@misc{Coroianu_Lucian._Autor_Nearest_2013,
 author={Coroianu, Lucian. Autor and Gągolewski, Marek. Autor and Grzegorzewski, Przemysław Wojciech. Autor},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2013},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. We generalize the results presented in Coroianu, Gagolewski, Grzegorzewski (2013). Here the n-knot piecewise linear fuzzy numbers for arbitrary n>= 2are examined instead of 1-knot fuzzy numbers. We prove some results on the existence and properties of the approximation operator. In particular, some theorems on the local uniform convergence and the convergence with respect to important characteristics of fuzzy numbers are proved. It seems that the n-knot piecewise linear approximation of fuzzy numbers is interesting both because of the theoretical like practical properties. Suggested concepts are illustrated by examples and algorithms ready for the practical use.},
 title={Nearest Piecewise Linear Approximation of Fuzzy Numbers – a General Case},
 type={Text},
 keywords={Fuzzy numbers, Liczby rozmyte, Approximation of fuzzy numbers, Aproksymacja liczb rozmytych, Aproksymacja, Piecewise linear approximation, Odcinkowa aproksymacja liniowa},
}