On pseudo-metric spaces induced by σ-⊥-decomposable measures

Xie, Jiancang; Li, Qingguo; Chen, Shui-Li; Gao, You

doi:10.1016/j.fss.2015.04.018

Cited by 4 publications

(2 citation statements)

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“…These notions have been widely used in various papers devoted to fuzzy topology [7,10,13,15,16,25,28]. Meanwhile, much research has focused on investigating the interplay between fuzzy measures, domain theory and fuzzy metric spaces [14,17,18,19,20,24,26,27].…”

Section: Introductionmentioning

confidence: 99%

Formal balls in fuzzy quasi-metric spaces

Gao¹,

Li²,

Guo³

et al. 2017

J. Nonlinear Sci. Appl.

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The notions of Yoneda completeness and Smyth completeness on fuzzy quasi-metric spaces are introduced and their relationship with other types of completeness including sequentially Yoneda completeness and bicompleteness are investigated. Then we use the standard Yoneda completeness to characterize the order-theoretical properties of the poset (BX, M ) of formal balls in a fuzzy quasi-metric space (X, M, ∧). The results show that if (BX, M ) is a dcpo, then (X, M, ∧) is standard complete and conversely, (BX, M ) forms a dcpo provided that (X, M, ∧) is standard Yoneda complete. Particularly, in a fuzzy metric space, we clarify three types of completeness which can be characterized by the directed completeness of the related poset of formal balls.

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Section: Introductionmentioning

confidence: 99%

Formal balls in fuzzy quasi-metric spaces

Gao¹,

Li²,

Guo³

et al. 2017

J. Nonlinear Sci. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The authors of [35] further use a topological approach to extend the t-conorm-based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets. In [36] we constructed a pseudo-metric (in the sense of Pap) on the measurable sets of a given -?-decomposable measure, and then analyzed the connection between the induced pseudo-metric and the -?-decomposable measure.…”

Section: Introductionmentioning

confidence: 99%