Interval-valued possibilistic fuzzy C-means clustering algorithm

Type-2 fuzzy sets have drawn increasing research attentions in the pattern recognition community, since it is capable of modeling various uncertainties that cannot be appropriately managed by usual fuzzy sets. Although it has been introduced to data clustering, most widely used clustering approaches based on type-2 fuzzy sets still suffer from inherent drawbacks, such as the sensitiveness to outliers and initializations. In this paper, we incorporate the interval-valued fuzzy sets into the hybrid fuzzy clustering scheme, and thus propose the interval-valued possibilistic fuzzy c-means (IPFCM) clustering algorithm. We use both fuzzy memberships and possibilistic typicalities to model the uncertainty implied in the data sets, and develop solutions to overcome the difficulties caused by type-2 fuzzy sets, such as the construction of footprint of uncertainty, type-reduction and defuzzification. We compare the proposed algorithm with five fuzzy clustering approaches, including the FCM, PCM, PFCM, IFCM and IPCM, on two-dimensional Gaussian data sets and four multi-dimensional benchmark data sets. We also apply these clustering techniques to segment the brain magnetic resonance images and natural images. Our results show that the proposed IPFCM algorithm is more robust to outliers and initializations and can produce more accurate clustering results.