We have investigated the solvability criteria of systems of partial fuzzy relational equations that employ the type of missing undefined values. The Dragonfly algebra in partial fuzzy theory is chosen for this investigation. It was shown in the previous work that a partial fuzzy relation ensuring the solvability of a given system exists. Such an existence requires the essential restriction of the underlying algebra having no zero divisors. In this talk, we show that this restriction can be relaxed and its substitution by another condition regarding the setting of the consequents may lead to the formation of the solvability criteria of the systems as well.  In particular, new models are derived to check whether a given system is solvable. And in the case of unsolvable systems, the optimal approximate solutions are approached.