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 stratifiedL-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.

Keywords:

Commutative unital quantale , Generalized GL-monoid , Stratified L-filter , Stratified L-generalized convergence space , Stratified L-topology , L-fuzzy dcpo , Fuzzy Scott topology