L. Valverde and S.V. Ovchinnikov

EECS Department, University of California, Berkeley

Technical Report No. UCB/CSD-87-331

, 1987

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1987/CSD-87-331.pdf

The representation theorem for F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F-transitive fuzzy relations on a set X, F being an Archimedian t-norm, is dense in the set of Z-transitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.

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BibTeX citation:

@techreport{Valverde:CSD-87-331,
    Author= {Valverde, L. and Ovchinnikov, S.V.},
    Title= {Representation of Fuzzy Symmetric Relations},
    Year= {1987},
    Month= {Mar},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1987/5998.html},
    Number= {UCB/CSD-87-331},
    Abstract= {The representation theorem for F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F-transitive fuzzy relations on a set X, F being an Archimedian t-norm, is dense in the set of Z-transitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.},
}

EndNote citation:

%0 Report
%A Valverde, L. 
%A Ovchinnikov, S.V. 
%T Representation of Fuzzy Symmetric Relations
%I EECS Department, University of California, Berkeley
%D 1987
%@ UCB/CSD-87-331
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1987/5998.html
%F Valverde:CSD-87-331