TY - JOUR
ID - 4653
TI - Quantale-valued fuzzy Scott topology
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Han, S. E.
AU - Lu, L. X.
AU - Yao, W.
AD - Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City
Jeonbuk, 561-756, Republic of Korea
AD - Department 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, China
AD - School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China
Y1 - 2019
PY - 2019
VL - 16
IS - 3
SP - 175
EP - 188
KW - Commutative unital quantale, Generalized GL-monoid, Stratified $L$-filter, Stratified $L$-generalized convergence space, Stratified $L$-topology
KW - $L$-fuzzy dcpo, Fuzzy Scott topology
DO - 10.22111/ijfs.2019.4653
N2 - 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.
UR - https://ijfs.usb.ac.ir/article_4653.html
L1 - https://ijfs.usb.ac.ir/article_4653_f35a750118ba0d313c54fcda469befe8.pdf
ER -