Endre Pap
A Generalization of the Utility Theory using a Hybrid Idempotent--Probabilistic Measure
Preprint series: ESI preprints

MSC:

90A10 Utility theory

62C05 General considerations

90A05 Decision theory, See also {62Cxx, 90B50, 90D35}

28E10 Fuzzy measure theory, See also {04A72, 26E50, 94D05}

Abstract: There is given an overview on the results related to the generalization of the
decision theory to non probabilistic uncertainty based on the characterization
of the families of operations involved in
generalized mixtures. It turns out that this is based on a
previous result on the characterization of the pair of continuous
t-norm $T$ and t-conorm $S$ such that the former is conditionally
distributive over the latter.
What is obtained is a family of mixtures that
combine probabilistic and idempotent (possibilistic) mixtures via
a threshold and the corresponding pseudo-additive hybrid
idempotent-probabilistic measure satisfies also all other required
conditions.

Keywords: Triangular conorm, triangular norm, hybrid idempotent-probabilistic measure, hybrid utility