An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation

Abstract

We extend our previous work on the linguistic summarization of time series data meant as the linguistic summarization of trends, i.e. consecutive parts of the time series, which may be viewed as exhibiting a uniform behavior under an assumed (degree of) granulation, and identified with straight line segments of a piecewise linear approximation of the time series. We characterize the trends by the dynamics of change, duration, and variability. A linguistic summary of a time series is then viewed to be related to a linguistic quantifier driven aggregation of trends. We primarily employ for this purpose the classic Zadeh's calculus of linguistically quantified propositions, which is presumably the most straightforward and intuitively appealing, using the classic minimum operation and mentioning other t-norms. We also outline the use of the Sugeno and Choquet integrals proposed in our previous papers. We show an application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an 8-year period, by presenting first an analysis of characteristic features of quotations, under various (degrees of) granulations assumed, and then by listing some more interesting and useful summaries obtained. We propose a convenient presentation of linguistic summaries focused on some characteristic feature exemplified by what happens “almost always,” “very often,” “quite often,” “almost never,” etc. All these analyses are meant to provide means to support a human user to make decisions. © 2010 Wiley Periodicals, Inc.