Implications over intuitionistic fuzzy sets

For the various definitions of implication of over intuitionistic fuzzy sets, the functions sg(x) and $\overline{sg}$(x) have been used:

$$ \text{sg}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x > 0 \\ 0 & \text{if } x \leq 0 \end{array},$$  $$ \overline{\text{sg}}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x < 0 \\ 0 & \text{if } x \geq 0 \end{array}.$$