Han, S., Lu, L., Yao, W. (2019). Quantale-valued fuzzy Scott topology. Iranian Journal of Fuzzy Systems, 16(3), 175-188. doi: 10.22111/ijfs.2019.4653

S. E. Han; L. X. Lu; W. Yao. "Quantale-valued fuzzy Scott topology". Iranian Journal of Fuzzy Systems, 16, 3, 2019, 175-188. doi: 10.22111/ijfs.2019.4653

Han, S., Lu, L., Yao, W. (2019). 'Quantale-valued fuzzy Scott topology', Iranian Journal of Fuzzy Systems, 16(3), pp. 175-188. doi: 10.22111/ijfs.2019.4653

Han, S., Lu, L., Yao, W. Quantale-valued fuzzy Scott topology. Iranian Journal of Fuzzy Systems, 2019; 16(3): 175-188. doi: 10.22111/ijfs.2019.4653

^{1}Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, Republic of Korea

^{2}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

^{3}School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China

Abstract

The aim of this paper is to extend the truth value table of lattice-valued convergence spaces to a more general case and then to use it to introduce and study the quantale-valued fuzzy Scott topology in fuzzy domain theory. Let $(L,*,\varepsilon)$ be a commutative unital quantale and let $\otimes$ be a binary operation on $L$ 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 the truth value table, we systematically propose the stratified $L$-generalized convergence spaces based on stratified $L$-filters, which makes various existing lattice-valued convergence spaces as special cases. For $L$ being a commutative unital quantale, we define a fuzzy Scott convergence structure on $L$-fuzzy dcpos and use it to induce a stratified $L$-topology. This is the inducing way to the definition of quantale-valued fuzzy Scott topology, which seems an appropriate way by some results.

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