Metric properties of the extended weighted semi-trapezoidal approximations of fuzzy numbers and their applications

Abstract

We compute the extended semi-trapezoidal approximation of a given fuzzy number, with respect to the weighted average Euclidean distance. The metric properties of the extended weighted semi-trapezoidal approximation of a fuzzy number, proved in the present article, help us to solve problems of weighted approximations (semi-trapezoidal and semi-triangular) under conditions and to obtain general results of aggregation of the weighted approximations. © 2012 Springer-Verlag Berlin Heidelberg.