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

T. M. G. Ahsanullah and Fawzi Al-Thukair ()
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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

New Mathematics and Natural Computation (NMNC), 2016, vol. 12, issue 02, 53-76

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.

Keywords: Triangular norms; probabilistic convergence space; enriched lattice-valued convergence structure; probabilistic convergence group; enriched lattice-valued convergence group; probabilistic uniform convergence space; enriched lattice-valued uniform convergence space; approach convergence structure; approach convergence group; category (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S179300571650006X

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