I. Introduction
In the classical fuzzy set theory, it is known that the family of cut-sets uniquely determines the starting fuzzy structure. Therefore, from the beginning of fuzzy era, identification of a fuzzy set by the collection of its cuts has been an important problem. For [0, 1]- valued fuzzy sets, as well as for particular lattice-valued ones, known relevant results were obtained by Negoita and Ralescu ([7], [8], [9], [10], [11]). Recently, many problems connected with the representation of collections of subsets as cuts of fuzzy sets (still for [0, 1]-valued fuzzy sets) have been formulated and solved by Jaballah and Saidi (see e.g., [4], [12], [13], [14]).