Linguistic summarization of time series using fuzzy logic with linguistic quantifiers: A truth and specificity based approach

We reformulate and extend our previous works (cf. Kacprzyk, Wilbik and Zadrozny [7,8,9,10,11,12,13,14,15,16,17]), mainly towards a more complex and realistic evaluation of results on the linguistic summarization of time series which is meant as the derivation of an linguistic quantifier driven aggregation of partial trends with respect to the dynamics of change, duration and variability. We use Zadeh's calculus of linguistically quantified propositions but, in addition to the basic criterion of a degree of truth (validity), we also use a degree of specificity to make it possible to account for a frequent case that though the degree of truth of a very general (not specific) summary is high, its usefulness may be low due to its low specificity. We show an application to the absolute performance type analysis of daily quotations of an investment fund.