Numerical solutions of fuzzy differential equations

Ma, Ming; Friedman, Menahem; Kandel, Abraham

doi:10.1016/s0165-0114(97)00233-9

Cited by 203 publications

(110 citation statements)

References 12 publications

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“…The basic definitions of fuzzy numbers and fuzzy sets are given in [9], [13], [22], [30]. In this section, some of them are reviewed.…”

Section: Preliminariesmentioning

confidence: 99%

“…One of the important topics in fuzzy mathematics and its applications is to solve fuzzy differential equations (FDEs) based on the definition of fuzzy derivative [7], [14], [15], [26], [27], [30]. One of the fundamental difference schemes to solve FDEs is Runge-Kutta methods which play the important role in numerical methods of solving ordinary differential equations [8], [16], [19], [21], [23], [36], [38].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical control of accuracy in the fuzzy Runge-Kutta methods to estimate the solution of a fuzzy differential equation

Araghi¹,

Kelishami²

2016

Journal of Fuzzy Set Valued Analysis

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In this paper, a reliable scheme is proposed to solve fuzzy differential equations by fuzzy Runge-Kutta method of order m. For this purpose, the stochastic arithmetic and CESTAC method are applied to validate the results. In order to implement the C++ codes, the CADNA library is used. In this case, the optimal step size is found. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic.

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“…The basic definitions of fuzzy numbers and fuzzy sets are given in [9], [13], [22], [30]. In this section, some of them are reviewed.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical control of accuracy in the fuzzy Runge-Kutta methods to estimate the solution of a fuzzy differential equation

Araghi¹,

Kelishami²

2016

Journal of Fuzzy Set Valued Analysis

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show abstract

“…For arbitrary u = (u(r), u(r)), v = (v(r), v(r)) and k > 0 we define addition u + v , subtraction u ⊖ v and scalar multiplication by k as (See [1,3]) The Hausdorff distance between fuzzy numbers given by d :…”

Section: Preliminariesmentioning

confidence: 99%

Evaluating customers' satisfaction in the industrial company with uncertainty

Jafarnejad¹,

Lotfi²

2014

Journal of Soft Computing and Applications

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In this paper, the evaluation of customers'satisfaction is investigated by using group decision making method under uncertainty. Here, we have used the Zadeh's fuzzy concept to model and measure the satisfaction. For this purpose, we have firstly applied the Delphi method with fuzzy Likert scales. Then, the fuzzy ELECTRE technique was used in order to ordering the index and questionnaires. For determining weights of the index we have applied the Zadeh's extension principle. On order to show the applicability of the proposed fuzzy approach, we have provided a case study which was applied in Isfahan Gas Company.

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“…Murugesan et al [16] compared fourth order RK methods based on variety of means and concluded that RK4CeM works very well to solve system of IVPs and they also developed [17] a new embedded RK method based on AM and CeM. The applicability of the RK4CeM : Division by zero, Error in RK4CeM formulae, and Stability analysis are discussed by Murugesan et al [15].…”

Section: Introductionmentioning

confidence: 99%

Fourth Order Runge-Kutta Method Based On Geometric Mean for Hybrid Fuzzy Initial Value Problems

Sharmila¹

2017

IOSR JM

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Numerical solutions of fuzzy differential equations

Cited by 203 publications

References 12 publications

Dynamical control of accuracy in the fuzzy Runge-Kutta methods to estimate the solution of a fuzzy differential equation

Dynamical control of accuracy in the fuzzy Runge-Kutta methods to estimate the solution of a fuzzy differential equation

Evaluating customers' satisfaction in the industrial company with uncertainty

Fourth Order Runge-Kutta Method Based On Geometric Mean for Hybrid Fuzzy Initial Value Problems

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