Using a variable as an operator

No, that syntax isn't available. The best you could do would be an eval(), which would not be recommended, especially if the $e came from user input (ie, a form), or a switch statement with each operator as a case

switch($e)
{
    case "||":
        if($a>$b || $c>$d)
            echo 'yes';
    break;
}

It's not possible, but you could use a function instead. Of course, you'd have to define them yourself. This would be fairly simple using PHP 5.3's closures:

$or = function($x, $y)
{
    return $x || $y;
};

if ($or($a > $b, $c > $d))
{
    echo 'yes';
};

Here's a function to add some vague and undefined "additional criteria" for narrowing down a list of products.

/**
 * Criteria checker
 *
 * @param string $value1 - the value to be compared
 * @param string $operator - the operator
 * @param string $value2 - the value to test against
 * @return boolean - criteria met/not met
 */
protected function criteriaMet($value1, $operator, $value2)
{
    switch ($operator) {
        case '<':
            return $value1 < $value2;
        case '<=':
            return $value1 <= $value2;
        case '>':
            return $value1 > $value2;
        case '>=':
            return $value1 >= $value2;
        case '==':
            return $value1 == $value2;
        case '!=':
            return $value1 != $value2;
        default:
            return false;
    }
}

Here's how I used it:

// Decode the criteria
$criteria = json_decode($addl_criteria);

// Check input against criteria
foreach ($criteria as $item) {
    // Criteria fails
    if (!criteriaMet($input[$item->key)], $item->operator, $item->value)) {
        return false;
    }
}