In order to give a model in terms of sets you have to make clear the objects (potential set elements) and the predicates you are talking about. All my attempts to dechiffere your secret language stop since I can find no clue to understand your NP. As a noninitiated of your secret science I'm satisfied to see that Ross La Haye seems to have the same problem.

Thank you so much @Sangeen Khan, I wish some one confirm your contribution here that it is really the correct way to present in set theory.

I can try to answer, but I think some conceptual clarification needs to be made. For example, if D is a document and S is a set of sensitive terms and NP is a D, that implies that NP is a document. But a document is a different type of an object than a sensitive term, so it doesn't seem to make sense that NP (considered as a set now) and S could be intersecting. At first I then thought that you meant that NP was a term in a document, but later you suggest that an NP could be an Identifier or a Medical Finding also. So you must mean the NP is a set of what I will call tokens that can occur in a document. For example, a word like "patient" could occur in a document, while an identifier such as social security number could occur in a document, while a medical finding in a document could be a simple statement like "Tumor" or a phrase such as "A tumor was found." I can't see how else to make sense of this, so that's the understanding I'm proceeding under. The set IF could be correctly defined, as the set of tokens in a document that are sensitive terms, but then (4) and(5) cannot be correct. This is so because I think you then want I to be the set of all Identifiers in a document and F to be the set of Medical Findings in a document, and clearly then IF I union F (which is how I interpret "IF = I + F".

That's the best I can do at this point. If you have any clarifications etc., I can try to be of further assistance.

In order to give a model in terms of sets you have to make clear the objects (potential set elements) and the predicates you are talking about. All my attempts to dechiffere your secret language stop since I can find no clue to understand your NP. As a noninitiated of your secret science I'm satisfied to see that Ross La Haye seems to have the same problem.

D is textual document , where NPs are set of Noun Phrases in the document

That helps a little... This model still needs substantial clarification. It sounds like you want IF to be the set of sensitive terms in a document D that are also noun phrases. I'm struggling to understand how a sensitive term could NOT be a noun phrase, so there seems to be some redundancy there. Also, it sounds like you want the set I to be the set of identifiers on document D that are also noun phrases. Similarly, it seems like you want F to be the set of all medical findings in document D that are also noun phrases. If so, it should be clear that equations 4 and 5 cannot be correct. If IF is the set of sensitive terms on document D that are also noun phrases, this does not entail that the elements of IF are either identifiers or medical findings. You would need to restrict IF accordingly, in which case I and F may become redundant.