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Relaxed Indistinguishability Relations and Relaxed Metrics: The Aggregation Problem

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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… Click to show full 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.

Keywords: indistinguishability fuzzy; indistinguishability; fuzzy relations; indistinguishability relations; pseudo metrics; relaxed indistinguishability

Journal Title: Axioms
Year Published: 2022

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