Semiconductor foundry manipulation is one of the most important core-competences of fabless integrated circuit (IC) design firms'. However, it is not easy for a fables IC design firm to select appropriate foundry strategies versus each stage of a technology life cycle (TLC). To satisfy multiple goals of time to market, profit maximization and quality assurance, fables IC design firms should choose appropriate foundries at various stage of a TLC. Albeit important, very few researches discussed how appropriate foundries can be determined. Thus, this research aims to develop a fuzzy integral based fuzzy multiple criteria decision making (FMCDM) framework. Considering the characteristic of inter-dependences between criteria, a non-additive fuzzy integral based FMCDM model will be proposed for assisting decisions' makers in evaluating the most appropriate foundry strategies. An empirical study based on evaluating appropriate foundry strategies will be leveraged to demonstrate the feasibility of the proposed fuzzy integral based FMCDM framework. Criteria for evaluating and selecting foundries over a TLC will be derived based on experts' opinions. Meanwhile, an empirical study of the selection of foundry strategies by a PC chipset fabless design firm will be leveraged for verifying the feasibility of the proposed FMCDM framework. The result is satisfactory. Meanwhile, the proposed framework can be leveraged for selecting appropriate foundry or provider strategies over a TLC.