Linguistic Summaries of Time Series: On Some Additional Data Independent Quality Criteria

We further extend our approach on the linguistic summarization of time series (cf. Kacprzyk, Wilbik and Zadrozny) 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). Basically, we present here some reformulation and extension of our works mainly by including a more complex evaluation of the linguistic summaries obtained. In addition to the basic criterion of a degree of truth (validity), we also use here as the additional criteria a degree of imprecision, specificity, fuzziness and focus. 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 remaining three degrees of imprecision, specificity and fuzziness for making a final choice of appropriate linguistic summaries. We show an application to the absolute performance type analysis of daily quotations of an investment fund.