Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity

The ambiguity was introduced to simplify the task of representing and handling of fuzzy numbers. We find the nearest real interval, nearest triangular (symmetric) fuzzy number, nearest trapezoidal (symmetric) fuzzy number of a fuzzy number, with respect to average Euclidean distance, preserving the ambiguity. A simpler and elementary method, to avoid the Karush-Kuhn-Tucker theorem and the laborious calculus associated with it and to prove the continuity is used. We give algorithms for calculus and several examples.The approximations are discussed in relation to data aggregation. (C) 2012 Elsevier Inc. All rights reserved.