One might go about providing a partial ordering of your values for (T,F,I).  In an epistemic context, one might value knowing some truth a bit more than knowing something as false, yet both are better than the uncertainty of not knowing.  On this basis, we might want to make the following assertions :

  (1,0,0) > (0,1,0), 

  (1,0,0) > (1,0,1), and

  (0,1,0) > (0,1,1).

One might go even further to have a general bias against uncertainty, with the tenet,

  (0,0,0) > (0,0,1).

Take a moment to contrast this ordering of values with one if we are reasoning about theories of agency or action.  In that context, determinism might be considered negatively, since uncertainty or indeterminism equates to freedom of action.  In such contexts, one might be tempted to assert,

  (0,0,0) < (0,0,1)

I look forward to hearing more about the context in which you intend to reason . . . 

(1, 1, 1) "in real life" corresponds to a logical paradox of the kind

"This sentence is false"

regarding (0, 0, 0), i would associate it to a statement completely irrelevant in the given context : not true, not false, not dubious, just irrelevant

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(T, F, I) : (1,0,0) (1,0,1), (1,1,0), (1,1,1), (0,0,0), (0,1,1), (0,1,0)

I think this is the order from best to worse.

But, a lot of confusion is there....

Is there any scenario where  we can use  (T, F, I) : (1,0,1), (1,1,0), (1,1,1), (0,0,0), (0,1,1) ?

In the above series  (1,0,0) is best and(0,1,0) is the worst case definitely. But others are having a lot of confusion.

So, it can be seen that ,

Where ever we are getting more than one 1's, the confusion of arises. To be specific,  If there is one '1' with either one or both other measures are having values greater than zero, than the situation falls into paradoxical zone.

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you might be interested in Smarandache's answer :

http://fs.gallup.unm.edu/NLasTheoryOfEverything.pdf

Beyond this ordering proposal, the main "take home comment" is that no ordering will fit all needs as the proper ordering will in particular depend on how you value indecision with respect to falsity, and this valuation is domain-dependent

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true (1,0,0) > weak true (1,1,0) > contradiction (1,0,1) > {ignorance (0,0,0), saturation (1,1,1)} > neutrality (0,1,0) > weak false (0,1,1) > false (0,0,1).

ignorance (0,0,0) and saturation (1,1,1) are not comparable.