  We define weighted geometric mean method of convergence for sequences in
$\mathbb{R}^+$ by using multiplicative calculus and obtain necessary and
sufficient conditions under which convergence of sequences in $\mathbb{R}^+$
follows from convergence of their weighted geometric means. We also obtain
multiplicative analogues of Schmidt type slow oscillation condition and Landau
type two-sided condition for the convergence in particular. Besides, we
introduce the concepts of $^{\oplus}$convergence, $^{\otimes}$convergence,
$(\bar{N},p)-^{\oplus}$convergence, $(\bar{G},p)-^{\otimes}$convergence for
sequences of intuitionistic fuzzy numbers (IFNs) and apply the aforementioned
conditions to achieve convergence in intuitionistic fuzzy number space.
Examples of sequences are also given to illustrate the proposed methods of
convergence.
