Mathematical Methods of Geoinformatics. II. Fuzzy-Logic Algorithms in the Problems of Abnormality Separation in Time Series

Mathematical methods of geoinformatics. III. Fuzzy comparisons and recognition of anomalies in time series

“…In this case, the initial information consists of observable time series of geophysical data [19][20][21][22]. This work continues the series of articles [1][2][3][4][5][6][7][8][9][10] in which a new approach is described that is developed by the authors and is oriented toward the investigation of anomalies (zones of increased activity). In this approach, an attempt is made to model discrete analogues of fundamental concepts of mathematical analysis, for example, limit, continuity, smoothness, connectivity and monotony, extremum, inflection, convexity, etc.…”

“…The DRAS and FLARS algorithms created within the framework of DMA [4,6], in contrast to those listed in Sec. 2, realize another approach to the modeling of reasoning and actions of man in searching for anomalies.…”

“…The development of the DRAS and FLARS algorithms is an attempt of modelling the logic of an interpreter that visually recognizes anomalies in a record with a view to automatedly using it later on for the analysis of large data arrays that cannot be manually processed. These algorithms estimate the boundaries of the sought-for anomalies and perform their morphological analysis in the form of the initial, central, and final stages with detecting strong and weak phases in the central stage [4]. A sufficient "flexibility" of the algorithms is provided by a large collection of "straightenings" [4,6] arising in modelling the interpreter operation.…”

“…These algorithms estimate the boundaries of the sought-for anomalies and perform their morphological analysis in the form of the initial, central, and final stages with detecting strong and weak phases in the central stage [4]. A sufficient "flexibility" of the algorithms is provided by a large collection of "straightenings" [4,6] arising in modelling the interpreter operation.…”

On the monitoring of seismic activity using the algorithms of discrete mathematical analysis

“…], morphological analysis of surface [Gvishiani et al, 1994[Gvishiani et al, , 2008detc. ], search for anomalies and trends in records [Gvishiani et al, , 2004[Gvishiani et al, , 2008a[Gvishiani et al, , 2008b[Gvishiani et al, , 2008cSoloviev et al, 2012aSoloviev et al, , 2012betc.]. All DMA algorithms are united by a common formal basis, based on fuzzy comparisons of numbers and proximity measures in discrete spaces.…”