Fuzzy types: a framework for handling uncertainty about types of objects

Like other kinds of information, types of objects in the real world are often found to be ®lled with uncertainty and/or partial truth. It may be due to either the vague nature of a type itself or to incomplete information in the process determining it even if the type is crisp, i.e., clearly de®ned. This paper proposes a framework to deal with uncertainty and/or partial truth in automated reasoning systems with taxonomic information, and in particular type hierarchies. A fuzzy type is formulated as a pair combining a basic type and a fuzzy truth-value, where a basic type can be crisp or vague (in the intuitive sense). A structure for a class of fuzzy truth-value lattices is proposed for this construction. The fuzzy subtype relation satisfying intuition is de®ned as a partial order between two fuzzy types. As an object may belong to more than one (fuzzy) type, conjunctive fuzzy types are introduced and their lattice properties are studied. Then, for reasoning with fuzzy types, a mismatching degree of one (conjunctive) fuzzy type to another is de®ned as the complement of the relative necessity degree of the former to the latter. It is proved that the de®ned fuzzy type mismatching degree has properties similar to those of fuzzy set mismatching degree, which allow a uni®ed treatment of fuzzy types and fuzzy sets in reasoning. The framework provides a formal basis for development of order-sorted fuzzy logic systems. Ó 2000 Elsevier Science Inc. All rights reserved.