From what I've observed it's definitely possible to be an INFP with strong Ti, but I have yet to meet an INTP with strong Fi - I would say that if an individual's Fi and Ti are equally strong, the Fi tends to roll over the Ti. However, I've got to know only one INTP into a great depth and she was so devoid of anything remotely resembling Fi that she was actually rather a case for a psychologist, so I don't think my sample is satisfying.
Nevertheless, the INFPs with high Ti I know:
INFP No. 1: My dad. He is a typical "absent-minded professor" and he is very intellectual, intelligent, knowledgeable and versatile and perfectly capable of Ti analysis. I think that according to Keirsey he would more likely belong to the NT temperament, but I suspect it's because he might be Enneagram 5w4. As he's clearly an intellectual I considered INTP for him for a long time, but then I undestood that he actually uses feeling for decisions and the INFP became clear. One can also feel that he's a deeply emotional person under his calm surface, and he doesn't throw his emotions aside. (This might be a stretch but I think that while deciding if one is a Fi-dom or a Ti-dom, the melancholic temperament is one of the indicators of a Fi-dom, and my dad is deeply melancholic.)
INFP No. 2: One of my closest friends. Her parents are an INTP and an INFP, which among other things probably affected her personality . Just like my dad, she's very likely a 5w4. She claims she was an INTP when she was a child and a young teenager - it was because she was bullied throughout all the elementary and middle school, and she built a wall of Ti around her, detaching herself from her emotions almost completely. However, when she came to a welcoming and nurturing environment at high school, her Fi personality (which was, I believe, her "default" personality from the start) started to get stronger again. As she is now, she is more capable of Ti analysis than most INFPs I know and she usually uses it when she's solving problems, but she always uses feeling for decisions, she's very self-analytical in a Fi way and she doesn't detach herself from her emotions at all.
INFP No. 3: Another friend of mine. At first she really reminded me of the INTP friend I mentioned at the beginning (the same "vibe" and body language, she loves Math...), but getting to know her better I found out that she's actually much more similar to my dad (they even have the exact same eyes...

). She tested as an ISFP, which is a nonsense regarding the S part but it confirms my F suspicion. She's very emotionally developed, but as she's deeply introverted she doesn't show it to just anyone; she's also deeply melancholic to the point of being depressive. Just like in the previous case, the Ti wall might have been something she attempted to build when she was bullied as a child, but I suppose that instead of truly getting detached as the friend above she became depressive.
All of the INFPs above seem very reserved, even sort of "aloof", at least on the surface. They really aren't the type that can be confused with ENFPs
VagrantFarce said:
I feel that my emotions are trustworthy. I use them to fine-tune my value system...I do this by waiting until I have a feeling, then checking it against what I believe I should feel. If the two are not consistent, I re-analyze why I believe I should feel otherwise. If it does not make sense or is inconsistent with the rest of my values, particularly the foundations of the value system, I alter the value until it is properly aligned. If the reason makes sense and retains an internal consistency with the rest of the value system, I figure out why I am feeling inappropriately. When I discover the core of the error, I can work to change the spiritual flaw in order to change the emotion. I continue focusing on appropriate attitudes until the actual emotion aligns with the value system again.
I agree with sofmarhof that this is really not a good description of a healthy Fi. Attempting to "change their emotions" is like buying a ticket for a depression tour for a Fi-dom. (Talking from my own experience -_-;;; ) You should understand that "values" and "feelings" aren't separate entities for Fi-doms. They are actually pretty identical. The word "value" is used very often when talking about Fi, but I'd say that simply "feeling" is better - how Fi-doms feel about things
constitute their values, not the other way round. Changing their feelings = changing their values. But as Fi-doms tend to be consistent in their feelings, this doesn't occur any often. Maybe I should mention that before I learnt about MBTI, I didn't really have the word "value" any high in my vocabulary - I rather thought that I always wanted to act according to my
conscience. I always wanted to have clear conscience, and as conscience is a deeply feeling thing and Fi-doms are deeply feeling people, they always want to act on what their feeling/conscience tells them, at least the healthy ones.