Numerical representation of transitive fuzzy relations

Authors:
Sergei Ovchinnikov
Affiliations:
Mathematics Department, San Francisco State University, San Francisco, CA
Venue:
Fuzzy Sets and Systems
Year:
2002

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Abstract

We show that there exists a continuous fuzzy quasi-order R on the set of real numbers R such that for any fuzzy quasiorder R on a finite set X there is a mapping f : X → R such that R(x, y) = R(f(x),f(y)) for all x, y ∈ X.