Alternative fuzzy c-regression models with tolerance

In this paper, we propose a robust fuzzy c-regression models, in which an alternative distance measurement is adopted in conjunction with the concept of tolerance. Fuzzy c-regression models (FCRM) is an FCM-type switching regression model, and can reveal intrinsic non-linear dependencies among exploratory variables and objective variables. We extend FCRM such that it can handle data with not only noise or outliers but also uncertainty of observations. The alternative distance measurement is responsible for handling noise or outliers while the uncertainty of observations is tuned based on the concept of tolerance. The characteristics of the proposed method are demonstrated through several numerical experiments.