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Fuzzy differential equations

Fuzzy Sets and Systems, 1987
A differential and integral calculus for fuzzy-set-valued mappings was developed in recent papers of Dubois and Prade, and Puri and Ralescu. The purpose of this paper is to study differential equations for fuzzy-set- valued mappings of a real variable whose values are normal, convex, upper semi-continuous and compactly supported fuzzy sets in \(R^ n\).
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Fuzzy differential equations

Fuzzy Sets and Systems, 2000
The authors consider the following fuzzy initial value problem \[ {du(t)\over dt}= f(t,u(t)),\quad t\in [0,\infty),\quad u(0)= u_0\in E^n,\tag{1} \] where \({du\over dt}\) denotes the Hukuhara derivative of function \(u,f:[0, \infty)\times E^n\to E^n\) is continuous, and the set \[ E^n:= \{u\in\mathbb{R}^n\to [0,1]\mid u\text{ satisfies (i)}\sim \text{(
Park, Jong Yeoul, Han, Hyo Keun
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Fuzzy Differential Equations

2015
Fuzzy differential equations (FDEs) appear as a natural way to model the propagation of epistemic uncertainty in a dynamical environment. There are several interpretations of a fuzzy differential equation. The first one historically was based on the Hukuhara derivative introduced in Puri-Ralescu [123] and studied in several papers (Wu-Song-Lee [150 ...
Luciana Takata Gomes   +2 more
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