  It is well-known fact that there exists 1-1 correspondence between so-called
double (or flou) sets and intuitionistic sets (also known as orthopairs). At
first glance, these two concepts seem to be irreconcilable. However, one must
remember that algebraic operations in these two classes are also defined
differently. Hence, the expected compatibility is possible. Contrary to this
approach, we combine standard definition of double set with operations which
are typical for intuitionistic sets. We show certain advantages and limitations
of this viewpoint. Moreover, we suggest an interpretation of our sets and
operations in terms of logic, data clustering and multi-criteria decision
making. As a result, we obtain a structure of discussion between several
participants who propose their "necessary" and "allowable" requirements or
propositions.
