Preference disaggregation method for value-based multi-decision sorting problems with a real-world application in nanotechnology

We consider a problem of multi-decision sorting subject to multiple criteria. In the newly formulated decision problem, besides performances on multiple criteria, alternatives get evaluations on multiple interrelated decision attributes involving preference-ordered classes. We propose a dedicated method for dealing with such a problem, incorporating a threshold-based value-driven sorting procedure. The Decision Maker (DM) is expected to holistically evaluate a subset of reference alternatives by indicating the quality or risk level on a pre-defined scale of each decision attribute. Based on these evaluations, we construct a set of interrelated preference models, one for each decision attribute, compatible with intra- and inter-decision constraints imposed by such indirect preference information. We also formulate a new way of dealing with potentially non-monotonic criteria by discovering local monotonicity changes in different performance scale regions. The marginal value functions for criteria with unknown monotonicity are represented as a sum of two value functions assuming opposing preference directions, one non-decreasing and the other non-increasing. This permits to obtain an aggregated marginal value function with an arbitrary non-monotonic shape. The practical usefulness of the approach is demonstrated on a case study concerning risk management related to handling (i.e., production, use, manipulation, and processing) nanomaterials in different conditions. We analyze the expert judgments and discuss the inferred preference models, which can be applied to support health and safety managers in reducing the possible risk associated with the respective exposure scenario.