Empty-stringizing of the false value in crisp and fuzzy granular hierarchical structures

When we describe fuzzy sets in an extensional way, those elements whose grades of membership is 0 are often omitted by convention. Also when we describe a subset in the extensional notation, we do not describe any element which does not belong to the set. Of course, such elements have grade 0 of the characteristic function of the subset. But such description is truly made just by intuitive convention ? In this paper we explain such convention in terms of the new concept of empty-stringizing in the granular hierarchical structures proposed by our previous papers.