A characterization of idempotent nullnorms

Nullnorms are generalization of triangular norms and conorms with a zero element anywhere in the unit interval. Nullnorms are built up from triangular norms and triangular conorms. If nullnorm is idempotent, then it is composed of a minimum and a maximum. The idea of this paper is to find minimal assumptions on an operation in order to get an idempotent nullnorm.