A PROMETHEE II-BELIEFapproach for multi-criteria decision-making problems with incomplete information

Multi-criteria decision aid methods consider decision problems in which many alternatives are evaluated on several criteria. These methods are used to deal with perfect information. However, in practice, it is obvious that this information requirement is too strict. In fact, the imperfect data provided by more or less reliable decision makers usually affect decision results, since any decision is closely linked to the quality and availability of information. In this paper, a PROMETHEE II-BELIEF approach is proposed to help multi-criteria decisions based on incomplete information. This approach solves problems with incomplete decision matrix and unknown weights within PROMETHEE II method. On the basis of belief function theory, our approach first determines the distributions of belief masses based on PROMETHEE II’s net flows, and then calculates weights. Subsequently, it aggregates the distribution masses associated with each criterion using Murphy’s modified combination rule in order to infer a global belief structure. The final alternative ranking is obtained via pignistic probability transformation. A case study of a real-world application concerning the location of a treatment center of waste from healthcare activities with infectious risk in the center of Tunisia is studied to illustrate the detailed process of the PROMETHEE II-BELIEF approach. Keywords: multiple criteria aid, incomplete information, PROMETHEE II method, belief function theory.