In Part I of this series of papers, a general approach for ordering fuzzy sets with respect to fuzzy orderings was presented. Part I also highlighted three limitations of this approach. The present paper addresses these lim- itations and proposes solutions for overcoming them. We rst consider a fuzzi cation of the ordering relation, then ways to compare fuzzy sets with di erent heights, and nally we introduce how to re ne the ordering relation by lexicographic hybridization with a di erent ordering method