Construction of Granular Derivatives and Solution of Granular Initial Value Problem

Batyrshin, Ildar

doi:10.1007/978-3-540-39675-8_12

Cited by 17 publications

(27 citation statements)

References 6 publications

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“…Each term represents a fuzzy granule of directions, and for instance in Batyrshin et al 5,24 there are presented many methods of constructing such a fuzzy granulation. The user may define membership functions of the particular linguistic terms.…”

Section: Dynamics Of Changementioning

confidence: 99%

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

Kacprzyk

Wilbik

Zadrożny

2010

Int. J. Intell. Syst.

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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

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Section: Dynamics Of Changementioning

confidence: 99%

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

Kacprzyk

Wilbik

Zadrożny

2010

Int. J. Intell. Syst.

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“…23 The user may also define membership functions of particular linguistic terms depending on his or her needs. Table IV, the evolution item created in Example 8 is actually associated to the trend slowly decreasing as the slope between 1 and 2 is equal to (315 − 330)/30 days = −1/2.…”

Section: Trend Databasesmentioning

confidence: 99%

Evolution patterns and gradual trends

Fiot

Masséglia

Laurent

et al. 2009

Int. J. Intell. Syst.

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Nowadays, many databases record ordered or temporally annotated data, such as Web access logs or genomic sequences. Therefore, sequence mining has become an important research area. Among these data mining approaches, sequential patterns aim at describing frequent behaviors. In the access data of a commercial Web site, one may, for instance, discover that "35% of customers successively buy a PSP then a memory stick and PSP games". To provide more complete information, fuzzy sequential patterns were designed, including quantitative values within the mining task. Such patterns, considering the previous example, would be "35% of customers buy a PSP, then they buy few games many times, and then they buy a high-capacity memory stick once." However, symbolic or fuzzy sequential patterns, in their current form, do not allow to extract temporal tendencies that are typical of sequential data. By means of temporal tendency mining, one may discover in the same access data that "An increasing number of purchases of PSP games during a very short period is frequently followed by a purchase of a high-capacity memory stick a few days later." It would be easy to conclude that the users either quickly succeed in registering or make several attempts before they look at the help page within a few seconds. To the best of our knowledge, no method has been designed for discovering this kind of patterns. Therefore, we propose, in this paper, two approaches that extract pattern-expressing trends or evolution. First, we define evolution patterns that summarize the evolution of the quantities in the data. We explain how they can be obtained from a quantitative sequence database. Second, we define gradual trends in fuzzy sequential data. These trends describe variations in the fulfillment of fuzzy properties according to time. For both kinds of patterns, we developed algorithms that were implemented and tested on real data. C 2009 Wiley Periodicals, Inc.

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“…The idea of CwW created by Lotfi Zadeh has been presented in scientific journals after 1990 (Zadeh, 1996a;1996b;2004;2006a;2006b;2009, Zadeh and. From the very beginning, CwW has been connected with fuzzy and interval arithmetic (Hansen, 1975;Kaufmann and Gupta, 1991;Piegat, 2001;Hanss, 2005;Tomaszewska, 2014), with granular computing (Batyrshin, 2002;Pedrycz and Gomide, 2007;Aliev et al, 2012;Piegat and Landowski, 2013a), with human-centric computing (Pedrycz and Gomide, 2007), with data mining, database querying and data analysis (Kacprzyk and Zadrożny, 1999;2010;Zadeh and Kacprzyk, 1999;Grzegorzewski and Hryniewicz, 2002;Batyrshin and Wageknecht, 2002), and with plant control (Zhou,676 A. Piegat and M. Pluciński the creator of the CwW idea, formulated many challenge problems.…”

Section: Introductionmentioning

confidence: 99%

Computing with words with the use of inverse RDM models of membership functions

Piegat

Pluciński

2015

International Journal of Applied Mathematics and Computer Science

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Computing with words is a way to artificial, human-like thinking. The paper shows some new possibilities of solving difficult problems of computing with words which are offered by relative-distance-measure RDM models of fuzzy membership functions. Such models are based on RDM interval arithmetic. The way of calculation with words was shown using a specific problem of flight delay formulated by Lotfi Zadeh. The problem seems easy at first sight, but according to the authors' knowledge it has not been solved yet. Results produced with the achieved solution were tested. The investigations also showed that computing with words sometimes offers possibilities of achieving better problem solutions than with the human mind.

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Construction of Granular Derivatives and Solution of Granular Initial Value Problem

Cited by 17 publications

References 6 publications

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

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

Evolution patterns and gradual trends

Computing with words with the use of inverse RDM models of membership functions

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