Generalization of Fuzzy C-Means Based on Neutrosophic Logic

This article presents a New Neutrosophic C-Means (NNCMs) method for clustering. It uses the neutrosophic logic (NL), to generalize the Fuzzy C-Means (FCM) clustering system. The NNCMs system assigns objects to clusters using three degrees of membership: a degree of truth, a degree of indeterminacy, and a degree of falsity, rather than only the truth degree used in the FCM. The indeterminacy degree, in the NL, helps in categorizing objects laying in the intersection and the boundary areas. Therefore, the NNCMs reaches more accurate results in clustering. These degrees are initialized randomly without any constraints. That is followed by calculating the clusters' centers. Then, iteratively, the NNCMs updates the membership values of every object, and the clusters' centers. Finally, it measures the accuracy and tests the objective function. The performance of the proposed system is tested on the six real-world databases: Iris, Wine, Wisconsin Diagnostic Breast Cancer, Seeds, Pima, and Statlog (Heart). The comparison between the two systems shows that the proposed NNCMs is more accurate.