Cloud elasticity provides a software system with the ability to maintain optimal user experience by automatically acquiring and releasing resources, while paying only for what has been consumed. The mechanism for automatically adding or removing resources on the fly is referred to as auto-scaling. The state-of-the-practice with respect to auto-scaling involves specifying threshold-based rules to implement elasticity policies for cloud-based applications. However, there are several shortcomings regarding this approach. Firstly, the elasticity rules must be specified precisely by quantitative values, which requires deep knowledge and expertise. Furthermore, existing approaches do not explicitly deal with uncertainty in cloud-based software, where noise and unexpected events are common. This paper exploits fuzzy logic to enable qualitative specification of elasticity rules for cloud-based software. In addition, this paper discusses a control theoretical approach using type-2 fuzzy logic systems to reason about elasticity under uncertainties. We conduct several experiments to demonstrate that cloud-based software enhanced with such elasticity controller can robustly handle unexpected spikes in the workload and provide acceptable user experience. This translates into increased profit for the cloud application owner.