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Existence and Uniqueness Theorem for the Cauchy Problem of Fuzzy Differential Equations under Non-Lipschitz Conditions
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作者 冯玉瑚 朱凡昌 《Journal of Donghua University(English Edition)》 EI CAS 2004年第4期139-142,共4页
Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and ... Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to now 展开更多
关键词 fuzzy set fuzzy differential equation existence and uniqueness non-Lipschitz condition.
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Instability Theorems for Fuzzy Differential Equations
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作者 高剑明 高国柱 《Journal of Donghua University(English Edition)》 EI CAS 2005年第5期78-80,共3页
Some instability results of the trivial solution of fuzzy differential equations via Lyapunov functions is elaborated.
关键词 fuzzy differential equations INSTABILITY
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On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations
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作者 Thabet Abdeljawad Awais Younus +1 位作者 Manar A.Alqudah Usama Atta 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第3期2163-2191,共29页
The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equation... The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equations.Our purpose in this study is to introduce the notion of fuzzy double Laplace transform,fuzzy conformable double Laplace transform(FCDLT).We discuss some basic properties of FCDLT.We obtain the solutions of fuzzy partial differential equations(both one-dimensional and two-dimensional cases)through the double Laplace approach.We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations. 展开更多
关键词 fuzzy conformable laplace transform fuzzy double laplace transform fuzzy conformable double laplace transform fuzzy conformable partial differential equation
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Numerical Solution of Second-Orders Fuzzy Linear Differential Equation 被引量:2
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作者 Junyang An Xiaobin Guo 《Applied Mathematics》 2021年第11期1118-1125,共8页
In this paper, the numerical solution of the boundary value problem that is two-order fuzzy linear differential equations is discussed. Based on the generalized Hukuhara difference, the fuzzy differential equation is ... In this paper, the numerical solution of the boundary value problem that is two-order fuzzy linear differential equations is discussed. Based on the generalized Hukuhara difference, the fuzzy differential equation is converted into a fuzzy difference equation by means of decentralization. The numerical solution of the boundary value problem is obtained by calculating the fuzzy differential equation. Finally, an example is given to verify the effectiveness of the proposed method. 展开更多
关键词 fuzzy Numbers fuzzy differential equations fuzzy Difference equation fuzzy Approximate Solution
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STABILITY ANALYSIS OF FUZZY DIFFERENTIAL EQUATIONS WITH DELAY
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作者 Zhu Wei 《Annals of Differential Equations》 2007年第4期603-607,共5页
In this paper, the exponential stability of fuzzy differential equations with delay is investigated. By employing the formula for the variation of parameters, inequality technique and the norm and measure of matrix, a... In this paper, the exponential stability of fuzzy differential equations with delay is investigated. By employing the formula for the variation of parameters, inequality technique and the norm and measure of matrix, an algebraic criterion for the exponential stability is obtained. 展开更多
关键词 exponential stability fuzzy differential equations DELAY measure of matrix
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Existence of solutions for implicit fuzzy differential inclusions 被引量:1
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作者 Chao MIN Nanjing HUANG +1 位作者 Zhibin LIU Liehui ZHANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第3期401-416,共16页
A class of implicit fuzzy differential inclusions (IFDIs) are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed s... A class of implicit fuzzy differential inclusions (IFDIs) are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions (FDIs) and fuzzy differential equations (FDEs), which might be helpful in the analysis of fuzzy dynamic systems. 展开更多
关键词 implicit fuzzy differential inclusion (IFDI) fuzzy differential equation (FDE) selection theorem stacking theorem
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Type 2 Possibility Factor Rotation in No-Data Problem
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作者 Houju Hori 《Applied Mathematics》 2023年第10期673-683,共11页
Uemura [1] discovered a mapping formula that transforms and maps the state of nature into fuzzy events with a membership function that expresses the degree of attribution. In decision theory in no-data problems, seque... Uemura [1] discovered a mapping formula that transforms and maps the state of nature into fuzzy events with a membership function that expresses the degree of attribution. In decision theory in no-data problems, sequential Bayesian inference is an example of this mapping formula, and Hori et al. [2] made the mapping formula multidimensional, introduced the concept of time, to Markov (decision) processes in fuzzy events under ergodic conditions, and derived stochastic differential equations in fuzzy events, although in reverse. In this paper, we focus on type 2 fuzzy. First, assuming that Type 2 Fuzzy Events are transformed and mapped onto the state of nature by a quadratic mapping formula that simultaneously considers longitudinal and transverse ambiguity, the joint stochastic differential equation representing these two ambiguities can be applied to possibility principal factor analysis if the weights of the equations are orthogonal. This indicates that the type 2 fuzzy is a two-dimensional possibility multivariate error model with longitudinal and transverse directions. Also, when the weights are oblique, it is a general possibility oblique factor analysis. Therefore, an example of type 2 fuzzy system theory is the possibility factor analysis. Furthermore, we show the initial and stopping condition on possibility factor rotation, on the base of possibility theory. 展开更多
关键词 Type 2 fuzzy Events Quadratic Mapping Formula Stochastic differential equation in fuzzy Event Possibility Principal Factor Analysis Possibility Oblique Factor Analysis Initial and Stopping Condition
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