Linguistic summarization of time series using a fuzzy quantifier driven aggregation
We propose new types of linguistic summaries of time-series data that extend those proposed in our previous papers. The proposed summaries of time series refer to the summaries of trends identified here with straight line segments of a piecewise linear approximation of time series. We first show how to construct such an approximation. Then we employ a set of features (attributes) to characterize the trends such as 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 but, extending our previous works, with different t-norms in addition to the basic minimum. We show an application to the analysis of time-series data on daily quotations of an investment fund over an eight year period, present some interesting linguistic summaries obtained, and show results for different t-norms. The results are very promising. (C) 2008 Elsevier B.V. All rights reserved.
linguistic quantifier t-norm time series analysis linguistic data summary fuzzy logic