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Cloud Computing is the latest rage in the world of technology. It has vast potential that can be tapped to the advantage of mankind. But there are some challenges which need to be resolved in order to fully utilise its potential. One of these challenges is trust evaluation. Since services are provided by service providers to clients, there has to be some notion of trust between them. This chapter first provides the basic introduction to cloud computing and fuzzy logic. On the basis of extensive literature survey, this chapter discusses trust and its need, in addition to use of fuzzy logic for the purpose of trust calculation in distributed environments and cloud computing till now. Trust calculation using fuzzy logic has been explained through the use of various models. At the end, the difficulties and applications of using fuzzy logic for trust evaluation are discussed along with research directions for future.