Characterization of transitivity in L-tolerance spaces by convergence and closure by Gunther Jaeger and T. M. G. Ahsanullah
We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, transitivity is characterized by convergence and diagonal axioms. Quantale-valued tolerance relations compatible with group structures are also characterized by convergence and it is shown that they are transitive.
Generalizing the notion of probabilistic convergence ring, where the underlying lattice is a specific quantale, we consider more general quantale to introduce the notions of quantale…
Considering a value quantale, we introduce a category of quantale-valued convergence transformation groups on quantale-valued convergence spaces.
In this article, we focus on discussing some subcategories of the category of probabilistic convergence groups, PConvGrp. In so doing, we introduce a category of probabilistic…