Combining intelligence elements with product–service systems (PSS) has become a significant requirement because of the recent increase in customers’ demands for smart products and services. In order to have a successful smart PSS that satisfies customers’ requirements, investigation and evaluation of the innovation value propositions (IVPs) became one of the critical necessities. The main advantage of adopting smart PSS is the ability to gather and process a large amount of information to help in decision making and development processes. This study proposes an integrated framework using DEMATEL and CRITIC methods based on the neutrosophic set. Due to the variant of the evaluation process and ambiguity in information, neutrosophic numbers can be used as an efficient expression to guarantee successful evaluation. By comparing the neutrosophic set with other approaches that deal with uncertainty and inconsistency of information, it is more powerful in handling uncertain judgments by considering the truth-membership function, falsity-membership function, and indeterminacy-membership function. Smart PSS can improve an overall quality in the healthcare sector extensively as many solution types, such as sensors, smart pills, and smart surgeries. An illustrative case of smart Continuous Glucose Monitoring (CGM) sensors is demonstrated to examine the proposed framework.