University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416320190629Quantale-valued fuzzy Scott topology175188465310.22111/ijfs.2019.4653ENS. E.HanDepartment of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City
Jeonbuk, 561-756, Republic of KoreaL. X.LuDepartment of Mathematics, College of Natural Science, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, Republic of Korea and School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050018, ChinaW.YaoSchool of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. ChinaJournal Article20171214The aim of this paper is to extend the truth value table of<br />lattice-valued convergence spaces to a more general case and<br />then to use it to introduce and study the quantale-valued fuzzy Scott<br />topology in fuzzy domain theory. Let $(L,*,\varepsilon)$ be a<br />commutative unital quantale and let $\otimes$ be a binary operation<br />on $L$ which is distributive over nonempty subsets. The quadruple<br />$(L,*,\otimes,\varepsilon)$ is called a generalized GL-monoid if<br />$(L,*,\varepsilon)$ is a commutative unital quantale and the operation $*$ is<br />$\otimes$-semi-distributive. For generalized GL-monoid $L$ as the<br />truth value table, we systematically propose the stratified<br />$L$-generalized convergence spaces based on stratified $L$-filters,<br />which makes various existing lattice-valued convergence spaces as<br />special cases. For $L$ being a commutative unital quantale, we<br />define a fuzzy Scott convergence structure on $L$-fuzzy dcpos and<br />use it to induce a stratified $L$-topology. This is the inducing way<br />to the definition of quantale-valued fuzzy Scott topology, which<br />seems an appropriate way by some results.https://ijfs.usb.ac.ir/article_4653_f35a750118ba0d313c54fcda469befe8.pdf