The problem of distributivity between binary operations in bifuzzy set theory

Pawel Drygas

In this work we study the functional equation given by the following condition
F(x, G(y, z)) = G(F(x, y),F(x, z))
for all x, y, z ∈ L*, i.e. distributivity equation.

The problem of distributivity is of great interest both for particular as well as fundamental reasons. This relates for instance to the theory of binary operations like triangular norms, triangular conorms etc. In this contribution we consider the distributivity between the operations on bifuzzy set theory. Mainly, we consider the decomposable operations (Theorem 1). In this class of operations the distributivity equation is equivalent to the distributivity between underlying operations. So, in this case we should consider the distributivity in the class of operations on the unit interval.

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