HYPERSPACE FUZZY BINARY RELATIONS

We associate with each implication operator in [0,1]-valued logic, und er certain conditions, an algorithm for extending a fuzzy (or ordinary ) binary relation psi from X to Y, to a fuzzy binary relation from I(X ) to I(Y), said to be a fuzzy hyperspace extension of psi. We show tha t our extension algorithms preserve a number of properties of binary r elations. As application to fuzzy topology, we show that each algorith m produces its notion of Hausdorff fuzzy T-uniformities, and related n otions. These subsume Lowen's definition of horizontal hyperspace fuzz y uniform structures, as a special case corresponding to the reciproca l of the Godel implication operator.