A new multi-criteria decision model based on incomplete dual probabilistic linguistic preference relations

The use of dual probabilistic linguistic term sets (DPLTSs) to represent the use’s preferences in decision making can reflect the decision maker’s cognitive certainty and uncertainty. Additionally, the appearance of incomplete preferences is a recurring phenomenon that must be taken into account if you want to make a successful decision. This paper presents a new multi-criteria decision model based on the incomplete dual probabilistic linguistic preference relations (IDPLPRs). We first propose a step-by-step repairing method to repair the linguistic section and probabilistic section of IDPLPRs separately. The superiority is that this step-by-step method conforms to the principle of element generation. After that, the consistency index based on the distance measure between the dual probabilistic linguistic preference relations (DPLPRs) is defined to check and improve the consistency of DPLPRs. Then the weights of criteria can be obtained by information fusion. Moreover, we construct optimistic and pessimistic data envelopment analysis models under the dual probabilistic linguistic environment to do the sorting process. Optimistic and pessimistic data envelopment analysis models can demonstrate the efficiency of each decision-making unit (DMU) from the perspective of the most and least favorable. Finally, we simulate a cased of 5G industry market to help enterprises choose appropriate 5G partners by using proposed methods.