The advent of different social networking sites has enabled people to easily connect all over the world and share their interests. However, Social Networking Sites are providing opportunities for cyber bullying activities that poses significant threat to physical and mental health of the victims. Social media platforms like Facebook, Twitter, Instagram etc. are vulnerable to cyber bullying and incidents like these are very common now-a-days. A large number of victims may be saved from the impacts of cyber bullying if it can be detected and the criminals are identified. In this work, a machine learning based approach is proposed to detect cyber bullying activities from social network data. Multinomial Naïve Bayes classifier is used to classify the type of bullying. With training, the algorithm classifies cyber bullying as- Shaming, Sexual harassment and Racism. Experimental results show that the accuracy of the classifier for considered data set is 88.76%. Fuzzy rule sets are designed as well to specify the strength of different types of bullying.