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Crisp and $L$-fuzzy ambiguous representations of closed subsets of one spaceby closed subsets of another space are introduced. It is shown that, for eachpair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguousrepresentations is a lattice and a compact Hausdorff Lawson upper semilattice.The categories of ambiguous and $L$-ambiguous representations are defined andinvestigated.

Ambiguous representations as fuzzy relations between sets