I don't know how your database is built or how you get the data after sending the form.
I don't know how you know about coding, but try something like this:
<ul class="nav nav-tabs">
<li class="active" id="chienTab" <?php if ($this->item->chien == 0) { echo style="display:none"; } ?>>
<a href="#chien" data-toggle="tab">
<?php echo(JText::_('TAB_CHIEN')); ?>
</a>
</li>
<li class="" id="chatTab" <?php if ($this->item->chat == 0) { echo style="display:none"; } ?>>
<a href="#chat" data-toggle="tab">
<?php echo(JText::_('TAB_CHAT')); ?>
</a>
</li>
<li class="active" id="poissonTab" <?php if ($this->item->poisson == 0) { echo style="display:none"; } ?>>
<a href="#poisson" data-toggle="tab">
<?php echo(JText::_('TAB_POISSON')); ?>
</a>
</li>
</ul>
after modifications according to your component, it should work
If you can not do it, send me the component and I'll make the change in it
Nicolas