Measure and integral with purely ordinal scales

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 survey Measuring and aggregation or integration techniques have a very long tradition. Here numbers play an important role. But how do humans perceive numbers? The numbers, say the set R of reals, support two basic structures, the algebraic structure defined by + and

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Dieter Denneberg, Michel Grabisch
• Keywords: Aggregation Functionals, CORR 2008, Education, Monotone Interval-valued Functions, Ordinal Model