -interactive arithmetic. The arithmetic was originally build to fuzzy numbers [7] and adapted to interval value in [6] in order to prove that the proposed numerical method is connected with the analytic solution of FDE via generalized Hukuhara derivative. This work will use the theoretical results presented in [6] to provide a numerical solution for the Malthus population model.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy numerical solution to the Malthusian model via Jγ-interactive arithmetic

Wasques,

Esmi,

Sacilotto

et al. 2023

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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This work provides a numerical solution to the Malthusian model, considering the initial condition as a fuzzy value. The numerical solution is provided from Euler's method, in which the operations built into the method are adapted to fuzzy numbers. This numerical solution is compatible with the analytical solution obtained from the generalized Hukuhara derivative. An example is presented to illustrate the methodology.

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Solutions of higher order linear fuzzy differential equations with interactive fuzzy values

Cited by 26 publications

References 20 publications

Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions

Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions

Fuzzy-fractional modeling and simulation of electric circuits using extended He-Laplace-Carson algorithm

Fuzzy numerical solution to the Malthusian model via Jγ-interactive arithmetic

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