Considering what she says to the Aeons she summons under normal circumstances it's fair to say that she both cares for her Aeons and emphathizes with them.

Quote Originally Posted by Kalm Traveller's Battle Quote List
Yuna Summons Valefor;
Yuna: Please, fight with us!

Yuna Summons Valefor;
Yuna: Please...

Yuna Summons Valefor;
Yuna: Hang in there.

Yuna Summons Valefor;
Yuna: Be strong...

Yuna Summons Ifrit;
Yuna: Will you...help us?

Yuna Summons Ixion;
Yuna: My names Yuna. Pleased to meet you.

Yuna Summons Shiva;
Yuna: Please help us.

Yuna Summons Bahamut;
Yuna: Oh, my...

Yuna Summons Yojimbo;
Yuna: Please, clear us a path!

Yuna Summons Anima;
Yuna: I will share your pain with you.

Yuna Summons the Magus Sisters;
Yuna: We need all your help!
And her bond with Valefor is clearly quite strong and special.