In this paper, we introduce and study a new type of convergence which is namely (λ, µ, ζ)-Zweier convergence and (λ, µ, ζ)-Zweier ideal convergence of triple sequences x = (xijk) in intuitionistic fuzzy normed spaces (IFNS), where λ = (λn), µ = (µm) and ζ = (ζp) are three non-decreasing sequences of positive real numbers such that each tend to infinity. Besides, we define and study (λ, µ, ζ)-Zweier Cauchy and (λ, µ, ζ)- Zweier ideal Cauchy sequences on the said space and establish some relations among them.problem.