Conditioned weighted L–R approximations of fuzzy numbers

We compute the extended weighted L–RL–R approximation of a given fuzzy number by a method based on general results in Hilbert spaces, the weighted average Euclidean distance being considered. The metric properties of the extended weighted L–RL–R approximation of a fuzzy number are proved. We elaborate on a general method to study the existence, uniqueness and to calculate the L–RL–R approximations of fuzzy numbers under the preservation of some parameters. We apply the results to find the weighted L–RL–R approximations preserving ambiguity and value and respectively width in the general and unimodal case.