# 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