AMPLE FIELDS

In this paper, we study the notion of an ample or complete field, a special case of the well-known fields and σ-fields of sets. These collections of sets serve as candidates for the domains of possibility and necessity measures, and are therefore important for the further development of a general fuzzy set and possibility theory. The existence of a one-one relationship between ample fields and atomic complete Boolean lattices is proven. Furthermore, the concept of measurability of general fuzzy sets w.r.t. ample fields is explored.