Relations between similarity-based systems, evaluating similarity to some prototypes, and fuzzy rule-based systems, aggregating values of membership functions, are investigated. Similarity measures based on information theory and probabilistic distance functions lead to a new type of membership functions applicable to symbolic data. Fuzzy membership functions on the other hand lead to a new typ...

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...

In this paper, we introduce a fuzzy set theoretic approach for dealing with uncertainty in images in the context of spatial and topological relations existing among the objects in the image. We propose an object-oriented graph theoretic model for representing an image and this model allows us to assess the similarity between images using the concept of (fuzzy) graph matching. Sufficient flexibi...

Similarities are an extension of equivalence relations to a fuzzy context. In this paper we introduce the class of similarity MV-algebras obtained as a generalization of the variety of MValgebras by adding a binary operator playing the role of similarity. We further introduce the similarity Łukasiewicz logic and we prove a completeness theorem.

Due to the scale and the decentralized nature of the Semantic Web, heterogeneities among concepts used are the rule rather than the exception. To provide a meaningful basis for tasks like reasoning over or discovery of semantic web services, similarity relationships must be defined among them in a semi-automatic way. Similarity computation schemes with single hierarchical concept relations are ...

Though the data integration problem of relational databases has been well studied, little work addresses the problem in the context of fuzzy relational databases. The fuzzy relational model relies on the specification of either a similarity relation or a proximity relation for each scalar domain in the fuzzy database. Without the constraint of max-min transitivity, proximity relations can be de...

Lewis–Stalnaker’s semantics for counterfactuals is based on the notion of similarity of possible worlds. Since the general notion of similarity is prominently studied in fuzzy mathematics, where it is modeled by fuzzy equivalence relations, it is natural to attempt at reconstructing Lewis’ and Stalnaker’s ideas in terms of fuzzy similarities. This paper sketches such a reconstruction; full deta...