Approximation of proximities by aggregating T-indistinguishability operators

Abstract

For a continuous Archimedean t-norm T a method to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T-transitive one is provided. It consists of aggregating the transitive closure R of R with a (maximal) T-transitive relation B contained in R using a suitable weighted quasi-arithmetic mean to maximize the similarity or minimize the distance to R.