Sentiment Analysis or in particular social network analysis (SNA) is a new research area which is increased explosively. This domain has become a very active research issue in data mining and natural language processing. Sentiment analysis (opinion mining) consists in analyzing and extracting emotions, opinions or attitudes from product’s reviews, movie's reviews, etc., and classify them into classes such as positive, negative and neutral, or extract the degree of importance (polarity). In this paper, we propose a new hybrid approach for classifying tweets into classes based on fuzzy logic and a lexicon based approach using SentiWordnet. Our approach consists in classifying tweets according to three classes: positive, negative or neutral, using SentiWordNet and the fuzzy logic with its three important steps: Fuzzification, Rule Inference/aggregation, and Defuzzification. The dataset of tweets to classify and the result of the classification are stored in the Hadoop Distributed File System (HDFS), and we use the Hadoop MapReduce for the application of our proposal.