A recent paper was dedicated to find the nearest fuzzy triangular approximations of a fuzzy number by using α-weighted valuations. We prove, by simple examples, that the results of approximations are not always triangular fuzzy numbers and that in fact they are not fuzzy sets. We give a correct solution of the problem of approximation in a more general case, and we study the properties of identity, additivity, translation invariance, scale invariance, and monotonicity of the new approximation operator.
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