An Algebraic Characterization of Cartesian Products of Fuzzy Relations
نویسنده
چکیده
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 Boolean relation algebras satisfying Tarski rule and point axiom was given by G. Schmidt and T. Strohlein, and cartesian products of Boolean relation algebras were investigated by B. J onsson and A. Tarski. Unlike Boolean relation algebras, fuzzy relation algebras are not Boolean but equipped with semi-scalar 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 de nition of point relations. Then a representation theorem for such relation algebras is deduced.
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