Aggregation of Fuzzy Relations: The Bounded Partial Metric Case

Abstract

[eng] In 2002, Pradera and Trillas faced the problem of merging a special kind of fuzzy relations, the so-called bounded metrics. They gave a description of functions that allow to fuse bounded metrics defined on a set into a bounded metric defined on the aforementioned set and preserving the bound. However, in many real-world scenarios, bounded metrics may fall short in capturing appropriately relationships among entities. In response to this limitation, the concept of bounded partial metric, in the sense of Matthews, emerges offering a broader perspective on distance functions. As introduced in 1994 by Matthews, the concept of partial metric extends the notion of metric allowing, among other things, that self-distances can be different from zero. Inspired, on the one hand, by the importance that bounded partial metrics have acquired in computer science and artificial intelligence and, on the other hand, by the observation that this type of fuzzy relations can be derived through aggregation, in this paper, we study the aggregation problem of bounded partial metrics. In this way, we provide the necessary conditions for a function to be able to serve as an aggregator for bounded partial metrics.