Decision making under uncertainty using imprecise probabilities

TL;DR

This paper reviews and compares various decision-making methods under imprecise probabilities, generalizes conditions for optimal decisions, and proposes an efficient computational approach with practical illustration.

Contribution

It introduces a generalized sufficient condition for the existence of optimal decisions and an efficient method for calculating them under multiple criteria.

Findings

Different decision criteria can lead to different choices.

A generalized condition ensures the existence of optimal decisions.

An efficient computational approach is demonstrated with a numerical example.

Abstract

Various ways for decision making with imprecise probabilities (admissibility, maximal expected utility, maximality, E-admissibility, $\Gamma$-maximax, $\Gamma$-maximin, all of which are well-known from the literature) are discussed and compared. We generalize a well-known sufficient condition for existence of optimal decisions. A simple numerical example shows how these criteria can work in practice, and demonstrates their differences. Finally, we suggest an efficient approach to calculate optimal decisions under these decision criteria.