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Abstract
We prove that for a given stationary fuzzy ultrametric space (in the sense of Kramosil & Michalek) it can induce a σ- ∨ -superdecomposable measure, by constructing a Hausdorff fuzzy pseudo-metric on its power set. We also prove that the restriction of the σ- ∨ -superdecomposable measure to the σ-algebra of all measurable sets is a σ- ∨ -decomposable measure. Finally we conclude this paper with two open problems.
Acknowledgements
The authors thank the anonymous reviewers for their valuable comments. This work was supported by The National Natural Science Foundation of China (Grant No. 11201512) and the Natural Science Foundation Project of CQ CSTC (cstc2012jjA00001).