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Most of the software estimates should be performed at the beginning of the life cycle, when we do not yet know the problem we are going to solve. Effort estimation is used to predict how many hours of work and how many workers are needed to develop a project. The effort invested in a software project is probably one of the most important and most analyzed variables in recent years in the process of project management. Estimating the effort with a high grade of reliability is a problem which has not yet been solved and even the project manager has to deal with it since the beginning. Fuzzy systems try to emulate cognitive processes of the brain with a rule base. The basic concept is inspired by the human processes where the decisional criteria are not clear cut, but blurred and it is difficult to find objective to make the decisions more precise and clear. Fuzzy decision systems are based on fuzzy logic that tries to reproduce the fuzzy human reasoning. The aim of this survey is to analyze the use of fuzzy logic in the existing models and to provide in depth review of software and project estimation techniques existing in industry and literature, its strengths and weaknesses.