Although cloud manufacturing offers greater flexibility and diversity than traditional manufacturing, it also presents greater uncertainty and variability. How to select stable cloud providers for material procurement (SSCPFMP) has become a critical supply chain optimization issue in cloud manufacturing. By extending the Group Role Assignment (GRA) model, this paper formalizes the problem. Moreover, we propose a new method for evaluating cloud providers that incorporates stability as an important criterion. Additionally, in order to complete the stability assessment as quickly as possible, we propose using the KB4 logic instead of the commonly used KB5 to mine potential cooperative relationships between cloud providers. We prove by deduction that KB4 and KB5 are equivalent. Largescale simulation experiments indicate that the KB4 logic performs significantly better than the KB5 logic, which can be improved by up to 43.78%. By using this method, decision makers are able to find more stable cloud providers for material procurement within a shorter timeframe.