We develop a purely ordinal model for aggregation operators for lattice valued functions, comprising as special cases quantiles, Ky Fan metrics and Sugeno integrals. For modelling 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 $[-1,1]$. Furthermore the lattice operations $\vee$, $\wedge$ are modified in order to mimic addition and multiplication of numbers of both signs.
Keywords. Quantile, Ky Fan metric, Sugeno integral, aggregation, reflection lattice.
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Authors addresses:
FB 3 Mathematik / Informatik
Universität Bremen
Postfach
D-28334 Bremen
Germany
E-mail addresses:
| Dieter Denneberg | denneberg@math.uni-bremen.de |