On Linguistic Summarization of Numerical Time Series Using Fuzzy Logic with Linguistic Quantifiers

Abstract

We consider an extension to the linguistic summarization of time series data proposed in our previous papers, in particular by introducing a new protoform of the duration based summaries, that is more intuitively appealing. We summarize trends identified here with straight segments of a piecewise linear approximation of time series. Then we employ, as a set of features, the duration, dynamics of change and variability, and assume different, human consistent granulations of their values. The problem boils down to a linguistic quantifier driven aggregation of partial trends that is done via the classic Zadeh’s calculus of linguistically quantified propositions. We present a modification of this calculus using the new protoform of a duration based linguistic summary. We show an application to linguistic summarization of time series data on daily quotations of an investment fund over an eight year period, accounting for the absolute performance of the fund.