A reference ideal model with evidential reasoning for probabilistic-based expressions

Due to experts' different cognitions, experiences, and knowledge backgrounds, their evaluations may be different, and none of them can be ignored, which leads to the development of the probabilistic linguistic term set (PLTS) and the probabilistic hesitant fuzzy set (PHFS). In practical situations, sometimes the optimal alternative exists in a reference ideal interval instead of the maximum or the minimum. This paper constructs a reference ideal model with evidential reasoning for the PLTS and the PHFS. At first, a maximum deviation method based on two hierarchical attributes is proposed, aiming at determining the attribute weights in a multi-attribute decision-making problem. Then, since the evaluations are provided with different forms and principles, a normalisation process can help to make the evaluations unified. Moreover, the evidential reasoning process is introduced to aggregate evaluation grades based on the probabilities in the probabilistic-based expressions. And the final decision results are obtained by applying the distance between the aggregated evaluation grades and the extreme values. Then, we use the proposed model for the potential chronic obstructive pulmonary disease patient evaluation to verify the operability. Besides, a comparative analysis is also conducted to prove the rationality of the model.