Representation of Fuzzy Symmetric Relations

L. Valverde and S.V. Ovchinnikov

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-87-331
March 1986

http://www.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.


BibTeX citation:

@techreport{Valverde:CSD-87-331,
    Author = {Valverde, L. and Ovchinnikov, S.V.},
    Title = {Representation of Fuzzy Symmetric Relations},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1986},
    Month = {Mar},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/5998.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 1986
%@ UCB/CSD-87-331
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/5998.html
%F Valverde:CSD-87-331