# Time Series Analysis by Fuzzy Logic Methods
## 5 Conclusions  
DMA comprises a set of algorithms designed to address various data analysis problems, such as clustering and tracing in multidimensional spaces, and time series analysis, including smoothing, searching for anomalies and trends, studying their morphology, and many more. These algorithms are built on a single formal basis and have a universal character. DMA is based on the idea that human perception of form, discreteness, and stochasticity is more natural and stable than mathematical models. In turn, this is explained by a flexible, adaptive human perception of the fundamental concepts of proximity, continuity, connectedness, and others. The technical basis of DMA, along with including classical mathematics, also includes fuzzy mathematics and fuzzy logic, since these are required as a means to model the actions of a person who thinks and operates not with numbers, but with fuzzy concepts [1; 2]. All this was addressed in this work, The nonformal logic of our approach to the morphological analysis of the record \(x(t)\) presented in the first part is one of the possible answers for a person traveling along a graph \(\Gamma_{x}\) to answer sixteen questions Section 2.1.3. The formulation of such answers, proposed in the second part of the paper presented is especially effective for smooth time series, which, in particular, include the basic straightening \(R_{x}\) of record \(x(t)\). The \(R\) morphological analysis (third part) facilitates understanding of the dynamics of the manifestation of property \(R\) on the record \(x(t)\). Despite the local nature of the straightening \(R\), this conclusion is no longer local. The same non-local character is the result of the final fourth part of the paper, concerning the search for mountains on the straightening \(R_{x}\), using the morphological measures of \"beginning\", \"peak\" and \"end\". Mountains are recognized with precise indications of boundaries, and initial and final stages, explicit indications of slopes and peaks (see Figure 6). The morphological quality of the recognition of mountain passes to the R-anomalies corresponding to them on the records serves as the basis for their further classification and encoding (see Figure 6). It is precisely because of these requirements for the recognition of extreme geomagnetic events that the MAGNUS (Monitoring and Analysis of Geomagnetic aNomalies in Unified Systems) is analytically complex [1], with an intellectual unit that includes DMA imposing formalization. The authors suggest further research in three directions. The first direction is to study the possibilities and properties of both elementary and morphological measures constructed in this paper (parameters, stability, and new logical connections in their constructions). The second direction us the creation of new constructions of elementary measures and, on their basis, of morphological ones. In other words, the search for new scenarios of DMA morphological analysis described in this paper us proposed. The third direction is to continue on from the results obtained in the present paper, applied to the analysis of magnetic storms, by seeking other, primarily physical, applications. All authors contributed to the study conception and design. Conceptualization, S.M.A., D.A.K., A.O.A. and B.V.D. ; Data curation, S.R.B. and A.O.A. ; Formal analysis, S.R.B. and A.O.A. ; Methodology, D.A.K., S.R.B., A.O.A. and B.V.D. ; Software, S.R.B. and A.O.A. ; Validation, D.A.K., A.O.A. and B.V.D. ; Writing--original draft, S.M.A. ; Writing--review & editing, D.A.K., A.O.A. and B.V.D. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was conducted in the framework of budgetary funding of the Geophysical Center of RAS, adopted by the Ministry of Science and Higher Education of the Russian Federation. **Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.