  We propose that an unsharp measurement-based process to generate genuine
multipartite entanglement from an entangled initial state with a fewer number
of qubits can be classified in two ways -- biased and unbiased inflation
protocols. In the biased case, genuine multipartite entanglement (GME) of the
resulting state obtained after a single measurement outcome is optimized,
thereby creating a possibility of states with high GME while in the unbiased
case, average GME is optimized over all possible outcomes. Interestingly, we
show that the set of two-qubit unsharp measurements can generate multipartite
states having different features according to GME measure, generalized
geometric measure, the monogamy-based entanglement measure, tangle and
robustness against particle loss quantified via persistency depending on the
rank of the unsharp measurement operators. Specifically, in the process of
producing three-qubit pure states, we prove that rank-$2$ measurements can
create only Greenberger Horne Zeilinger (GHZ)-class states while only W-class
states are produced with rank-$4$ measurements although rank-$3$ measurements
are capable to generate both. In the case of multipartite states with an
arbitrary number of qubits, we report that the average content of genuine
multipartite entanglement increases with the decrease of the rank in the
measurement operators although the persistency decreases with the rank, both in
the biased as well as unbiased protocols.
