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Links between Probabilistic Convergence Groups Under Triangular Norms and Enriched Lattice-Valued Convergence Groups

Author

Listed:
  • T. M. G. Ahsanullah

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

  • Fawzi Al-Thukair

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

Abstract

We propose here two types of probabilistic convergence groups under triangular norms; present some basic facts, and give some characterizations for both the cases. We look at the possible link from categorical point of view between each of the proposed type and enriched lattice-valued convergence group. We produce several natural examples on probabilistic convergence groups under triangular norms. We also present a notion of probabilistic uniform convergence structure in a new perspective, showing that every probabilistic convergence group is probabilistic uniformizable. Moreover, we prove that this probabilistic uniform structure maintains a close connection with a known enriched lattice-valued uniform convergence structure.

Suggested Citation

  • T. M. G. Ahsanullah & Fawzi Al-Thukair, 2016. "Links between Probabilistic Convergence Groups Under Triangular Norms and Enriched Lattice-Valued Convergence Groups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 53-76, July.
    • Handle: RePEc:wsi:nmncxx:v:12:y:2016:i:02:n:s179300571650006x
    DOI: 10.1142/S179300571650006X
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