On Existence and Uniqueness of Solutions to the Fuzzy Dynamic Equations on Time Scales

Fard, Omid Solaymani; Bidgoli, Tayebeh Aliabdoli; Rivaz, Azim

doi:10.3390/mca22010016

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…The optic disc cup and the parameters of the optic plate were used in the assessment of the glaucoma clutter. Fard et al [6] utilized a Support Vector Machine (SVM) when calculating the Fcut done through the use of random mass transformation. Among the various detection techniques, background image-based detection of the retina plays an important role as it was subjected to noninvasive detection methods.…”

Section: Literature Reviewmentioning

confidence: 99%

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

Kavitha,

Raj,

Kautish

et al. 2024

CMES

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The intuitive fuzzy set has found important application in decision-making and machine learning. To enrich and utilize the intuitive fuzzy set, this study designed and developed a deep neural network-based glaucoma eye detection using fuzzy difference equations in the domain where the retinal images converge. Retinal image detections are categorized as normal eye recognition, suspected glaucomatous eye recognition, and glaucomatous eye recognition. Fuzzy degrees associated with weighted values are calculated to determine the level of concentration between the fuzzy partition and the retinal images. The proposed model was used to diagnose glaucoma using retinal images and involved utilizing the Convolutional Neural Network (CNN) and deep learning to identify the fuzzy weighted regularization between images. This methodology was used to clarify the input images and make them adequate for the process of glaucoma detection. The objective of this study was to propose a novel approach to the early diagnosis of glaucoma using the Fuzzy Expert System (FES) and Fuzzy differential equation (FDE). The intensities of the different regions in the images and their respective peak levels were determined. Once the peak regions were identified, the recurrence relationships among those peaks were then measured. Image partitioning was done due to varying degrees of similar and dissimilar concentrations in the image. Similar and dissimilar concentration levels and spatial frequency generated a threshold image from the combined fuzzy matrix and FDE. This distinguished between a normal and abnormal eye condition, thus detecting patients with glaucomatous eyes.

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Section: Literature Reviewmentioning

confidence: 99%

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

Kavitha,

Raj,

Kautish

et al. 2024

CMES

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Existence and uniqueness of solutions to the second order fuzzy dynamic equations on time scales

Fard

Bidgoli

2017

Adv Differ Equ

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In this paper, we introduce a new metric space to study the existence and uniqueness of solutions to second order fuzzy dynamic equations on time scales. In this regard, we use Banach's fixed point theorem to prove this result. Also, we see that this metric guarantees an elegant and easier proof for the existence of solutions to second order fuzzy dynamic equations on time scales.MSC: Primary 34A05; secondary 34N07

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Initial Value Methods for the Numerical Simulation of Fuzzy Two-Point Boundary Value Problems Using General Linear Method

Attili

2021

International Journal of Fuzzy System Applications

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This article considers the numerical simulation of fuzzy two-point boundary value problems (FBVP) using general linear method (GLM). The author derived the method, which is a combination of a Runge-Kutta type method and multi-step method. It is originally designed to solve initial value problems. It requires fewer function evaluations than the traditional Runge-Kutta methods making it computationally more efficient in achieving the required accuracy. The author will utilize the combination of the GLM with initial value methods to solve the linear fuzzy BVP's and a shooting-like method for the nonlinear cases. Numerical testing and simulation of several examples, considered by other authors, will be presented to show the efficiency of the proposed method.

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On Existence and Uniqueness of Solutions to the Fuzzy Dynamic Equations on Time Scales

Cited by 3 publications

References 20 publications

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

Existence and uniqueness of solutions to the second order fuzzy dynamic equations on time scales

Initial Value Methods for the Numerical Simulation of Fuzzy Two-Point Boundary Value Problems Using General Linear Method

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