Ambiguous representations as fuzzy relations between sets

Authors:
Oleh Nykyforchyn;Dušan Repovš
Affiliations:
Vasyl' Stefanyk Precarpathian National University, Shevchenka 57, Ivano-Frankivsk, 76025, Ukraine;Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia and Faculty of Education, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

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