Double fuzzy $\alpha$- $\mathrm{ð}$-continuous multifunctions

Various types of double fuzzy continuity of fuzzy multifunctions are introduced in this paper. These types are double fuzzy upper and lower $\alpha$- $\mathrm{ð}$-continuous, almost $\alpha$- $\mathrm{ð}$-continuous, weakly $\alpha$- $\mathrm{ð}$-continuous and almost weakly $\alpha$- $\mathrm{ð}$-continuous multifunctions. Double fuzzy ideals are playing the main role in defining these types of continuous multifunctions. All implications associated with these types are ensured; also, many examples are introduced to illustrate these implications, and to explain the advantages of these new types of continuity for some previous definitions.