Decision-making framework with q-rung picture fuzzy linguistic information and its applications to logistics hubs during disaster response establishment

In the decision-making matrix of modern interactive multi-attribute group decision-making (MAGDM) models, we find such syntactic-semantic forms of presentation of experts' cognitive information that thoroughly ensure the expert's maximum intellectual activity in the decision-making process. Both quantitative and qualitative experts’ activities are considered in q-rung picture fuzzy linguistic sets (q-RPFLSs) environment. The operations based on dual Archimedean t-norms and s-norms on q-rung picture fuzzy linguistic numbers (q-RPFLNs) are defined, which ensure the closure of operation results in q-RPFLNs. The extensions of the Choquet integral averaging (CA) and geometric (CG) operators for q-RPFLNs-arguments are constructed. In order to increase consideration of interaction between attributes in MAGDM models, Archimedean q-RPFLSs associated probability averaging and geometric operators are introduced, which in the q-RPFLNs environment, in a certain sense, represent the extensions of the CA and CG operators. The new operators are averaging type aggregation operators. In order to better illustrate the obtained results, a practical, high-value interactive MAGDM problem - temporary logistics hubs location selection problem is considered. The different results of the extended Choquet aggregations compared to the classical Choquet integral aggregations are explained, which are mainly due to the high degree of attributes interaction in decision-making procedure. The obtained results are also compared to the ranked aggregations of well-known decision-making methods such as TOPSIS, VIKOR and TODIM.