An Intuitionistic Fuzzy Approach to Fuzzy Clustering of Numerical Dataset
Fuzzy c-means (FCM) clustering is one of the most widely used fuzzy clustering algorithms. However, the main disadvantage of this algorithm is its sensitivity to noise and outliers. Intuitionistic fuzzy set is a suitable tool to cope with imperfectly defi
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Abstract Fuzzy c-means (FCM) clustering is one of the most widely used fuzzy clustering algorithms. However, the main disadvantage of this algorithm is its sensitivity to noise and outliers. Intuitionistic fuzzy set is a suitable tool to cope with imperfectly defined facts and data, as well as with imprecise knowledge. So far, there exists a little investigation on FCM algorithm for clustering intuitionistic fuzzy data. This paper focuses mainly on two aspects. Firstly, it proposes an intuitionistic fuzzy representation (IFR) scheme for numerical dataset and applies the modified FCM clustering for clustering intuitionistic fuzzy (IF) data and comparing results with that of crisp and fuzzy data. Secondly, in clustering of IF data, different IF similarity measures are studied and a comparative analysis is carried out on the results. The experiments are conducted for numerical datasets of UCI machine learning data repository.
Keywords Clustering Fuzzy c-means fuzzy similarity measure
Intuitionistic fuzzy data Intuitionistic
N. Karthikeyani Visalakshi (&) S. Parvathavarthini Kongu Engineering College, Perundurai, Erode, Tamil Nadu, India e-mail: [email protected] S. Parvathavarthini e-mail: [email protected] K. Thangavel Periyar University, Salem, Tamil Nadu, India e-mail: [email protected]
G. S. S. Krishnan et al. (eds.), Computational Intelligence, Cyber Security and Computational Models, Advances in Intelligent Systems and Computing 246, DOI: 10.1007/978-81-322-1680-3_9, Springer India 2014
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N. Karthikeyani Visalakshi et al.
1 Introduction Clustering algorithms seek to organize a set of objects into clusters such that objects within a given cluster have a high degree of similarity, whereas objects belonging to different clusters have a high degree of dissimilarity. Clusters can be hard or fuzzy in nature based on whether each data object has to be assigned exclusively to one cluster or allowing each object to be assigned to every cluster with an associated membership value. The Fuzzy C-Means (FCM) algorithm is sensitive to the presence of noise and outliers in data [1]. To enhance robustness of FCM, different researchers proposed different methodologies [1–3]. Intuitionistic fuzzy sets (IFSs) [4] are generalized fuzzy sets, which use the hesitancy originating from imprecise information. Pelekis et al. [5] introduced an Intuitionistic Fuzzy Representation (IFR) scheme for color images and an Intuitionistic Fuzzy (IF) similarity measure through which a new variant of FCM algorithm is derived. But this cannot be directly used for clustering numerical datasets. Hence, robust fuzzy clustering is proposed in this paper to make FCM algorithm as noise insensitive, by dealing with IF data. Real data are converted into IFR, before clustering, in order to achieve the benefit of IFSs in fuzzy clustering. A comparative study is made on fuzzy clustering of crisp, fuzzy, and IF data, and the performance of IF clustering is measured using four different IF similarity measures. The rest of this pap
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