Higher Order Initial Value Problem with Interactive Fuzzy Conditions

Wasques, Vinícius Francisco; Laureano, Estêvão Esmi; Barros, Laécio Carvalho de; Pedro, Francielle Santo; Sussner, Peter

doi:10.1109/fuzz-ieee.2018.8491465

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…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%

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%

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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“…Complete correlation is one type of interactivity that was introduced by Fullér et al [19,20], for two fuzzy numbers. Subsequently, the authors of [21,22] proposed an extension of this notion for n fuzzy numbers, where n > 2, and they called this relation linear interactivity.…”

Section: Fuzzy Set Theorymentioning

confidence: 99%

“…The joint possibility distribution J L was used in several problems such as fuzzy differential equations [7,21,22] and least square problems [23,24]. However this joint possibility distribution can only be applied to fuzzy numbers that have a colinear relationship between their membership functions.…”

Section: Fuzzy Set Theorymentioning

confidence: 99%

Numerical Solution for Fuzzy Initial Value Problems via Interactive Arithmetic: Application to Chemical Reactions

Wasques¹,

Esmi²,

Barros³

et al. 2020

IJCIS

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This paper studies numerical solutions for fuzzy initial value problems, where the initial conditions are given by interactive fuzzy numbers. The fuzzy solution is given by a numerical method that employs the arithmetic of interactive fuzzy numbers and yields a fuzzy number at each instant of time. The computational cost of the numerical method is also provided. The chemical decay reaction model is considered in order to illustrate that different types of interactivity produce different solutions for initial value problems. In addition, we present an application to the Lotka-Volterra model of oscillating chemical reactions.

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“…This concept was introduced by Fullér et al [3,8] for two fuzzy numbers. Subsequently, the authors of [11,15] proposed an extension of this notion for n fuzzy numbers, n > 2. The fuzzy numbers A 1 , .…”

Section: Fuzzy Sets Theorymentioning

confidence: 99%

“…The JPD J L can be used in several problems, for example, in fuzzy differential equations [2,11,15] and least squared methods [12]. However this JPD can only be applied to fuzzy numbers that have a co-linear relationship among their membership functions, which means that it can not be used for fuzzy numbers that do not have the same shape.…”

Section: Fuzzy Sets Theorymentioning

confidence: 99%

Numerical Solution for Lotka-Volterra Model of Oscillating Chemical Reactions with Interactive Fuzzy Initial Conditions

Wasques

Esmi

Barros

et al. 2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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In this paper we study Lotka-Volterra model of oscillating chemical reactions via fuzzy differential equations, where the initial conditions are given by interactive fuzzy numbers. The concept of interactivity is associated with the notion of joint possibility distribution. The fuzzy solution is given by a numerical method which considers fuzzy arithmetic with interactivity. We present some examples to illustrate that different types of interactivity produce different solutions.

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Higher Order Initial Value Problem with Interactive Fuzzy Conditions

Cited by 10 publications

References 16 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

Numerical Solution for Fuzzy Initial Value Problems via Interactive Arithmetic: Application to Chemical Reactions

Numerical Solution for Lotka-Volterra Model of Oscillating Chemical Reactions with Interactive Fuzzy Initial Conditions

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