Relaxed Indistinguishability Relations and Relaxed Metrics: The Aggregation Problem

Abstract

The main purpose of this paper is to study the relationship between those functions that aggregate relaxed indistinguishability fuzzy relations with respect to a collection of t-norms and those functions that merge relaxed pseudo-metrics, extending the classical approach explored for pseudo-metrics and indistinguishability fuzzy relations. Special attention is paid to the distinguished class of SSI-relaxed indistinguishability fuzzy relations showing that functions merging this special type of relaxed indistinguishability fuzzy relations can be expressed through functions aggregating SSD-relaxed pseudo-metrics. Outstanding differences between those functions aggregating indistinguishability fuzzy relations and those that aggregate their counterpart separating points are shown.