DPS Clustering: New Results

Agayan, S. M.; Богоутдинов, Ш. Р.; Дзебоев, Б. А.; Dzeranov, Boris V.; Kamaev, D. A.; Osipov, Maxim

doi:10.3390/app12189335

Cited by 4 publications

(2 citation statements)

References 13 publications

(44 reference statements)

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“…The problem of trends (see Section 1.1) in this work is solved within the framework of discrete mathematical analysis (DMA)-a new approach to data analysis, researcheroriented and occupying an intermediate position between hard mathematical methods and soft intellectual ones [25][26][27][28][29].…”

Section: Solution Of the Problem Of Trends And On The Basis Of Discre...mentioning

confidence: 99%

Trends and Extremes in Time Series Based on Fuzzy Logic

Agayan,

Bogoutdinov,

Kamaev

et al. 2024

Mathematics

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The authors develop the theory of discrete differentiation and, on its basis, solve the problem of detecting trends in records, using the idea of the connection between trends and derivatives in classical analysis but implementing it using fuzzy logic methods. The solution to this problem is carried out by constructing fuzzy measures of the trend and extremum for a recording. The theoretical justification of the regression approach to classical differentiation in the continuous case given in this work provides an answer to the question of what discrete differentiation is, which is used in constructing fuzzy measures of the trend and extremum. The detection of trends using trend and extremum measures is more stable and of higher quality than using traditional data analysis methods, which consist in studying the intervals of constant sign of the derivative for a piecewise smooth approximation of the original record. The approach proposed by the authors, due to its implementation within the framework of fuzzy logic, is largely focused on the researcher analyzing the record and at the same time uses the idea of multiscale. The latter circumstance provides a more complete and in-depth understanding of the process behind the recording.

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Section: Solution Of the Problem Of Trends And On The Basis Of Discre...mentioning

confidence: 99%

Trends and Extremes in Time Series Based on Fuzzy Logic

Agayan,

Bogoutdinov,

Kamaev

et al. 2024

Mathematics

Self Cite

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“…Similar to wavelet analysis, the µP f measure visualizes what is happening at f and allows us to better understand the nature of the process behind it. Formal analysis of µP f , including the extraction of useful information about f , can be performed using Image Processing, as well as morphological and cluster DMA methods [Agayan et al, 2021a[Agayan et al, , 2020[Agayan et al, , 2022. This is the motivation for the research presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

Regression Derivatives and Their Application in the Study of Magnetic Storms

Agayan,

Bogoutdinov,

Sidorov

et al. 2024

Russian Journal of Earth Sciences

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Discrete Mathematical Analysis (DMA) is a data analysis method that uses fuzzy mathematics and fuzzy logic. DMA involves the active participation of the researcher in the study of records, offering technologies and algorithms for analyzing records through the properties of interest to the researcher. In the present work, such properties are related to regression derivatives, and the results obtained are applied to magnetic records. The possibilities of the method in the morphological analysis of geomagnetic storms are demonstrated on the example of three strongest storms that have occurred since the beginning of the current 25th solar cycle.

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Strong Earthquake-Prone Areas in the Eastern Sector of the Arctic Zone of the Russian Federation

et al. 2022

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This paper continues the series of publications by the authors on the recognition of areas prone to the strongest, strong, and significant earthquakes using the FCAZ system-analytical method. The areas prone to earthquakes with М ≥ 5.5 in the eastern sector of the Arctic zone of the Russian Federation were recognized. It is shown that certain potential high seismicity zones are well confined to the boundaries of the Eurasian, North American, and Okhotsk tectonic plates. In addition, according to the results of the FCAZ recognition, some areas located at a sufficient distance from the main tectonic structures of the studied region were also recognized as highly seismic. The results of the study, among other factors, justify the use of the assessment of the completeness magnitude in the catalog for choosing the set of recognition objects for the FCAZ method.

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DPS Clustering: New Results

Cited by 4 publications

References 13 publications

Trends and Extremes in Time Series Based on Fuzzy Logic

Trends and Extremes in Time Series Based on Fuzzy Logic

Regression Derivatives and Their Application in the Study of Magnetic Storms

Strong Earthquake-Prone Areas in the Eastern Sector of the Arctic Zone of the Russian Federation

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