Measure, error and intrinsic fuzziness: a mathematical study of vagueness

Abstract

 An operative method is proposed to evaluate degrees of membership, in situations when imprecise observations are made in a repeated way. The procedure is developed for limited subsets of the real axis R, but can be extended to R^N. The analysis of a special case in R² shows the existence of sets whose membership function does not become a characteristic function, even when the inaccuracy of sampling vanishes and the observations are made in absolutely precise way.