On decomposable measures constructed by using stationary fuzzy pseudo-ultrametrics

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.