Te: Cuddy is an organizer who likes to be in charge, thus the never ending power struggle between herself and House. She prioritizes her time and is a bit of a workaholic, though certainly not to the point of House. That said, she’s also pro at delegating. Before committing to any medicinal procedure, she asks House for evidence. Her primary focus is on getting things done and shows care by doing things for people. She keeps House at the hospital primarily for his usefulness (that’s the only reason she doesn’t fire him). She’s also fairly unaffected by House’s sexist remarks.
Si: Cuddy likes to run things according to previously established methods. She’s aware of both change and the lack of change over time. When her carefully crafted plans don’t work out how she expects, she reacts emotionally. She always explains her reasoning for everything and doesn’t appreciate that House doesn’t explain himself. Cuddy likes life to be structured and routine.
Ne: Cuddy is reluctant to trust instinct, and when she does, it usually doesn’t lead her to safety. She can be creative in her pranks against House, and learns to find humour in his often childish behavior. She’s interested in new ideas, but needs them explained before she’ll except them.
Fi: Under stress, Cuddy’s emotions can get the better of her. At first, she has trouble sacrificing her workaholic life for her the child she thought she always wanted. She also has difficulty emotionally connecting to her child at first, though she eventually breaks the barrier. Her sense of morality is more black and white than House’s and she has difficulty finding morality in his ability to look at everyone purely objectively.
Cuddy is frequently typed as an ENTJ and an ESFJ. However, Cuddy has absolutely no Ni (let alone Ni in an upper function). She also doesn’t have any Fe (especially not in an upper function.
A lot of the House characters who are T types often get typed as Fs simply because they’re emotional in contrast to House.