One illustrative method disclosed herein includes the steps of performing a directed self-assembly process to form a DSA masking layer, performing at least one process operation to remove at least one of the features of the DSA masking layer so as to thereby define a patterned DSA masking layer with a DSA masking pattern, performing at least one process operation to form a patterned transfer masking layer having a transfer masking pattern comprised of a plurality of features that define a plurality of openings in the transfer masking layer, wherein the transfer masking pattern is the inverse of the DSA masking pattern, and performing at least one etching process through the patterned transfer masking layer on a layer of material to form a plurality of trench/via features in the layer of material.