@misc{Coroianu_Lucian._Autor_Piecewise_2014,
 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={2014},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={We discuss the solution to the problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric. A piecewise linear representation of Fuzzy Numbers is important as far as computer implementation of extension principle-based arithmetic operations is concerned. First of all, we generalize the results presented in Coroianu, Gagolewski, Grzegorzewski, Nearest piecewise linear approximation of fuzzy numbers, FSS 233 (2013), pp. 26-51. Here the n-knot piecewise linear fuzzy numbers for arbitrary n > 2 are examined instead of 1-knot fuzzy numbers. We prove some results on the existence and properties of the approximation operator. Secondly, we study the limiting behavior of the introduced approxima¬tion operator, like the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity. Finally, we provide a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers. Suggested concepts are illustrated by examples and algorithms ready for the practical use.},
 title={Piecewise Linear Approximation of Fuzzy Numbers – a Discussion on Algorithms, Arithmetic Operations and Stability of Fuzzy Number Characteristics},
 type={Text},
 keywords={Fuzzy numbers, Liczby rozmyte, Approximation of fuzzy numbers, Piecewise linear approximation},
}