AN ALGEBRAIC CHARACTERIZATION OF CARTESIAN PRODUCTS OF FUZZY RELATIONS | Zendy

Hitoshi Furusawa | Zendy

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AN ALGEBRAIC CHARACTERIZATION OF CARTESIAN PRODUCTS OF FUZZY RELATIONS

Author(s) -

Hitoshi Furusawa

Publication year - 1997

Publication title -

bulletin of informatics and cybernetics

Language(s) - English

Resource type - Journals

eISSN - 2435-743X

pISSN - 0286-522X

DOI - 10.5109/13465

Subject(s) - characterization (materials science) , mathematics , cartesian product , algebraic number , fuzzy logic , cartesian coordinate system , algebra over a field , pure mathematics , discrete mathematics , computer science , artificial intelligence , geometry , materials science , mathematical analysis , nanotechnology

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 Schmidt and Strohlein, and cartesian products of Boolean relation alge bras were investigated by JOnsson and 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 definition of point relations. Then a representa tion theorem for such relation algebras is deduced.

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