Nearest piecewise linear approximation of fuzzy numbers

The problem of the nearest approximation of fuzzy numbers by piecewise linear 1-knot fuzzy numbers is discussed. By using 1-knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study. They might be also perceived as a generalization of the trapezoidal approximations. Moreover, these approximations possess some desirable properties. Apart from theoretical considerations approximation algorithms that can be applied in practice are also given. (C) 2013 Elsevier B.V. All rights reserved.