Uncertain and fuzzy object bases: A data model and algebraic operations

Abstract

Fuzzy set theory and probability theory are complementary for soft computing, in particular object-oriented systems with imprecise and uncertain object properties. However, current fuzzy object-oriented data models are mainly based on fuzzy set theory or possibility theory, and lack of a rigorous algebra for querying and managing uncertain and fuzzy object bases. In this paper, we develop an object base model that incorporates both fuzzy set values and probability degrees to handle imprecision and uncertainty. A probabilistic interpretation of relations on fuzzy sets is introduced as a formal basis to coherently unify the two types of measures into a common framework. The model accommodates both class attributes, representing declarative object properties, and class methods, representing procedural object properties. Two levels of property uncertainty are taken into account, one of which is value uncertainty of a definite property and the other is applicability uncertainty of the property itself. The syntax and semantics of the selection and other main data operations on the proposed object base model are formally defined as a full-fledged algebra. © 2011 World Scientific Publishing Company.