Given the increasingly significant role of small and medium-sized enterprises (SMEs) in the global economy and the ever more competitive markets in which these companies operate, SMEs’ ability to adopt artificial intelligence (AI) technologies is of utmost importance. Due to constantly evolving social, environmental, and technological scenarios, the managers of these firms must increasingly focus on incorporating new tools such as AI into SME operations in order to enjoy their benefits. However, the subjectivity and complexity of this adaptation process makes integrated analyses of key factors challenging. The present study sought to develop a multi-criteria decision-support system that applies cognitive mapping and the decision-making trial and evaluation laboratory technique in a neutrosophic context. The main objective is to overcome the limitations of previous studies and models by structuring the decision problem and identifying and understanding which factors should be central to adaptation initiative analyses. A panel of experts in AI were recruited to facilitate the construction of an analysis system that takes into account indeterminacy in decision-making processes. The results were validated by both the panel members and project managers at COTEC Portugal—a leading think-and-action network that seeks to advance technology diffusion and business innovation cooperation. The proposed system’s practical implications and benefits are also analyzed.