PROCEEDINGS IPMU '08

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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