An axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making with linguistic fuzzy truth degrees

A regret theory-based GEDM method with heterogeneous probabilistic hesitant information and its application to emergency plans selection of COVID-19

Emergency events are happening with increasing frequency, inflicting serious damage on the economic development and human life. A reliable and effective emergency decision making method is great for reducing various potential losses. Hence, group emergency decision making (GEDM) has drawn great attention in past few years because of its advantages dealing with the emergencies. Due to the timeliness and complexity of GEDM, vagueness and regret aversion are common among decision makers (DMs), and decision information usually needs to be expressed by various mathematical forms. To this end, this paper proposes a novel GEDM method based on heterogeneous probabilistic hesitant information sets (PHISs) and regret theory (RT). Firstly, the PHISs with real numbers, interval numbers and linguistic terms are developed to depict the situation that decision group sways precariously between several projects and best retain the original assessment. In addition, the score functions, the divergence functions and some operations of the three types of PHISs are defined. Secondly, the normalization model of PHISs is presented to remove the influence of different dimensions on information aggregation. Thirdly, group satisfaction degree (GSD) based on the score functions and the divergence functions is combined with RT for completely portraying the regret perception of decision group. Then, we introduce Dempster-Shafer (DS) theory to determine the probabilities of future possible states for emergency events. Finally, an example of coronavirus disease 2019 (COVID-19) situation is given as an application for the proposed GEDM method, whose superiority, stability and validity are demonstrated by employing the comparative analysis and sensitivity analysis.