The selection of the most effective surgical approach is a critical decision in major surgery. With several approaches available, it is important to select the one that will have the most beneficial effect on the patient's health. Multi criteria decision making techniques are essential for identifying the most effective surgical approach to optimize patient health. Therefore, we develop a two novel decision making models under the double hierarchy linguistic information to select the best surgical approach for patient health. A more flexible way to express uncertainty and fuzziness in the surgical approach information is possible using the double hierarchy linguistic term set, which is made up of the first and second hierarchy linguistic term sets. Initially, we discuss the double hierarchy linguistic term set and its aggregation operator based on the Aczel-Alsina norms, as well as some basic properties of the Aczel-Alsina aggregation operator under the double hierarchy linguistic term sets. Next, we develop two novel decision making models under double hierarchy linguistic information, known as the WASPAS method and the double hierarchy linguistic neural network with the Aczel-Alsina aggregation operator. After that, we apply the proposed decision making models to select the most effective surgical approach to optimize patient health. For this, we collect the information about the surgical approach from the three highly qualified experts of the surgical approach. Further, we follow the procedure of the proposed models to compute the final output and select the most effective surgical approach to optimize patient health. After that, we evaluate the sensitivity of the proposed models in the context of surgical decision making. Moreover, we evaluate the validity and efficiency of the proposed decision making models by comparing them with existing decision making models.