Advanced manufacturing technology (AMT) is defined as a modern method of production incorporating highly automated and sophisticated computerized design and operational systems. Hence, an investment decision to adopt AMT is a strategic decision. A group decision making process is stressful when group members have different views under multiple and conflicting criteria. Satisfying group members' opinions has a critical impact on a decision. In this chapter, a multiple criteria group decision making problem under a fuzzy environment is used for the selection among AMTs. Choquet integral methodology is used for this selection. A strategic investment problem of a company for a suitable Automated Storage/Retrieval System (AS/RS) is considered and discussed.