On linguistic summarization of time series using fuzzy logic with linguistic quantifiers

We discuss first the concept of a linguistic summary of a time series in the setting proposed by the authors1 and then its extension to cover some additional types of summaries that concern the duration of (partial) trends identified here as straight line segments of a piece-wise linear approximation of a time series. Then, we use the features that characterize the trends: the slope of the line segment, the goodness of approximation and the length of the trend. The derivation of a linguistic summary of a time series is then related to a linguistic quantifier driven aggregation of trends. For this purpose we employ the classic Zadeh's calculus of linguistically quantified propositions in its basic form with the minimum operation. We present some results of a linguistic summarization of time series data on daily quotations of an investment fund over an eight year period, i.e. some best linguistic summaries with their associated degrees of truth (validity). The results obtained provide much insight into the very essence of the time series data, and prove to be promising.