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Abstract
The discrete mathematical analysis (DMA) is a series of algorithms aimed at the solution of basic problems of data analysis: clustering and tracing in multidimensional arrays, morphological analysis of reliefs, search for anomalies and trends in records etc. All the DMA algorithms are of universal nature, joined by the same formal foundation, based, in its turn, on fuzzy logic (FL) and fuzzy mathematics (FM). The current study finalizes the search for the anomalies in one-dimensional time series within the scope of DMA: here the initial concept of an interpreter’s logic gets its additional development. First, the formal expert’s opinions are more fully expressed, and this is realized with the more complex measures of activity (the concept of straightenings (Gvishiani et al. 2003; Gvishiani et al. 2004; Zlotnicki et al. 2005) is replaced by the measures of activity which come to the fore): second, for the junction of anomalies, a recently created DPS (Discrete Perfect Sets) algorithm is used DPS (Discrete Perfect Sets) (Agayan et al. 2011; Agayan et al. 2014).
Highlights
The current study finalizes the search for the anomalies in one-dimensional time series within the scope of discrete mathematical analysis (DMA): here the initial concept of an interpreter’s logic gets its additional development
The time series f is analyzed by an expert ε
It is supposed that the expert ε has a point of view on the dynamic pattern of f in every node t ∈ T, and a number of questions is posed at this time
Summary
The discrete mathematical analysis (DMA) is a series of algorithms aimed at the solution of basic problems of data analysis: clustering and tracing in multidimensional arrays, morphological analysis of reliefs, search for anomalies and trends in records etc. Let us formulate the first two questions: Question 1: To what extent μɛf(t) ∈ [0, 1] is the dynamic pattern of the time series f the expert ɛ is interested in, expressed (how active is it) in the node t? It becomes possible to instill the content to the complicated activity of f by the plurality of dynamical indicators D in the node t ∈ T: mDf (t ) = *DÎD (mDf (t )) (5) It is the construction (1) by which the view of expert ε on the dynamics of f is commonly modeled (Gvishiani et al 2004). For a record f (Fig. 4), the simple measures of activity μLf (Fig. 2) and μOf (Fig. 3), were constructed They correspond to the dynamical indicators of jaggedness (2) and scatterness (3). Their search is realized using the DPS algorithm in two stages
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