Designing Fuzzy Relations in Orthogonal Persistence Object-Oriented Database Engines

Abstract

Semantic relations between concepts or data are common modelling devices in various knowledge representation approaches. Fuzzy relations can be defined as fuzzy subsets of the cartesian product of a number of domains, extending the notion of crisp relation. Associations in object-oriented modelling - and more specifically in the Unified Modelling Language - can be interpreted as crisp relations on the classifiers they connect, and thus the concept of association can be extended to its fuzzy counterpart by representing a fuzzy relation on the classes involved in the association. In this paper, the resolution form of a fuzzy relation is described as a convenient way to represent fuzzy associations in objectoriented programming languages, thus enabling an efficient practical representation mechanism for them. Specific cases of fuzzy relations can also be dealt with by adding semantic constraints to fuzzy associations. One of the most interesting cases is that of similarity relations, which essentially generalize the notion of object equality to the fuzzy case. Fuzzy relations can be stored in orthogonally persistent object databases by using the described fuzzy association design, as illustrated in this paper with a case study that uses the db4o persistence engine.