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In the framework of Henkin style higher-order fuzzy logic LΠ ω we construct fuzzy real numbers as fuzzy Dedekind cuts over crisp rationals, and show some of their properties provable in LΠ ω . The definitions of algebraic operations and a theory of fuzzy intervals are sketched.dblp:conf/eusflat/Behounek05 fatcat:xtggzssi7bdxrmisxgynjibtee