DOI 10.1007/s11063-007-9035-z Neural Processing Letters (2007) 25:157–169 © Springer 2007 iMLP: Applying Multi-Layer Perceptrons to Interval-Valued Data  ANTONIO MU ˜ NOZ SAN ROQUE 1,⋆ , CARLOS MAT ´ E 1 , JAVIER ARROYO 2 and ´ ANGEL SARABIA 1 1 Instituto de Investigaci´ on Tecnol´ ogica (IIT), Escuela T´ ecnica Superior de Ingenier ´ ia (ICAI), Universidad Pontiﬁcia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain. E-mails: amunoz@upcomillas.es, cmate@upcomillas.es, asarabia@upcomillas.es 2 Departamento de Ingenie´ na del Software e Inteligencie Artiﬁcial, Universidad Complutense, Profesor Garc ´ ia-Santesmases s/n, 28040 Madrid, Spain. E-mail: javier.arroyo@tdi.ucm.es Abstract. Interval-valued data offer a valuable way of representing the available informa- tion in complex problems where uncertainty, inaccuracy or variability must be taken into account. In addition, the combination of Interval Analysis with soft-computing methods, such as neural networks, have shown their potential to satisfy the requirements of the deci- sion support systems when tackling complex situations. This paper proposes and analyzes a new model of Multilayer Perceptron based on interval arithmetic that facilitates handling input and output interval data, but where weights and biases are single-valued and not inter- val-valued. Two applications are considered. The ﬁrst one shows an interval-valued func- tion approximation model and the second one evaluates the prediction intervals of crisp models fed with interval-valued input data. The approximation capabilities of the proposed model are illustrated by means of its application to the forecasting of daily electricity price intervals. Finally, further research issues are discussed. Key words. feed-forward neural network, function approximation, interval analysis, interval data, interval neural networks, symbolic data analysis, time series forecasting Abbreviations: iMLP – interval Multilayer Perceptron; INN – Interval Neural Network; MAPE – Mean Absolute Percentage Error; MLP – Multilayer Perceptron 1. Introduction 1.1. artiﬁcial neural networks, intervals and decision sciences Artiﬁcial neural networks have found increasing consideration in management sci- ence, leading to successful applications in various domains, including business and operations research (see e.g. [1–3]), forecasting (see e.g. [4–6]), and data mining (see e.g. [7,8]). In decision support systems, the Multilayer Perceptron (MLP) is one of the most popular neural network models (see e.g. [2,9]). This is due to the fact that its archi- tecture is very clear and the algorithm is parsimonious. Successful application of  Research funded by Universidad Pontiﬁcia Comillas. ⋆ Author for correspondence.