Abstract
Referring only to closed L-fuzzy sets we introduce a concept of probabilistic topological spaces including random metric spaces ([17]) statistical metric spaces ([9][15]) and fuzzy uniform spaces studied by Lowen [11]. In particular probabilistic topologies in the sense of Frank [5] satisfying the additional property (R3) are equivalent to systems of closed [0, 1]-fuzzy sets. Moreover random topologies as well as fuzzy topologies ([3],[13]) equipped with the property (03) can be considered as probabilistic topologies.
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Höhle, U. Probabilistische Topologien. Manuscripta Math 26, 223–245 (1978). https://doi.org/10.1007/BF01167724
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DOI: https://doi.org/10.1007/BF01167724