Multi-Criteria Decision Making with Overlapping Criteria

Vol 24, No 3; Article by Mohammed Shahid Abdulla; September 2012

Multi-criteria decision making (MCDM) tries to aggregate decisions on multiple criteria to form a unified opinion about a system or product which is being evaluated on these criteria.

The evidential reasoning (ER) algorithm for MCDM aggregates the per-criteria assessment of multiple experts, one each for every attribute (or subsystem or criterion) of a given system, with further possibility of sub-criteria being aggregated in a recursive, hierarchical fashion based on a criteria tree. Further, using the Dempster-Schafer rule of combination, ER calculates a consolidated assessment even if the participating experts express an opinion with a "can't say" component.

Two variants of ER are proposed in this article; both handle a scenario where more than one expert assesses an attribute of a system or product. The first algorithm handles the case of multiple experts who assess an attribute of a larger system. In particular, a formula for the case of two experts assessing a single attribute is given with the technique generalising to higher degrees of overlap. Numerical experiments compare a naive modification of ER for this scenario which results in poorer detection -- up to 25% lower than the proposed algorithm.

The second algorithm is used when experts do not rule on the same criterion, but have overlapping areas of expertise among the subsystems. The assumption made is that these subsystems are considered to be distinct areas of expertise, with an overlap between them, but the degree of overlap cannot be precisely quantified, nor an expert assigned to assess performance on the overlapping points within these criteria. A comparison is made with a variant of ER in the literature and the proposed algorithm demonstrates encouraging performance.

Both algorithms are explained as examples of novel "exclusive" and "inclusive" methods of performing ER-based MCDM.