We introduce a class of fuzzy numbers with the explicit form of the membership function written by G-PDMF, which stands for Gaussian-Probability Density Membership Function. Each fuzzy number, denoted by $\tilde{x}$, can be uniquely identified by a vector $[x; d^-, d^+, \mu^-,\mu^+]$. Here $x$ represents the major part of the fuzzy number, $d^-$ (resp. $d^-$) is the length of the compact support on the left side (resp. right side), $\mu^-$ and $\mu^+$ represents the shape of the left side and right side, respectively.  We define five operators: addition, subtraction, multiplication, scalar multiplication and division. We show that, under our definitions, the G-PDMF space has a nice algebraic structure and one can establish a new way to enter the world of fuzzy equations.