With the rapid growth of electronic commerce on the Internet, it becomes increasingly important to have effective, secure, and low-cost methods of handling the monetary aspect of the on-line transactions. Recently, a number of electronic payment services have been introduced to the Web. An agent-based approach for electronic payment services is appealing since payment agents can proactively monitor the latest market information and autonomously select the best settlement option on behalf of their customers. However, because of the intrinsically dynamic nature of the Internet, these payment agents are faced with the challenges of making good decisions based on uncertain and incomplete market information. Possibilistic logic provides an expressive language to capture these uncertainties, and a robust and powerful reasoning method to make sound decisions by considering the uncertainties related to the activities in payment settlements. In addition, possibilistic deduction can be used to explain and justify an agent's decisions. Enhanced explanatory capability promotes users' trust and satisfaction, and this is essential in agent-mediated electronic commerce. This paper proposes an agent-based electronic payment service. In particular, how possibilistic logic can be applied to the development of intelligent payment agents is discussed.