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Clustering has emerged as an important tool for discovering the structure of data. Among the clustering methods, fuzzy c-means (FCM) has increased its wide attention in recent years. Owing to the huge amount of data, the existence of uncertainty in the dataset, computational complexity and noise-corrupted data, the FCM algorithm finds it difficult to produce a good clustering result. This paper proposes effective objective functions of FCM with the combination of entropy function, tolerance and kernel distance functions in order to effectively cluster the more complicated data into appropriate groups. This paper provides an effective way of computing membership degrees and updating cluster centers by minimizing the proposed novel objective functions. To reduce the computational time of the proposed algorithm, we develop a prototype initialization algorithm for assigning the initial cluster centers instead of random initialization. To show the effectiveness of proposed methods, we implement the proposed methods on a two-dimensional artificial dataset and more complicated synthetic control chart time series dataset. We prove the superiority of the proposed methods through the clustering validity, number of iteration and the strength of the membership. [ABSTRACT FROM PUBLISHER]