Remarks and corrections to the triangular approximations of fuzzy numbers using ?-weighted valuations
A recent paper was dedicated to find the nearest fuzzy triangular approximations of a fuzzy number by using ?-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.
approximation fuzzy number triangular fuzzy number