Fuzzy types and their lattices

Fuzzy sets and fuzzy logic are essential approaches to uncertain and vague information representation and reasoning. This paper is focused on uncertainty about types of objects and reasoning with it. A fuzzy type is formulated as a pair of a basic type and a truth-value, where a basic type can be crisp or vague (in the intuitive sense). A structure for a class of truth-value lattices is proposed for this construction. Then, fuzzy type lattices are developed with the fuzzy sub-type partial order satisfying intuition, and fuzzy type intersection and union operations. The result forms a basis for development of an order-sorted fuzzy logic system.