Multi-criteria decision making (MCDM), especially fuzzy MCDM process, is the most suitable approach for evaluating strategic decisions. However, in most cases, the Type-1 fuzzy form is insufficient for addressing uncertainty. The Type-2 fuzzy set is a more powerful tool for characterizing uncertainty in complex problems for several domains. The symmetric shape of Gaussian functions better fits most real cases. In many areas, this Gaussian feature serves to describe complex situations in terms of knowledge representation and to resolve critical decision problems. Therefore, a wide usage of Gaussian Type-2 fuzzy sets is expected; however, because of their complexity, very few studies can be found in the literature. The details of Type-2 Gaussian fuzzy sets have not been thoroughly studied. The foundation of interval-valued Type-2 (IT2) Gaussian fuzzy sets with finite ranges, which are called Finite Interval Type-2 (FIT2) Gaussian fuzzy numbers, is proposed in this study. Then, arithmetic operations on FIT2 Gaussian fuzzy numbers and a ranking procedure are derived and adapted to the strategic selection process. The extended TODIM method with FIT2 Gaussian fuzzy numbers is integrated into a real economic evaluation of a medical device selection problem. This problem is detailed with technical and economical criteria. In this study, a healthcare device selection problem is analyzed from the perspectives of clinicians, biomedical engineers, and healthcare investors. The case study is characterized through an evaluation process in which different experts' perspectives are considered. Finally, a comparison of the results derived from different multi-criteria solution processes is presented.