عدم قطعیت مدل سازی در تحلیل پذیری چند ضلعی تصادفی  Modelling uncertainty in stochastic multicriteria acceptability analysis

1. Introduction When facilitating decisions it sometimes happens that some inputs to the preference model either cannot be assessed at all or can only be assessed within relatively large bounds of uncertainty (e.g. [1,12,13]). This can happen for a number of reasons: a lack of time, a politically sensitive problem context, or a lack of decision maker (DM) involvement, for example. Whatever the reason, in these cases the DM is unable or unwilling to express him or herself with the degree of precision required by conventional decision aids. We call decision problems which must be addressed under such conditions “low-involvement” decisions. The question is what, if any, decision support can be provided in such situations. Stochastic multicriteria acceptability analysis (SMAA [25,19]) is a family of decision models that can be used with arbitrarily precise preference information. It addresses low-involvement decision-making by providing information about the types of preferences (if any) that would lead to the selection of each alternative. In this paper we use a simulation experiment to evaluate the ability of SMAA to approximate results obtained using multiattribute utility theory (MAUT) where preferences are represented by a multiplicative utility function. In particular, we ask how closely results computed from a key output from SMAA (the acceptability index) can approximate those obtained using MAUT. In doing so we hope to provide a broad indication of the losses that are possible if facilitators choose to use a low-involvement decision aid such as SMAA rather than compelling DMs to be more precise in their assessment of certain types of preference information – for example, using more detailed problem structuring. We also wish to test the robustness of the SMAA approach to various aspects of the decision process: the size of the decision problem, the way attribute evaluations are distributed, the underlying preference functions, the accuracy of assessed information, the amount of preference information gathered, and the way in which the acceptability index is constructed.