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On decomposable measures constructed by using stationary fuzzy pseudo-ultrametrics. (English) Zbl 1280.28018
Summary: We prove that for a given stationary fuzzy ultrametric space (in the sense of Kramosil & Michalek) it can induce a \(\sigma\)-\(\vee\)-superdecomposable measure, by constructing a Hausdorff fuzzy pseudo-metric on its power set. We also prove that the restriction of the \(\sigma\)-\(\vee\)-superdecomposable measure to the \(\sigma\)-algebra of all measurable sets is a \(\sigma\)-\(\vee\)-decomposable measure. Finally, we conclude this paper with two open problems.

MSC:
28E10 Fuzzy measure theory
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