We introduce three broad classes of nullnorms on a bounded lattice and lay bare the structure of their members. For that purpose, we introduce particular subsets of a bounded lattice, called upper (resp. lower) beams, and appropriate associative operations on them, called beam (resp. dual beam) operations, which conveniently generalize triangular norms (resp. triangular conorms). It is shown that nullnorms in the first (resp. second) class are characterized by a triangular conorm (resp. triangular norm) and a beam operation (resp. dual beam operation), while nullnorms in the third class are characterized by a triangular conorm and a triangular norm. We also discuss the relationships among these three classes.

我们在有界格上引入了三大类零范数，并揭示了它们的成员结构。为此，我们引入了有界晶格的特定子集，称为上（或下）梁，以及对它们的适当关联运算，称为梁（分别为双梁）运算，可方便地推广三角范数（或三角共形） . 结果表明，第一类（相应的第二类）中的零范数具有三角共形（相应的三角范数）和光束操作（相应的双光束操作）的特征，而第三类中的零范数以三角共形为特征和三角范数。我们还讨论了这三个类之间的关系。