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:

$$\text{sg}(x) = \begin{cases} 1 \text{ if } x > 0 \\ 0 \text{ if } x \leq 0 \end{cases},$$  $$ \overline{\text{sg}}(x) = \begin{cases} 0 \text{ if } x > 0 \\ 1 \text{ if } x \leq 0 \end{cases}.$$

