Fuzzy Prokhorov metric on the set of probability measures
The authors consider a fuzzy analogue of the Prokhorov metric defined on the set of all probability measures of a compact fuzzy metric space. They prove that this metric induces the weak-\(*\) convergence of probability measures on a compact metrizable space. Their reason for studying the space of probability measures on fuzzy metric spaces is twofold. First, they use the property of spaces of probability measures to be absolute extensors and this allows them to solve the problem of (continuous) extension of a fuzzy metric defined on a closed subspace. The second reason to investigate the spaces of probability measures is their applicability to the theory of probabilistic systems.
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