Abstract
Abstract We associate with each implication operator in [0, 1]-valued logic, under certain conditions, an algorithm for extending a fuzzy (or ordinary) binary relation φ from X to Y , to a fuzzy binary relation from I X to I Y , said to be a fuzzy hyperspace extension of φ. We show that our extension algorithms preserve a number of properties of binary relations. As application to fuzzy topology, we show that each algorithm produces its notion of Hausdorff fuzzy T -uniformities, and related notions. These subsume Lowen's definition of horizontal hyperspace fuzzy uniform structures, as a special case corresponding to the reciprocal of the Godel implication operator.
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