Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
On the differentiability of set-valued functions defined on a Banach space and mean value theorem
Applied Mathematics and Computation
Rough-Fuzzy Hybridization: A New Trend in Decision Making
Rough-Fuzzy Hybridization: A New Trend in Decision Making
A First Course in Fuzzy Logic, Third Edition
A First Course in Fuzzy Logic, Third Edition
First order linear fuzzy differential equations under generalized differentiability
Information Sciences: an International Journal
Rough Derivatives in Rough Function Model and Their Application
FSKD '07 Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery - Volume 03
The Theory and Application of Rough Integration in Rough Function Model
FSKD '07 Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery - Volume 03
Note on "Numerical solutions of fuzzy differential equations by predictor-corrector method"
Information Sciences: an International Journal
Comparation between some approaches to solve fuzzy differential equations
Fuzzy Sets and Systems
Fuzzy transforms of higher order approximate derivatives: A theorem
Fuzzy Sets and Systems
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To predict the future state of a physical system, we must know the differential equations x = f(x) that describe how this state changes with time. In many practical situations, we can observe individual trajectories x(t). By differentiating these trajectories with respect to time, we can determine the values of f(x) for different states x; if we observe many such trajectories, we can reconstruct the function f(x). However, in many other cases, we do not observe individual systems, we observe a set X of such systems. We can observe how this set X changes, but not how individual states change. In such situations, we need to reconstruct the function f(x) based on the observations of such "set trajectories" X(t). In this paper, we show how to extend the standard differentiation techniques of reconstructing f(x) from vector-valued trajectories x(t) to general set-valued trajectories X(t).