Based on the probabilistic interval-valued intuitionistic hesitant fuzzy set (PIVIHFS), this paper introduces the Maclaurin symmetric mean operator and the Archimedean norm, and constructs a multi-attribute decision model based on the PIVIHF Maclaurin symmetric mean (PIVIHFMSM) operator. The model is used to describe the decision information of the decision expert inputting multiple parameter values. The decision maker can select the appropriate parameter value according to subjective consciousness such as risk preference to make decision. The problems of uncertainty and lack of decision information in the decision-making process are avoided. Firstly, the definition and ordering method of the PIVIHFS and the Archimedean norm are reviewed. Then, the PIVIHFMSM operator is proposed, and its excellent properties and common forms are studied. Finally, the decision-making method based on the PIVZHFMSM operator is proposed, comparison analysis of which is conducted to prove its feasibility and effectiveness. This paper expands the PIVIHFS theory and application fields, and provides new ideas for the relevance of decision attributes and the possible lack of decision information.