Which type of analogy involves words that have

antonym
antonym

synonym
synonym

item/category
item/category

degreee opposite meanings?

The type of analogy that involves words with antonym-antonym and synonym-synonym pairs is called a Word Relationship analogy.

For example:
Antonym-Antonym:
Hot : Cold :: Tall : Short

Synonym-Synonym:
Happy : Joyful :: Bright : Radiant

Degree opposite meanings analogy is called an Antonym analogy.
For example:
Weak : Strong :: Dull : Bright