Linguistic characterization of time series

The goal of this paper is to provide an overview of applications of special soft computing theories - the fuzzy transform and fuzzy natural logic - to analysis, forecasting and mining information from time series. The focus is especially placed on the ability of methods of fuzzy natural logic to provide information in sentences of natural language. Our approach is based on the decomposition of time series into three components: the trend-cycle, seasonal component and noise. The trend-cycle is extracted using the F-transform, and its course is characterized by automatically generated linguistic description. The latter is then used to forecast the trend-cycle. The trend-cycle can be, furthermore, decomposed into trend (general tendency) and cycle. The former is computed again using the F-transform. Moreover, the F1-transform makes it possible to estimate the direction of the trend, which can then be characterized by expressions of natural language (stagnating, slightly increasing, sharply decreasing, etc.). Finally, we focus on selected problems of mining information from time series. First, we suggest an algorithm for finding intervals of monotonous behavior and then show how the theory of intermediate quantifiers (a constituent of fuzzy natural logic) and generalized Aristotle's syllogisms can be applied to automatic summarization of information on time series.