Fig. 1. Champagne monthly series from January 1962 to April 1969, data in bottles per month.

Fig. 2. Membership functions of the three fuzzy objectives based on Table 4, for the champagne data.

Fig. 3. Average MAPE across different forecast horizons using each seasonal subset of series, for the 111 series.

Fig. 4. Average MAPE across different forecast horizons for all 111 series: a comparison of our method (both in its additive and multiplicative version) with some of the best methods in the M-competition.

Best-practice solutions (χ,ζ) obtained applying Stage I (S_MAPE, S_RMSE and S_MAD) and Stage II (S_NLP), for the champagne data

Model fitting errors for the best-practice solutions described in Table 1, for the champane data

Post-sample accuracy for the solutions in Table 1 and the solution provided by Chatfield and Yar (1991), for the champagne data

Shape and tolarence parameters of the membership functions of the fitting, for the champane data

Parametric solutions of the (FP) problem and fitting errors for different degrees of global satisfaction, for the champagne data

Average MAPE for all 111 series across different forecasting horizons, using multiplicative seasonality: a comparison of four initial solutions

Average MAPE for all 111 series across different forecasting horizons, using additive seasonality: a comparison of four initial solutions

Some sample percentiles of the average MAPE for each one of the 111 series, using multiplicative seasonality only: a comparison of four criteria to calculate initial values

Average MAPE fit for all 111 series, and for each seasonal subset of series

Average MAPE across some forecast horizons, using all 111 series and for each subset of series

Average MAPE across different forecast horizons for all 111 series, comparing our method (including both its additive and multiplicative version) with some of the best methods in the M-competition