Fuzzy transform; evaluative linguistic expressions; time series

In this paper, higher-order fuzzy transform is presented and its application in the analysis and forecasting of time series is demonstrated. The use of F$^m$-transform in the time series analysis is motivated by its better approximation properties and smoother results. In our case, we applied $F^1$-transform for estimation of smoother trend-cycle and its slope. By combining the latter and tools based on the formal theory of evaluative linguistic expressions, we are able to generate automatically linguistic evaluation of the trend of time series in various time slots.