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Matrix expression of finite Boolean-type algebras

Author

Listed:
  • Fu, Shihua
  • Cheng, Daizhan
  • Feng, Jun-e
  • Zhao, Jianli

Abstract

This paper provides a systematic matrix description for finite Boolean- type algebras (BTAs). A BTA is decomposed into Boolean-type lattice (BTL) and a complementation algebra (CA). When the object set is finite, the matrix expressions of BTL and CA (and then of BTA) are presented. Via their matrix expression, the construction and certain properties of BTAs are investigated, including the homomorphism and isomorphism, as well as the decomposition. Moreover, straightforward verifiable conditions are obtained to detect the properties above by means of logical matrices operations.

Suggested Citation

  • Fu, Shihua & Cheng, Daizhan & Feng, Jun-e & Zhao, Jianli, 2021. "Matrix expression of finite Boolean-type algebras," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s009630032030833x
    DOI: 10.1016/j.amc.2020.125880
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    References listed on IDEAS

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    1. Zhao, Guodong & Wang, Yuzhen & Li, Haitao, 2016. "A matrix approach to modeling and optimization for dynamic games with random entrance," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 9-20.
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    Cited by:

    1. Wang, Jianjun & Liu, Wen & Fu, Shihua & Xia, Jianwei, 2022. "On robust set stability and set stabilization of probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Guo, Peilian & Han, Changda, 2021. "Nash equilibrium and group strategy consensus of networked evolutionary game with coupled social groups," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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