As it is challenging to adapt trust management to accommodate different individual preferences due to the growing adoption of artificial intelligence (AI) in smart cities, this paper conducts a review of the internal and external factors that influence trust, such as personal values, personality traits, and cultural background. The paper focuses on the critical role of communication in human-machine interactions, particularly in the context of AI technologies. To strengthen trust in smart city systems, we propose a Framework for AI Trust enHancement (FAITH) to integrate personalized communication strategies with individual preferences. The proposed FAITH framework is validated through two case studies in healthcare and the results derived from case studies not only deepen the understanding of trust management systems in smart cities but also provide insights for how to cater different preferences in trust management systems.