Minimum cost strategic weight assignment for multiple attribute decision-making problem using robust optimization approach

In practical multiple attribute decision-making (MADM) problems, the interest groups or individuals intentionally set attribute weights to achieve their own benefits. In this case, the rankings of alternatives are changed strategically, which is the strategic weight assignment problem in MADM. However, the attribute weights cannot be changed easily and usually need a compensation. Some research denoted the compensation as costs and assumed that they are deterministic. In this paper, we study the strategic weight assignment based on robust optimization theory, which assumes that the uncertain costs reside in the uncertainty sets. With perturbation vector varying in box set, ellipsoid set and polyhedron set, it allows the costs to be considered with several different uncertain levels. A series of mixed 0–1 robust optimization models are constructed to set a strategic weight vector for a desired ranking of a particular alternative. Finally, an example based on the actual anti-epidemic performance data from 14 provinces and cities illustrates the validity of the proposed models. Comparison between the certainty model and the three robust models illustrates that uncertain unit adjustment costs always lead to the higher weight assignment costs. And a further comparative analysis highlights the influence that the weight assignment costs will increase as the uncertain levels increase.