Graph-based document models are effective in revealing inter-dependencies in unstructured text data. Natural language processing (NLP) systems that employ such models as intermediate representations perform well. This work introduces a fuzzy graph-based document model and uses fuzzy logic techniques to illustrate its usefulness in text summarization. The proposed system receives a text document as input and identifies some of its sentence-level aspects, including sentence position, sentence length, numerical data, theme word, proper noun, title feature, uppercase feature, and sentence similarity. The fuzzy membership value of each feature is computed from the sentences. We propose a novel algorithm to construct the fuzzy graph as an intermediate representation of the input document. The Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metric is used to evaluate the model. The work also shows that the model allows adaptation of new features to the existing feature set so as to improve the goodness of applications.