Robust clustering techniques are real life clustering techniques for noisy data. They work efficiently in the presence of noise. Fuzzy C-means (FCM) is the first clustering algorithm, based upon fuzzy sets, proposed by J C Bezdek but it does not give accurate results in the presence of noise. In this paper, FCM and various robust clustering algorithms namely: Possibilistic C-Means (PCM), Possibilistic Fuzzy C-means (PFCM), Credibilistic Fuzzy C-means (CFCM), Noise Clustering (NC) and Density Oriented Fuzzy C-Means (DOFCM) are studied and compared based upon robust characteristics of a clustering algorithm. For the performance analysis of these algorithms in noisy environment, they are applied on various noisy synthetic data sets, standard data sets like DUNN data-set, Bensaid data set. In comparison to FCM, PCM, PFCM, CFCM, and NC, DOFCM clustering method identified outliers very well and selected more desirable cluster centroids.