Modeling Interactive Multiattribute Decision-Making via Probabilistic Linguistic Term Set Extended by Dempster–Shafer Theory

Abstract

In multiattribute decision-making (MADM), more and more attention is paid to the interaction between attributes when considering the actual decision environment. As a result, interactive MADM has become an emerging and challenging area of research whose success will greatly facilitate the development of decision-making. This paper models the interactive MADM problem and its contribution is multifaceted. First, the concept of probabilistic linguistic term set (PLTS) is extended by Dempster–Shafer theory (DST), which helps to express more uncertain information, followed by some basic operations, such as score function and aggregation operator. In virtue of evidential best-worst method and the principle of maximum entropy, then a novel nonadditive measure determination method is developed based on the 2-order additive measure to better model the interaction between attributes. Further, the generalized PLTS-based Choquet integral is defined by which generalized PLTSs on a nonadditive measure can be reasonably aggregated. Finally, an interactive MADM model is constructed and the technical details are described. The proposed approach is implemented to select the supplier for medical devices, and its effectiveness is emphasized by comparison with other methods.