A reasonable approximation of a fuzzy number should have
a simple membership function, be close to the input fuzzy number, and
should preserve some of its important characteristics. In this paper we
suggest to approximate a fuzzy number by a piecewise linear 1-knot fuzzy
number which is the closest one to the input fuzzy number among all
piecewise linear 1-knot fuzzy numbers having the same core and the same
support as the input. We discuss the existence of the approximation op-
erator, show algorithms ready for the practical use and illustrate the
considered concepts by examples. It turns out that such an approxima-
tion task may be problematic.
کلید واژگان :
Approximation of fuzzy numbers; core; fuzzy number; piece- wise linear approximation; support.
