Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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