Similarity relations: the calculation of minimal generating families
Fuzzy Sets and Systems
Fuzzy Sets and Systems
On extended fuzzy relational model with proximity relations
Fuzzy Sets and Systems
Cluster analysis based in fuzzy relations
Fuzzy Sets and Systems - Special issue on clustering and learning
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
On Fuzzy Conditionals Generalising the Material Conditional
IPMU '92 Proceedings of the 4th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems: Advanced Methods in Artificial Intelligence
Algorithms for the computation of T-transitive closures
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
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Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R of R with a (maximal) T -transitive relation B contained in R. The second one computes the closest homotecy of R or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Łukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a Mintransitive relation (a similarity) is given in the last section of the paper.