A note on trapezoidal approximations of fuzzy numbers

In this paper, we propose some generalized and new properties of the trapezoidal approximations of fuzzy numbers. First, we claim that the trapezoidal approximation operator is linear with respect to the operations of fuzzy numbers. Second, we show a new property concerning the centroid points of fuzzy numbers. Furthermore, a comment for computing the trapezoidal approximations is provided. Finally, some properties about the distance between a fuzzy number and its trapezoidal approximation are proved. (C) 2006 Elsevier B.V. All rights reserved.