A safe sequential screening technique for solving multi-attribute choice problems under ranked weights

Despite the increasing complexity of real-world multi-attribute decision-making (MADM) situations, the decision-makers have no problems in providing some incomplete (also called imprecise or partial) information about attribute (importance) weights. Often, incomplete weight information takes the form of weights bounded between upper and lower limits, ranked weights, etc. In this work, we deal with the important class of multi-attribute choice problems (MACPs) in which incomplete weight information consists of a ranking of weights. Prominent solution methods for such MACPs can be classified into dominance measuring methods (DMMs), or ordinal surrogate-weighting schemes. The object of the present article is to circumvent the shortcomings of the most efficacious solution methods that can be used to solve the MACPs under-ranked weights. To that end, we devise here an original safe sequential screening technique named the "TCA-algo'' method. The newly devised method follows three steps: (1) the decision matrix is normalized (if needed) and Pareto dominated alternatives are screened out, (2) a tentative choice alternative (TCA) is nominated from among Pareto optimal alternatives, and (3) the nominated TCA is tested using an appropriate dominance rule established herein. The second and third steps of the suggested method are repeated until a final choice alternative (FCA) is reached. Numerical examples and experimental results show convincingly that the TCA-algo method outperforms prominent solution methods.