An algebraic formalization of fuzzy relations

Abstract This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by Schmidt and Strohlein. 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 improve the definition of point relations. Then by using relational calculus, a representation theorem for such relation algebras is deduced without Tarski rule.

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