Linguistic Summaries of Time Series Using a Degree of Appropriateness as a Measure of Interestingness

Abstract

We further extend our approach to the linguistic summarization of time series (cf. Kacprzyk, Wilbik and Zadro˙zny [9, 10, 11, 12]) in which an approach based on a calculus of linguistically quantified propositions is employed, and the essence of the problem is equated with a linguistic quantifier driven aggregation of partial scores (trends). In addition to the basic criterion of a degree of truth (validity), we also use as a degree of appropriateness as an additional quality criterion. However, for simplicity and tractability, we use in the first shot the degrees of truth (validity) and focus, which usually reduce the space of possible linguistic summaries to a considerable extent, and then – for a usually much smaller set of linguistic summaries obtained – we use the degree of appropriateness to make a final choice as it gives us an additional quality of being able to detect how surprising, i.e. valuable, a linguistic summary obtained is. We also mention relations to natural language generation (NLG) as pointed out recently by Kacprzyk and Zadro˙zny [19]. We show an application to the absolute performance type analysis of daily quotations of an investment fund, and the numerical results are promising. The linguistic summaries obtained using this additional quality criterion of a degree of appropriateness seem to better reflect human intents and interest.