In the realm of service-oriented manufacturing, the selection of equipment maintenance strategies in the supply chain presents both challenges and opportunities. The demand for equipment maintenance in the service-oriented manufacturing industry addresses the limitations of traditional methods when confronted with complexity and uncertainty. To tackle these issues, this paper introduces an analytical model of probabilistic linguistic term sets and proposes a generalized weighted power averaging operator for probabilistic linguistic term sets, along with a probabilistic linguistic generalized power ordered weighted averaging operator. These operators showcase superior properties in assembling evaluation information from indicators. The proposed method effectively addresses the issues of limited rationality and subjective experience faced by decision makers in equipment maintenance strategy selection, while also overcoming the reliance on subjective expert judgment and neglecting correlations among indicators. The feasibility and effectiveness of the proposed method are validated through its application to the problem of selecting the best equipment maintenance strategy for a service-oriented manufacturing supply chain.