A great impetus for the study of resilience in critical infrastructures (CIs) is found in the large number of initiatives and international research programmes from U.S., EU, and Asia. Politicians, decision makers, and citizens are now aware of the drastic consequences that can have the cascading effects of an adverse event in these large scale infrastructures. However, the study of resilience in CIs is challenging for several reasons, among which their large scale and interdependencies. We have to consider also that adverse events, e.g., attacks, natural hazards, or man-made disasters, suddenly occur and evolve rapidly, giving us little time to take decisions and react to them. Approximate reasoning and rapid decision making have to be considered requirements for resilience analysis of CIs. The main result presented in this paper relates to a systemic integration of granular computing (GrC) and resilience analysis for CIs. Each phase of our approach presents distinctive aspects but, overall, we argue the merit of this paper consists in the originality of the study, being this the first work that combines GrC and resilience analysis of CIs. This paper reports an illustrative example that shows how to apply our results, and a discussion on the necessary contextualizations and extensions of the GrC results to be better adapted for CIs resilience.