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
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
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
How to reconstruct the system's dynamics by differentiating interval-valued and set-valued functions
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
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In many practical applications, it is useful to represent a function f(x) by its fuzzy transform, i.e., by the ''average'' values F"i=@!f(x).A"i(x)dx@!A"i(x)dxover different elements of a fuzzy partitionA"1(x),...,A"n(x) (for which A"i(x)=0 and @?"i"="1^nA"i(x)=1). It is known that when we increase the number n of the partition elements A"i(x), the resulting approximation gets closer and closer to the original function: for each value x"0, the values F"i corresponding to the function A"i(x) for which A"i(x"0)=1 tend to f(x"0). In some applications, if we approximate the function f(x) on each element A"i(x) not by a constant but by a polynomial (i.e., use a fuzzy transform of a higher order), we get an even better approximation to f(x). In this paper, we show that such fuzzy transforms of higher order (and even sometimes the original fuzzy transforms) not only approximate the function f(x) itself, they also approximate its derivative(s). For example, we have F"i^'(x"0)-f^'(x"0).