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The notions of doubt Atanassov's intuitionistic fuzzy sub-implicative ideals and doubt Atanassov's intuitionistic fuzzy -ideals of -algebras are introduced. We show that an Atanassov's intuitionistic fuzzy subset of -algebras is an Atanassov's intuitionistic fuzzy sub-implicative ideal if and only if the complement of this Atanassov's intuitionistic fuzzy subset is a doubt Atanassov's intuitionistic fuzzy sub-implicative-ideal. We prove that any doubt Atanassov's intuitionistic fuzzy -ideal is always a doubt Atanassov's intuitionistic fuzzy sub-implicative ideal. Moreover, some other properties about doubt Atanassov's intuitionistic fuzzy sub-implicative ideals and doubt Atanassov's intuitionistic fuzzy -ideals of -algebras are given.