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An Algebraic Formalization of Fuzzy Relations

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概要 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 s...atisfying Tarski rule and point axiom has been given by G. Schmidt and T. 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.続きを見る

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登録日 2009.04.22
更新日 2017.01.20