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This paper provides an algebraic characterization of mathematical structures formed by cartesian products of fuzzy relations with sup-min composition. A simple proof of a representation theorem for Bo...olean relation algebras satisfying Tarski rule and point axiom was given by Schmidt and Strohlein, and cartesian products of Boolean relation algebras were investigated by Jonsson and Tarski. Unlike Boolean relation algebras, fuzzy relation algebras are not Boolean but equipped with semiscalar multiplication. First we present a set of axioms for fuzzy relation algebras and add axioms for cartesian products of fuzzy relation algebras. Second we improve the definition of point relations. Then a representation theorem for such relation algebras is deduced.show more
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