Distributive equation of implications based on continuous triangular norms
نویسندگان
چکیده
In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T1(y, z)) = T2(I(x, y), I(x, z)), when T1 is a continuous but not Archimedean triangular norm, T2 is a continuous Archimedean triangular norm and I is an unknown function. Our methods of proof can be applied to the three other functional equations related closely to the distributive equation of implication.
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