SELECT *, MATCH (`name`, `author`) AGAINST ('+моя_строка' IN BOOLEAN MODE) as REL
FROM `editions`
WHERE MATCH (`name`, `author`) AGAINST ('+моя_строка' IN BOOLEAN MODE)
ORDER BY REL DESC
LIMIT 0, 10
SELECT `name`,
MATCH(`name`) AGAINST ('+Пупкин' IN BOOLEAN MODE) AS REL1,
MATCH(`name`) AGAINST ('+пупкин' IN BOOLEAN MODE) AS REL2,
MATCH(`name`) AGAINST ('+ПУПКИН' IN BOOLEAN MODE) AS REL3,
MATCH(`name`) AGAINST ('+пУПКИН' IN BOOLEAN MODE) AS REL4
FROM `test`;
+-----------------+--------------------+--------------------+--------------------+--------------------+
| `name` | `REL1` | `REL2` | `REL3` | `REL4` |
+-----------------+--------------------+--------------------+--------------------+--------------------+
| 'Вася Пупкин' | 0.0906190574169159 | 0.0906190574169159 | 0.0906190574169159 | 0.0906190574169159 |
| 'вася пупкин' | 0.0906190574169159 | 0.0906190574169159 | 0.0906190574169159 | 0.0906190574169159 |
| 'Дуся Пупкина' | 0 | 0 | 0 | 0 |
| 'Маша Люськина' | 0 | 0 | 0 | 0 |
+-----------------+--------------------+--------------------+--------------------+--------------------+
SET CHARACTER SET utf8
SET NAMES utf8
За место utf8 можете поставить подходящую вам кодировку.