Learning relations of objects has recently emerged as a new promising trend for supervised machine learning. Case-based reasoning (CBR) is a subfield of machine learning, which attempts to solve new problems by reusing previous experiences. There is a close link between learning of relations and case-based reasoning in the sense that relation analysis between cases is a core task in a CBR proce...

This paper is devoted to the duality between fuzzy sets and equality relations. It comprises various results that allow to interchange from one framework to the other. Finally it is shown that in fuzzy reasoning the inherent similarity characterized by equality relations cannot be avoided.

Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

This paper introduces a new approach for decision support. It is characterized by a collaborative decision making process relying on the implicit sharing of preferences and experience between di erent individuals facing similar decision problems. A recommendation principle is described, based on fuzzy ltering methods de ned from individual fuzzy preference relations and fuzzy similarity relatio...

In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of...

Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy T–similarity relations are used to define the optimistic and pessimistic fu...

In this work we consider a very general principle for fuzzy rule interpolation methods based on an interpretation of the generalized modus ponens rule in terms of closeness relations. Then we present two particular instances of the general principle when the closeness relations are defined from parametric families of similarity fuzzy relations on the input and output spaces. The case of multipl...

Aggregation of non-finite families of transitive relations is studied and applied to calculate the degrees of inclusion and similarity of fuzzy quantities (fuzzy subsets of an interval of the real line).

The fuzzy logic operators are used to decide the following multicriteria decision-making problem. A finite set of alternatives is evaluated by a set of fuzzy criteria, i.e., fuzzy relations, which may be either fuzzy preference, or similarity, or likeness relations. The problem is to construct an evaluation procedure to compare the set of alternatives according to the whole set of criteria, i.e...

This paper addresses the added value that is provided by using distance-based fuzzy relations in flexible query answering. To use distances and/or concepts of gradual similarity in that domain is not new. Within the last ten years, however, results in the theory of fuzzy relations have emerged that permit a smooth and pragmatic, yet expressive and effective, integration of ordinal concepts too....