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Aggregation Through Composition: Unification of Three Principal Fuzzy Theories

  • Irina PerfilievaEmail author
  • Anand P. Singh
  • S. P. Tiwari
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)

Abstract

This paper shows that the theories of fuzzy rough sets, F-transforms and fuzzy automata can be unified in the framework of fuzzy relational structures. Specifically, the key concepts in such theories are represented as lattice-based aggregations in the form of compositions with suitable fuzzy relations. Furthermore, it is shown that the principal parts of morphisms between all considered fuzzy relational structures coincide.

Keywords

Fuzzy relation Fuzzy rough set F-transform Fuzzy automata 

Notes

Acknowledgment

This work is supported by University of Ostrava grant lRP201824 “Complex topological structures”. The additional support was also provided by the Czech Science Foundation (GAČR) through the project of No. 18-06915S.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Irina Perfilieva
    • 1
    Email author
  • Anand P. Singh
    • 1
  • S. P. Tiwari
    • 2
  1. 1.Institute for Research and Applications of Fuzzy ModelingOstrava 1Czech Republic
  2. 2.Indian Institute of Technology (ISM)DhanbadIndia

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