On \((L,M)\)-fuzzy quasi-uniform spaces (Q2372279)

Let \(L,M\) be completely distributive lattices. For each set \(X\), \(H(L^X)\) denotes the set of all join-preserving functions \(d:L^X\to L^X\) such that \(A\leq d(A)\) for all \(A\in L^X\). An \((L,M)\)-quasi-uniformity on a set \(X\) is a map \(H(L^X)\to M\) subject to certain conditions. This paper investigates the relations between the category of \((2,M)\)-quasi-uniform spaces and that of \((L,M)\)-quasi-uniform spaces as well as the relations between \((2,M)\)-quasi-uniform spaces and pointwise \((L,M)\)-quasi-uniform spaces.