Aggregation of equivalence relations

Peter C. Fishburn, Ariel Rubinstein

    Research output: Contribution to journalArticle

    Abstract

    Each of n attributes partitions a set of items into equivalence classes. A consistent aggregator of the n partitions is defined as an aggregate partition that satisfies an independence condition and a unanimity condition. It is shown that the class of consistent aggregators is precisely the class of conjunctive aggregators. That is, for each consistent aggregator there is a nonempty subset N of the attributes such that two items are equivalent in the aggregate partition if and only if they are equivalent with respect to each attribute in N.

    Original languageEnglish (US)
    Pages (from-to)61-65
    Number of pages5
    JournalJournal of Classification
    Volume3
    Issue number1
    DOIs
    StatePublished - Mar 1 1986

    Keywords

    • Classification
    • aggregation
    • conjunctive aggregator
    • consistency

    ASJC Scopus subject areas

    • Mathematics (miscellaneous)
    • Psychology (miscellaneous)
    • Statistics, Probability and Uncertainty
    • Library and Information Sciences

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