Partial quasi-metrics and fixed point theory: an aggregation viewpoint

Abstract

[eng] In many fields of applied sciences, the aggregation of numerical values, in order to get a final one which allows to make a decision, plays a central role. Many times these numerical values represent dissimilarities and the merged value can be interpreted as a global dissimilarity. Inspired, on the one hand, by the interest that causes the dissimilarities aggregation problem and, on the other hand, by the utility of generalized dissimilarities in applied sciences, we focus our work on the problem of merging the so-called partial quasi-metrics, which have been introduced in the literature with the aim of developing a framework that allows to unify the notion of metric, quasi-metric and partial metric under a unique one. Concretely, we characterize those functions that merge a collection of partial quasi-metrics into a new one. Moreover, a few relationships between this kind of functions and those that merge (quasi-)metrics and partial metrics are discussed. Furthermore, a general fixed point result for contractions obtained through aggregation functions is given.