Population growth model via interactive fuzzy differential equation

Pedro, Francielle Santo; Barros, Laécio Carvalho de; Esmi, Estevão

doi:10.1016/j.ins.2018.12.076

Cited by 38 publications

(10 citation statements)

References 20 publications

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“…Indeed, the applications of FDEs are not limited to the theory of control, but they have been proposed in studying biomathematics [192], diabetes mellitus [193], [194], cerebrospinal fluid pressure [126], hydrologic process [195], water movement in a horizontal column [196], epidemic model [197], population growth model [82], [98], Newton's law of cooling [72], electric circuits [72], [198], and the brain tumor [199]. Moreover, some of the other proposed applications of FDEs can be found in [200] for a predatorprey model, in [201] for production inventory model, in [72] for an economical investment, and in [202] for oil palm frond.…”

Section: Applications Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

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Since the term "Fuzzy differential equations" (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.

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Section: Applications Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

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“…Let A, B be f -interactive fuzzy numbers. According to [4,13], the arithmetic operation B * f A is obtained by…”

Section: F-interactive Fuzzy Numbersmentioning

confidence: 99%

“…It is worth to notice that, when one considers the uniform distribution, the Equation (4.2) reflects the covariance between the characteristic functions of [A] α and [B] α . According to [13], if A, B ∈ R F \ R are f -interactive, where f is a monotone continuous function and B = f (A), then (4.3…”

mentioning

confidence: 99%

HIV Viral Dynamic under Treatment with Intracellular Delay and Virus Decay as Interactive Parameters

Prata¹,

Jafelice²,

Cabral³

et al. 2021

TCAM

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Treatment with antiviral drugs for human immunodeficiency virus type 1 (HIV-1) infection causes a rapid reduction in plasma viral load. Viral decline occurs in several stages and provides information on important kinetic constants of virus replication in vivo and pharmacodynamic properties. We present a mathematical model that not only considers the intracellular phase of the viral life cycle, defined as the time between the infection of a cell and the production of new viral particles, but we also consider that this parameter together with the virus decay are interactive fuzzy numbers.

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“…Y). This principle is naturally used in many areas of fuzzy mathematics such as fuzzy arithmetics, approximation reasoning, simulations, and even recently with the notion of interactivity incorporated [1,2]. To point out one particular application, we need to introduce the so-called discrete dynamical system.…”

Section: Introductionmentioning

confidence: 99%

On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones

Kupka

Škorupová

2021

Mathematics

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Zadeh’s extension principle is one of the elementary tools in fuzzy set theory, and among other things, it provides a natural extension of a real-valued continuous self-map to a self-map having fuzzy sets as its arguments. The purpose of this paper is to introduce a new algorithm that can be used for simulations of fuzzy dynamical systems induced by interval maps. The core of the proposed algorithm is based on calculations including piecewise linear maps, and consequently, an implementation of an optimization algorithm (in our case, particle swarm optimization) was prepared to obtain necessary piecewise linear approximations. For all parts of this algorithm, we provide detailed testing and numerous examples.

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Population growth model via interactive fuzzy differential equation

Cited by 38 publications

References 20 publications

A Review on Fuzzy Differential Equations

A Review on Fuzzy Differential Equations

HIV Viral Dynamic under Treatment with Intracellular Delay and Virus Decay as Interactive Parameters

On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones

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