Ample Fields
نویسندگان
چکیده
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.
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Ample fields as a basis for possibilistic processes
Ample fields play an important role in possibility theory. These fields of subsets of a universe, which are additionally closed under arbitrary unions, act as the natural domains for possibility measures. A set provided with an ample field is then called an ample space. In this paper we generalise Wang’s notions of product ample field and product ample space. We make a topological study of ampl...
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