Measure and integral with purely ordinal scales

Dieter Denneberg and Michel Grabisch
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Dieter Denneberg: Universität Bremen [Deutschland] = University of Bremen [Germany] = Université de Brême [Allemagne]

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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

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Date: 2004
Note: View the original document on HAL open archive server: https://hal.science/hal-00272078v1
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Published in Journal of Mathematical Psychology, 2004, 48 (1), pp.15-27

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