P-IT2IFCM: Probabilistic Interval Type-2 Intuitionistic Fuzzy c-Means Clustering Algorithm

The recently introduced ‘Improved Probabilistic Intuitionistic Fuzzy c-Means algorithm (IPIFCM)’ provides a Probabilistic Euclidean Distance Measure (PEDM) based computationally efficient clustering technique. Since IPIFCM is defined on Type-1 Atanassov Intuitionistic Fuzzy Sets (AIFS), it is unable to capture the uncertainty of the membership and non-membership values of a given datapoint induced by the hesitancy factor of the AIFS. Interval Type-2 Fuzzy Sets (IT2 FSs) deals with the uncertainty in the membership values. In this paper, we incorporate IT2 FSs in the IPIFCM algorithm by introducing upper bound and lower bound of the membership (and non-membership) values of each datapoint to model the change caused by the hesitancy factor. Accordingly, this paper proposes the ‘Probabilistic Interval Type-2 Intuitionistic clustering algorithm’ (P-IT2IFCM), which uses the interval probabilistic weights for PEDM to propose ‘Interval Type-2 Probabilistic Euclidean Distance Measure’ (IT2PEDM). The proposed algorithm provides superior results to existing Fuzzy c-Means (FCM) algorithms such as the basic FCM algorithm, IFCM algorithm, Kernelized-IFCM algorithm and IPIFCM algorithm when executed over various benchmark UCI datasets.