Aggregation of Indistinguishability Fuzzy Relations Revisited

Juan- De-Dios González-Hedström, Juan-José Miñana and Oscar Valero
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Juan- De-Dios González-Hedström: Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, IB, Spain
Juan-José Miñana: Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, IB, Spain
Oscar Valero: Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, IB, Spain

Mathematics, 2021, vol. 9, issue 12, 1-12

Abstract: Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

Keywords: aggregation; indistinguishability fuzzy relation; extended pseudo-metric; additive generator; continuous Archimedean t-norm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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