Measure and integral with purely ordinal scales

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Measure and integral with purely ordinal scales

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by Dieter Denneberg , Universität Bremen , Michel Grabisch , Université Paris , I Panthéon-sorbonne

Venue:	J. of Mathematical Psychology
Citations:	7 - 5 self

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@ARTICLE{Denneberg_measureand,
    author = {Dieter Denneberg and Universität Bremen and Michel Grabisch and Université Paris and I Panthéon-sorbonne},
    title = {Measure and integral with purely ordinal scales},
    journal = {J. of Mathematical Psychology},
    year = {}
}

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Abstract

We develop a purely ordinal model for aggregation functionals for lattice valued functions, comprising as special cases quantiles, the Ky Fan metric and the Sugeno integral. For modeling findings of psychological experiments like the reflection effect in decision behaviour under risk or uncertainty, we introduce reflection lattices. These are complete linear lattices endowed with an order reversing bijection like the reflection at 0 on the real interval [−1,1]. Mathematically we investigate the lattice of non-void intervals in a complete linear lattice, then the class of monotone interval-valued functions and their inner product. 1 Motivation and

Keyphrases

purely ordinal scale complete linear lattice reflection lattice real interval monotone interval-valued function aggregation functionals psychological experiment reflection effect decision behaviour ky fan inner product ordinal model non-void interval special case quantiles

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