Linguistic summarization of time series using linguistic quantifiers: Augmenting the analysis by a degree of fuzziness

Taking as a point of departure our works on linguistic summarization of time series (cf. Kacprzyk, Wilbik and Zadrozny [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]) in which an approach based on a calculus of linguistically quantified propositions was proposed, and the essence of the problem was equated with a linguistic quantifier driven aggregation of partial scores (trends), we present here some reformulation and extension mainly towards a more complex evaluation of results resulting linguistic summaries obtained. We use the classic Zadehpsilas calculus of linguistically quantified propositions but, in addition to the basic criterion of a degree of truth (validity), we also use as the second criterion a degree of fuzziness to make it possible to account for a frequent case that though the degree of truth of a very general (not precise) summary is high, its usefulness may be low due to its high fuzziness. We show an application to the absolute performance type analysis of daily quotations of an investment fund.