Fuzzy ultrametrics on the set of probability measures

Savchenko, A. M.; Zarichnyi, Mykhailo

doi:10.1016/j.top.2009.11.011

Cited by 14 publications

(11 citation statements)

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“…As a particular case, if`¼^and (M,`) is a strong fuzzy metric, we obtain the notion of fuzzy ultrametric (Gregori et al, 2010;Savchenko & Zarichnyi, 2009):…”

Section: Preliminariesmentioning

confidence: 99%

“…Furthermore we will prove that the restriction of the s-_-superdecomposable measure to the s-algebra of all measurable sets is a s-_-decomposable measure. It should be noted that in our definition of the Hausdorff fuzzy pseudo-metric we remove the compactness condition which is necessary in the previous literatures (Repovš, Savchenko, & Zarichnyi, 2011, Rodríguez-López & Romaguera, 2004, Savchenko & Zarichnyi, 2009). This paper is divided into four sections.…”

Section: Introductionmentioning

confidence: 99%

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On decomposable measures constructed by using stationary fuzzy pseudo-ultrametrics

Qiu

Zhang

2013

International Journal of General Systems

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We prove that for a given stationary fuzzy ultrametric space (in the sense of Kramosil & Michalek) it can induce a s-_-superdecomposable measure, by constructing a Hausdorff fuzzy pseudo-metric on its power set. We also prove that the restriction of the s-_-superdecomposable measure to the s-algebra of all measurable sets is a s-_-decomposable measure. Finally we conclude this paper with two open problems.

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“…As a particular case, if`¼^and (M,`) is a strong fuzzy metric, we obtain the notion of fuzzy ultrametric (Gregori et al, 2010;Savchenko & Zarichnyi, 2009):…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On decomposable measures constructed by using stationary fuzzy pseudo-ultrametrics

Qiu

Zhang

2013

International Journal of General Systems

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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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“…In particular, a fuzzy Prokhorov metric and ultrametric defined on the set of all probability measures in a compact fuzzy metric space have been developed in [31,32]. Cao et.…”

Section: Introductionmentioning

confidence: 99%