Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the language of bounded lattices using variables and constants. We also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted minimum and maximum functions, and present their characterizations, accordingly. Moreover, we discuss normal form representations of these functions

Qualitative integrals and desintegrals as lower and upper possibilistic expectations

International audienceAny capacity (i.e., an increasing set function) has been proved to be a lower possibility measure and an upper necessity measure. Similarly, it is shown that any anti-capacity (i.e., a decreasing set function) can be viewed both as an upper guaranteed possibility measure and as a lower weak necessity measure. These results are the basis for establishing that qualitative integrals (including Sugeno integrals) are lower and /or upper possibilistic expectations wrt a possibility measure, while qualitative desintegrals are upper or lower possibilistic expectations wrt a guaranteed possibility measure. The results are presented in a qualitative finite setting, the one of multiple criteria aggregation

Orness For Idempotent Aggregation Functions

Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the ornessa measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.This work has been partially supported by the research projects MTM2015-63608-P of the Spanish Government and IT974-16 of the Basque Government

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