The successful usage of fuzzy systems can be seen in many application domains owing to their capabilities to model complex systems by exploiting knowledge of domain experts. Their accuracy and performance are, however, primarily dependent on the design of its membership functions and control rules. The commonly employed technique to design membership functions is to exploit the knowledge of domain experts. However, in certain application domains, the knowledge of domain experts are limited and therefore, cannot be relied upon. Alternatively, optimization techniques such as genetic algorithms are utilized to optimize the various design parameters of fuzzy systems. In this paper, we report a case study of optimizing the membership functions of a fuzzy system using genetic algorithm, which is an important part of our recently developed cloud elasticity framework. This work aims to improve the overall performance of the framework. Results obtained from this research work demonstrate performance improvement in comparison with our previous experimental settings.