Links between probabilistic convergence groups under triangular norms and enriched lattice-valued convergence groups

Journal Article

Al-Thukair, TMG Ahsanullah, Fawzi . 2016

• Publication Work Type: Original Reserach
• Publication Online URL: http://www.worldscientific.com/toc/nmnc/12/02?ai=u2&ui=1p44&af=H
• Magazine \ Newspaper: New Mathematics and Natural Computation
• Issue Number: 2
• Volume Number: 12
• Pages: 53 -76

Publication 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.