By Peterson in his book were proposed intermediate quantifiers which lie between classical quantifiers. Their mathematical definition was introduced by Novák and we call these quantifiers as fuzzy intermediate quantifiers.
From relations between fuzzy intermediate quantifiers (contrary, contradictory, sub-contrary, sub-altern, superaltern) can be created graded cube of opposition which was introduced by Murinová.
Similarly, as we can create logical syllogisms from classical quantifiers, we can create several forms of fuzzy syllogisms from fuzzy intermediate quantifiers. The main goal of the presentation will be to introduce new forms of strongly valid fuzzy syllogisms that related to the second face and other faces of graded cube of opposition.