Probabilistic hesitant fuzzy set (PHFS) effectively solves the inconsistency of expert preferences in multi-attribute decision making (MADM). The aggregation operator based on Aczel-Alsina operator can effectively determine the particular priorities of information with consistency. However, the aggregation operator based on Aczel-Alsina operator in the existing literature is not extended to PHFS, and the unknown weight case and the correlation among multiple attributes are ignored, which leads to the reduction of the application scope and reliability of the decision method. To solve these problems, we propose PHF Aczel-Alsina power weighted averaging (PHFAAPWA) operator, PHF Aczel-Alsina power weighted geometric (PHFAAPWG) operator under unknown weights, as well as some properties and special cases of the proposed operators are discussed. And then, we use this operator to propose a method to solve the MADM problem of probabilistic hesitant fuzzy sets. Finally, there illustrates an instance of telemedicine service quality evaluation, and a series of comparative analysis is carried out to verify the rationality and superiority of the operator.