An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation

Abstract

We extend our previous work on the linguistic summarization of time series data meant as the linguistic summarization of trends, i.e. consecutive parts of the time series, which may be viewed as exhibiting a uniform behavior under an assumed (degree of) granulation, and identified with straight line segments of a piecewise linear approximation of the time series. We characterize the trends by the dynamics of change, duration, and variability. A linguistic summary of a time series is then viewed to be related to a linguistic quantifier driven aggregation of trends. We primarily employ for this purpose the classic Zadeh's calculus of linguistically quantified propositions, which is presumably the most straightforward and intuitively appealing, using the classic minimum operation and mentioning other t-norms. We also outline the use of the Sugeno and Choquet integrals proposed in our previous papers. We show an application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an 8-year period, by presenting first an analysis of characteristic features of quotations, under various (degrees of) granulations assumed, and then by listing some more interesting and useful summaries obtained. We propose a convenient presentation of linguistic summaries focused on some characteristic feature exemplified by what happens "almost always," "very often," "quite often," "almost never," etc. All these analyses are meant to provide means to support a human user to make decisions. C

Comprehensiveness and interpretability of linguistic data summaries: A natural language focused perspective

“…However, the truth degree alone is too weak a criterion for the goodness of a linguistic summary, and some other quality (validity) criteria have been proposed exemplified by, e.g., Yager's [33] measure of informativeness, and then five additional measures proposed by Kacprzyk and Yager [17] and Kacprzyk, Yager and Zadrożny [18]: truth, degrees of imprecision, covering and appropriateness, and a length of a summary. For even more measures, see Kacprzyk, Wilbik and Zadrożny [15], [16]. Unfortunately, though all those measures can better capture than the truth degree alone how good a linguistic summary is, the comprehensiveness of some of them to an average user may be questionable.…”

“…b) Dynamic summaries: In a series of our previous papers, which culminated in Kacprzyk, Wilbik and Zadrożny [15], [16], and Wilbik and Kacprzyk [32], we proposed to apply linguistic summaries to time series data. From our point of view, this approach boils down to a special treatment of the timestamp which is assumed to be among the attributes A characterizing the data set under consideration.…”

Some Notes on Extracting Linguistic Summaries Built with Epistemic Modalities and Natural Language Connectives of Equivalence

“…Over the last years, the group of temporally-related linguistic summaries has been an object of intensive theoretical study and application-oriented development. Although the body of results is still rather modest, as compared to previously mentioned groups of linguistic summaries, however, it consists of strong computational models (see [11,14,15] for interesting and valuable examples). Again, all of them are in many ways related to the original concept of linguistic variable [20] and Zadeh's paradigm of computing with words [13,24,25].…”

On a benchmark related assessment of the performance of mutual (investment) funds

“…One topic is the analysis of past performance for which we have proposed and used linguistic summaries of time series. In our works [3], [5], [4] segments (trends) derived from consecutive values have been used. We have used the following (classical) protoforms of linguistic summaries employed: "among all y's Q are P " exemplified by "among all segments (of time series), most are slowly increasing" and "among all Ry's Q are P " exemplified by "among all short segments (of time series), most are slowly increasing".…”