Gradient pre-shaped fuzzy C-means algorithm (GradPFCM) for transparent membership function generation

Linguistic terms are widely used in fuzzy modeling. The generation of membership functions for the linguistic terms is usually done by fuzzy C-means algorithm (FCM). However, most of FCM-based membership function generation algorithms consider little on the transparency or the understandability of the resulting membership functions. This paper proposes a gradient pre-shaped fuzzy C-means (GradPFCM) algorithm to generate better transparent membership functions. GradPFCM will preserve the predefined transparent shapes of membership functions during the process of the gradient descent based optimization of the clustering algorithm. Numeric experiments based on data collected in a civil project demonstrate the feasibility and superiority of the proposed new algorithm.