  In this paper, we give a new approach for the study of Weyl-type theorems.
Precisely we introduce the concepts of spectral valued and spectral
partitioning functions. Using two natural order relations on the set of
spectral valued functions, we reduce the question of relationship between
Weyl-type theorems to the study of the set difference between the parts of the
spectrum that are involved. This study solves completely the question of
relationship between two spectral valued functions, comparable for one or the
other order relation. Then several known results about Weyl-type theorems
becomes corollaries of the results obtained.
