Quantale-valued fuzzy Scott topology

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Han S.E.; LU L.X.; YAO W.

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Journal: Iranian Journal of Fuzzy Systems Year:2019 | Volume:16 | Issue:3 Page(s): 175-188

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Information Journal Paper

Title

Quantale-valued fuzzy Scott topology

Author(s)

Han S.E. | LU L.X. | YAO W. | Issue Writer Certificate

Keywords

Commutative unital quantaleQ2

Generalized GL-monoidQ2

Stratified L-filterQ2

Stratified L-generalized convergence spaceQ2

Stratified L-topology;L-fuzzy dcpoQ2

Fuzzy Scott topologyQ2

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; ∗ ; ") be a Commutative unital quantale and let ⊗ be a binary operation on L which is distributive over nonempty subsets. The quadruple (L; ∗ ; ⊗ ; ") is called a Generalized GL-monoid if (L; ∗ ; ") is a Commutative unital quantale and the operation ∗ is ⊗-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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APA: Copy

Han, S.E., LU, L.X., & YAO, W.. (2019). Quantale-valued fuzzy Scott topology. IRANIAN JOURNAL OF FUZZY SYSTEMS, 16(3 ), 175-188. SID. https://sid.ir/paper/113319/en

Vancouver: Copy

Han S.E., LU L.X., YAO W.. Quantale-valued fuzzy Scott topology. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2019;16(3 ):175-188. Available from: https://sid.ir/paper/113319/en

IEEE: Copy

S.E. Han, L.X. LU, and W. YAO, “Quantale-valued fuzzy Scott topology,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 16, no. 3 , pp. 175–188, 2019, [Online]. Available: https://sid.ir/paper/113319/en

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