DECISION MAKING IN HETEROGENEOUS UNCERTAINTY ENVIRONMENT

Purpose: This study develops a theoretical model for decision making under both probabilistic risk and fuzzy possibility. The use of the latter allows modeling of non-probabilistic concepts such as "similarity" and "ignorance" that are frequently encountered in medical decision situations. An example is to select antidepressant for a patient based on the outcomes of clinical trials for populations with different-but-similar health profiles [Zimmerman et al. Am J Psychiatry 2002].

Method: The method we propose is to combine the subjective expected utility theory (SEU) for decision under risk with our decision model for possibililty theory [Giang & Shenoy. European Journal of Operational Research 2005]. One of puzzling issue in decision under uncertainty is the violation of sequential/dynamical consistency which is a fundamental property of SEU. An act is evaluated to different values depending on the orders by which uncertainty variables are realized. We argue that feature is unavoidable and the sequence of variables realization is an information necessary in determining the value of an act. Given a sequence of variables, an act is evaluated by a folding-back procedure. The expectation formula is used to fold a probabilistic variable and the formula in [Giang & Shenoy, 2005] to fold a possibilistic variable.

Result: We prove properties of this new method formally as well as by simulation. In particular, we formalize the selection of antidepressant for a patient as a decision problem. Each medication is formalized as an act whose outcome depends on a possibility variable representing "similarity" between given patient and the populations of clinical trials and a probability variable representing the chance outcome in the RCTs.

Conclusion: We develop a new decision model that extends the classical expected utility model to handle both risk and non-probabilistic uncertainty expressed by fuzzy possibility theory. This model can be used to analyze and optimize medical decision problems. Cited Reference Zimmerman M, Mattia JI, Posternak MA: Are subjects in pharmacological treatment trials of depression representative of patients in routine clinical practice? Am J Psychiatry 2002;159:469–473. Giang and Shenoy, 2005] Giang, P. H. and Shenoy, P. P. (2005). Two axiomatic approaches to decision making using possibility theory. European Journal of Operational Research, 162(2):450–467