<p>Logistics service provider selection is a skilled and effective technique used to evaluate and identify third-party enterprises or organizations capable of managing and performing logistics tasks on behalf of a business. In this study, we aim to propose a logistics service provider selection method based on aggregation operators and fuzzy sets. First, we analyze the Aczel-Alsina operational laws building on the intuitionistic hesitant fuzzy sets technique, which combines hesitant fuzzy and intuitionistic fuzzy models. Subsequently, we derive power averaging/geometric aggregation operators for the intuitionistic hesitant fuzzy model based on Aczel-Alsina operational laws, called the intuitionistic hesitant fuzzy Aczel-Alsina power averaging operator, intuitionistic hesitant fuzzy Aczel-Alsina weighted power averaging operator, intuitionistic hesitant fuzzy Aczel-Alsina power geometric operator, and intuitionistic hesitant fuzzy Aczel-Alsina weighted power geometric operator, with their flexible and basic properties such as idempotency, monotonicity, and boundedness. The existing model of drastic aggregation operators, max–min aggregation operators, and algebraic aggregation operators are the special cases of the proposed theory. To address the selection of logistics service providers using the proposed operators, we explore the multi-attribute decision-making methods to evaluate the required problems. Finally, we compare the ranking results of the invented model with those of existing technologies to describe the effectiveness and stability of the proposed methods.</p>