On dynamic behavior of second-order exponential-type fuzzy difference equation

Zhang, Qianhong; Zhang, Wenzhuan; Lin, Fubiao; Li, Dongyang

doi:10.1016/j.fss.2020.07.021

Cited by 8 publications

(5 citation statements)

References 24 publications

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“…In [19-22, 25, 26, 28-31], Using Zadeh extension principle, the authors obtained dynamical behaviors of some fuzzy difference equations. However, utilizing g-division of fuzzy numbers, Zhang et al [23,24] studied the dynamical behaviors of some nonlinear fuzzy difference equations. Compared with the former, The advantage is that the support sets of positive fuzzy solution of latter is smaller than those of former.…”

Section: Proofmentioning

confidence: 99%

“…Due to the advantage of FDE in dealing with inherent imprecision, the study on qualitative features of these models has become an important research topic both from theoretical viewpoint and in applications. Therefore, in the last decades, there has been an increasing results on the study of FDE (see [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]). It is found that fuzzy set theory has potential in the application of fuzzy differential equations and fuzzy time series (see [34][35][36][37][38][39][40]).…”

Section: Introductionmentioning

confidence: 99%

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Qualitative analysis of second-order fuzzy difference equation with quadratic term

Zhang

Ou-Yang

Pan

et al. 2022

J. Appl. Math. Comput.

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In this paper, we explore the qualitative features of a second-order fuzzy difference equation with quadratic term $$\begin{aligned} x_{n+1}=A+\frac{Bx_{n}}{x_{n-1}^2},\ \ n=0,1,\ldots . \end{aligned}$$ x n + 1 = A + B x n x n - 1 2 , n = 0 , 1 , … . Here the parameters $$A, B\in \Re _F^+$$ A , B ∈ ℜ F + and the initial values $$x_0, x_{-1}\in \Re _F^+$$ x 0 , x - 1 ∈ ℜ F + . Utilizing a generalization of division (g-division) of fuzzy numbers, we obtain some sufficient condition on the qualitative features including boundedness, persistence, and convergence of positive fuzzy solution of the model, Moreover two simulation examples are presented to verify our theoretical analysis.

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Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Qualitative analysis of second-order fuzzy difference equation with quadratic term

Zhang

Ou-Yang

Pan

et al. 2022

J. Appl. Math. Comput.

Self Cite

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“…In recent years, there has been a great interest in research with fuzzy difference equations and stability of fuzzy difference equations. [20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Fuzzy Set and Fuzzy Difference Equationsmentioning

confidence: 99%

A Mathematical Model of Susceptible Diabetes Complication (SDC) Model in Discrete Time Fuzzy and Crisp Environment

Merdan

Şişman

2022

Cumhuriyet Science Journal

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In this study, we examined the mathematical model of the discrete-time equation system with susceptible diabetes complication (SDC), which is known to be caused by environmental and genetic factors in a fuzzy environment. From the diabetes complication (DC) model, the susceptible diabetes complication (SDC) model is being developed. It was obtained using definitions of how the behavior of this model changes in a fuzzy environment. A nonlinear differential equation system transforms the sensitive diabetes complication (SDC) model into a discrete time equation system. Stability analysis of the model with jury criterion was examined. In addition, numerical solutions and graphics of the analysis of the discrete model in fuzzy environment are obtained by using the MATLAB package program.

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“…As is well known, the generalized division of fuzzy numbers has better certainty compared to classical division. Therefore, studying fuzzy difference equations with generalized division has more important practical significance [10,11]. Inspired by the above content, this work uses the generalized division (g-division) of fuzzy numbers to analyze a class of second-order nonlinear fuzzy difference equation…”

Section: Introductionmentioning

confidence: 99%

On a Fuzzy Difference Equation Based on Generalized Division

Jia,

Zhang,

Wang

et al. 2023

Advances in Transdisciplinary Engineering

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In this work, a second-order fractional fuzzy difference equation is investigated. Firstly, the fuzzy difference equation is transformed into the corresponding ordinary difference equations with parameters based on the fuzzy set theory and generalized division of fuzzy number. And then, the existence and uniqueness of the solution for the ordinary difference equations are proved by the mathematical induction, the mixed iteration method and the inequality technique. Finally, the existence and uniqueness of the solution for the fractional fuzzy difference equation is obtained.

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On dynamic behavior of second-order exponential-type fuzzy difference equation

Cited by 8 publications

References 24 publications

Qualitative analysis of second-order fuzzy difference equation with quadratic term

Qualitative analysis of second-order fuzzy difference equation with quadratic term

A Mathematical Model of Susceptible Diabetes Complication (SDC) Model in Discrete Time Fuzzy and Crisp Environment

On a Fuzzy Difference Equation Based on Generalized Division

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