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The fuzzy metric space based on fuzzy measure

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Xie J., Li Q., Chen S., Huang H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
603-612
EN
In this paper, we study the relation between a fuzzy measure and a fuzzy metric which is induced by the fuzzy measure. We also discuss some basic properties of the constructed fuzzy metric space. In particular, we show that the nonatom of fuzzy measure space can be characterized in the constructed fuzzy metric space.
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Scott convergence and fuzzy Scott topology onL-posets

100%
Liu H., Chen L.
Open Mathematics
|
2017
|
tom 15
|
nr 1
815-827
EN
We firstly generalize the fuzzy way-below relation on an L-poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified L-generalized convergence structure on an L-poset. In terms of that, L-fuzzy Scott topology and fuzzy Scott topology are considered, and the properties of fuzzy Scott topology are discussed in detail. At last, we investigate the Scott convergence of stratified L-filters on an L-poset, and show that an L-poset is continuous if and only if the Scott convergence on it coincides with the convergence with respect to the corresponding topological space.
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