Granular Auto-regressive Moving Average (grARMA) Model for Predicting a Distribution from Other Distributions. Real-world Applications

Industrial products are often output in batches at discrete times. A batch gives rise to distributions of measurements, one distribution per variable of interest. There may be a need for modeling to predict a distribution from other distributions. This work represents a distribution by a fuzzy interval number (FIN) interpreted as an information granule. Based on vector lattice theory it is shown that the lattice F₊ of positive FINs is a cone in a non-linearly tunable, metric, linear space. In conclusion, a multivariate granular autoregressive moving average (grARMA) model is proposed for predicting a distribution from other distributions. A recursive neural network implementation is shown. We report preliminary results regarding two real-world applications including, first, industrial fertilizer production and, second, environmental pollution monitoring along seashore in northern Greece. The far-reaching potential of novel techniques is discussed.