  This paper examines operad structures derived from poset matrices by
formulating a set of new construction rules for poset matrices. In this
direction, eleven different partial composition operations will be introduced
as the basis for the construction of poset matrices of any given size by
extending the combinatorial setting of species of structures to poset matrices.
Three of these partial composition operations are shown to define an operad
structure for poset matrices. The structural properties of poset matrices and
their duals are then studied based on their associated operad constructions.
