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<p><b>Abstract</b>—Discrete mathematical analysis (DMA) is a method of analyzing discrete data that actively uses fuzzy mathematics (FM) and fuzzy logic (FL), allowing it to take into account the opinion and experience of a researcher in its work to a much greater extent than classical methods. The latest results of DMA on the study of discrete functions using FL, clustering in complex multidimensional arrays, as well as a constructive description of the diversity of solutions of systems of linear algebraic equations (SLAE) allow us to propose a new version of geophysical integration, in which FM and FL, and therefore the researcher, play a major role. The work presents the concept of geophysical integration, which is based on the theoretical apparatus of DMA, FM, and FL and practical, geophysical results of the application of DMA as evidential examples.</p>

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Fuzzy Mathematics Methods for Comprehensive Analysis of Geophysical Data

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • S. M. Agayan,
  • Sh. R. Bogoutdinov,
  • A. A. Soloviev,
  • B. A. Dzeboev,
  • B. V. Dzeranov,
  • M. N. Dobrovolsky

摘要

Abstract—Discrete mathematical analysis (DMA) is a method of analyzing discrete data that actively uses fuzzy mathematics (FM) and fuzzy logic (FL), allowing it to take into account the opinion and experience of a researcher in its work to a much greater extent than classical methods. The latest results of DMA on the study of discrete functions using FL, clustering in complex multidimensional arrays, as well as a constructive description of the diversity of solutions of systems of linear algebraic equations (SLAE) allow us to propose a new version of geophysical integration, in which FM and FL, and therefore the researcher, play a major role. The work presents the concept of geophysical integration, which is based on the theoretical apparatus of DMA, FM, and FL and practical, geophysical results of the application of DMA as evidential examples.