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This paper describes an application of fuzzy set theory to real problems. These problems refer to concepts, policies, strategies and techniques of quality sysmtems of industrial and services organizations. The paper focuses on the quality evaluation process used to verify if the quality level of productive processes, products, services and general resources (mainly human resources) are reaching better values. The parameters and criteria from the National Brazilian Quality Award are used as a reference. Basic concepts of fuzzy set theory were applied to these concepts and criteria. So it was possbile to define a more adequate way to evaluate almost 40,000 organizations, which are submitted, annually, to the evaluation process to conquer the Award. The obtained results show the theoretical and practical adjustment of fuzzy sets to quality systems and quality evaluation processes.