Survey of utilisation of fuzzy technology in Medicine and Healthcare

Abbod, Maysam F.; Keyserlingk, Diedrich Graf v.; Linkens, D.A.; Mahfouf, Mahdi

doi:10.1016/s0165-0114(99)00148-7

Cited by 177 publications

(69 citation statements)

References 113 publications

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“…Fuzzy ordinary differential equations are suitable mathematical models to model dynamical systems in which there exist uncertainties or vagueness. These models are used in various applications including, population models [26,30] mathematical physics [9], and medicine [3,7] An ordinary differential equation involving linear FIVP can be considered to be the simplest case to test the effectiveness of proposed methods for solving FDE. The explicit Runge-Kutta methods have been widely used in the solution of FIVPs.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of nth order fuzzy initial value problems by six stages

Jameel¹,

Anakira²,

Alomari³

et al. 2016

J. Nonlinear Sci. Appl.

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The purpose of this paper is to present a numerical approach to solve fuzzy initial value problems (FIVPs) involving n-th order ordinary differential equations. The idea is based on the formulation of the six stages Runge-Kutta method of order five (RKM56) from crisp environment to fuzzy environment followed by the stability definitions and the convergence proof. It is shown that the n-th order FIVP can be solved by RKM56 by transforming the original problem into a system of first-order FIVPs. The results indicate that the method is very effective and simple to apply. An efficient procedure is proposed of RKM56 on the basis of the principles and definitions of fuzzy sets theory and the capability of the method is illustrated by solving second-order linear FIVP involving a circuit model problem.

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Section: Introductionmentioning

confidence: 99%

Numerical solution of nth order fuzzy initial value problems by six stages

Jameel¹,

Anakira²,

Alomari³

et al. 2016

J. Nonlinear Sci. Appl.

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“…The first-order linear FDEs occurred in many real-world applications such as engineering [1], medicine (see [2], [3]), finance [4] and population models [5]. The problems are permeating with uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Fourth Order Diagonally Implicit Multistep Block Method for Solving Fuzzy Differential Equations

Ramli¹,

Majid²

2016

Int. J. of Pure and Appl. Math.

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Abstract:A fourth order diagonally implicit multistep block method is introduced to approximate the solution of fuzzy differential equations (FDEs). The problem is interpreted by using Seikkala's derivative. This method approximates two points simultaneously in a block along the interval. The Lagrange interpolating polynomial is applied in the formation of the formulas. The stability and convergence of this method at each computation points are given. Numerical solutions of this method are compared with the Runge-Kutta method of order four (RK(4)). The numerical results are given to highlight the performance of the proposed method when solving FDEs.

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“…Particulary, the study of fuzzy differential equation forms a suitable setting for mathematical modeling of real world problems in which uncertainties or vagueness pervade. In fact, fuzzy differential equations is a very important topic from theoretical point of view [5], [6], [7], [9] and also it has applications, for example, in population models [4], civil engineering [8], medicine [1], [2].…”

Section: Introductionmentioning

confidence: 99%