On Modular Fuzzy Equivalences, Aggregation and Modular Pseudo-Metrics

Abstract

[eng] Since the introduction of the notion of fuzzy equivalence, many studies have explored theoretical aspects and its applications. In particular, two theoretical aspects have attracted the attention of many researchers. On the one hand, methods for generating from a collection of fuzzy equivalences a new one by means of aggregation have been extensively studied. On the other hand, the relation between fuzzy equivalences and pseudo-metrics has been profusely explored. Moreover, characterizations of those functions that are useful for merging a collection of fuzzy equivalences have been provided in terms of particular constructions of functions that aggregate extended pseudo-metrics in such a way that the construction takes advantage of the aforementioned duality relation. This type of characterizations are yet to be examined in the modular framework. This is why, in this paper, we focus our efforts on obtaining modular versions of the previously mentioned characterizations through the use of the duality relationship. Furthermore, we finally compare our new correspondences to the ones coming from the non modular scenario, pointing out their differences