As a very important tool for dealing with both crisp data and fuzzy data, fuzzy regression analysis based on interval regression analysis has become an active area of research. Some neural network related methods for nonlinear interval regression analysis have been proposed on the assumption that given training data are totally "good" data. The performance of these methods will significantly worsen when the training data are spoiled by outliers. In this paper, we introduce the concepts of polarity and quality of the training data, on the basis of which we propose two robust learning algorithms for determining a robust nonlinear interval regression model, which makes a feature of a new cost function for reflecting not only the polarity of the training data but also the estimated knowledge about the quality of the training data. The two robust algorithms are derived in a manner similar to the back-propagation (BP) algorithm. Simulation results show that our robust algorithms outperform the existing methods remarkably in two aspects when outliers are present: (1) They are robust against outliers; (2) Their rates of convergence are improved to some extent.