On the Complexity of Standard Forms for Multioperations of rank k

Multioperations of rank k are defined as functions mapping k-element set A to the set of all its subsets. Values of a multioperation for inputs equal to one-element sets are given and values for other sets are calculated as a union of values on one-element sets. Superposition of multioperations is defined in the same way. Multioperation is a generalization of different models of uncertainty, incomplete and partial operations and hyperoperations. Standard forms representing multioperations are defined using intersection multioperation. It is natural to define complexity of a standard form as the number of its components. This paper generalizes previous exact bounds on complexity of n-ary multioperations of rank 2 to multioperations of rank k.