Decision under Uncertainty : the Classical Models

This chapiter of a collective book is dedicated to classical decision models under uncertainty, i.e. under situations where events do not have "objective" probabilities with which the Decision Marker agrees. We present successively the two main theories, their axiomatic, the interpretation and the justification of their axioms and their main properties : first, the general model of Subjective Expected Utility due to Savage (Savage, 1954), second, the Anscombe-Aumann (1963) theory, in a different framework. Both theories enforce the universal use of a probabilistic representation. We then discuss this issue in connection with the experimental result known as the Ellsberg paradox.Uncertainty, subjective probability, Subjective Expected Utility, Savage, Anscombe and Aumann, Ellsberg paradox.

Enhancing declarative process models with DMN decision logic

Modeling dynamic, human-centric, non-standardized and knowledge-intensive business processes with imperative process modeling approaches is very challenging. Declarative process modeling approaches are more appropriate for these processes, as they offer the run-time flexibility typically required in these cases. However, by means of a realistic healthcare process that falls in the aforementioned category, we demonstrate in this paper that current declarative approaches do not incorporate all the details needed. More specifically, they lack a way to model decision logic, which is important when attempting to fully capture these processes. We propose a new declarative language, Declare-R-DMN, which combines the declarative process modeling language Declare-R with the newly adopted OMG standard Decision Model and Notation. Aside from supporting the functionality of both languages, Declare-R-DMN also creates bridges between them. We will show that using this language results in process models that encapsulate much more knowledge, while still offering the same flexibility