Clones of incompletely specified operations

Abstract

Incompletely specified operations coincide with partial operations. For a given set A, they both assign elements from A to some tuples of elements from A. But, what does it mean that no value is assigned to a tuple? In case of partial operations, it means that the function is not defined and the input tuple can not appear, while in case of incompletely specified operations, the function is defined, but the output value is not specified. We introduce the notion of composition of incompletely specified operations and corresponding definition of a clone of such operations, and make comparison with clones of total, clones of partial and clones of hyper operations. This leads to a survey of similar results holding for incompletely specified operations. © 2012 IEEE.