The semiconductor industry has a unique vertically disintegrated structure that consists of various firms specializing in a narrow range of the value chain. To ensure manufacturing and logistics efficiency, the semiconductor manufacturers considerably rely on 3PL suppliers to achieve supply chain excellence. However, 3PL supplier selection is a complex decision-making process involving multiple selection criteria. The goal of this paper is to identify the key 3PL selection criteria by employing the nonadditive fuzzy integral approach. Unlike the traditional multicriterion decision-making (MCDM) methods which often assume independence among criteria and additive importance weights, the nonadditive fuzzy integral is a more effective approach to solve the dependency among criteria, vagueness in information, and essential fuzziness of human judgment. In this paper, we demonstrate an empirical case that employs the nonadditive fuzzy integral to evaluate the importance weight of selection criteria and choose the most appropriate 3PL supplier. The research result can become a valuable reference for manufacturing companies operating in comparable situations. Moreover, the systematic framework presented in this study can be easily extended to the analysis of other decision-making domains.