Quantale-valued fuzzy Scott topology

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varepsilon)$ is called a generalized GL-monoid if$(L,*,varepsilon)$ is a commutative unital quantale and the operation $*$ is$otimes$-semi-distributive. For generalized GL-monoid $L$ as thetruth value table, we systematically propose the stratified$L$-generalized convergence spaces based on stratified $L$-filters,which makes various existing lattice-valued convergence spaces asspecial cases. For $L$ being a commutative unital quantale, wedefine a fuzzy Scott convergence structure on $L$-fuzzy dcpos anduse it to induce a stratified $L$-topology. This is the inducing wayto the definition of quantale-valued fuzzy Scott topology, whichseems an appropriate way by some results.