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Algebra of Clusterizable Relations

  • Boris Kulik
  • Alexander Fridman
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 836)

Abstract

Relations are usually represented in a space of attributes whose values differ only in names similar to algebra of sets. The order of the values or any other preference measures are not significant for such attributes. The paper proposes a mathematical model based on n-tuple algebra (NTA), for relations in which the values of attributes are ordered. For this case, a mathematical tool has been developed that can be used to perform not only the previously discussed methods and means of logical-semantic analysis on the basis of NTA, including analysis of defeasible reasoning and logic-probabilistic analysis, but also to analyze the order and connectivity of structures and implement clustering methods. The concept of granules is introduced, the power of connectivity between the granules is defined, and methods to calculate distances between the disconnected granules are proposed. The obtained dependencies make it possible to extend the scope of classification techniques.

Keywords

N-tuple algebra Logical-semantic analysis Ordered attribute Clusterization 

Notes

Acknowledgments

The authors would like to thank the Russian Foundation for Basic Researches (grants 16-29-04424, 16-29-12901, 18-07-00132, 18-01-00076, and 18-29-03022) for partial funding of this work.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Problems in Mechanical EngineeringRussian Academy of Sciences (RAS)St. PetersburgRussia
  2. 2.Institute for Informatics and Mathematical ModellingKola Science Centre of RASApatityRussia

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