I read a sentence in "The Hindu" which was:
The Narendra Modi government has set much at store by India's improved ranking in terms of the EDB index.
Shouldn't there be "improving" instead of "improved"?
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The at of "set much at store" seems out of place, but that's rather an aside.
"...by India's improved ranking" suggests that they are saying the fact it has improved is important, that they are claiming to be successful based on the fact it has improved. The present perfect of the main verb fits with this.
"...by India's improving ranking", without changing the rest of the sentence, suggests that what is important to them, what they are using to claim success, is the fact that it is currently improving.
If you change word order and tense a little you can get the same gist with a little different emphasis. Change it to "...by improving India's ranking" suggests that they are not just claiming success based on the ranking improving, but claiming that they have directly improved it themselves. It isn't just to their credit, but they are actively responsible for it happening.
Change "has set" to "sets", and you get the slightly altered sense that it is a current focus, that it is being actively promoted in terms of PR. If it's just "has set" it might not be a current priority or focus, or not being actively promoted in the same way.
"Set much at store" is not an idiom I recognise at all: I would say "set great store". I thought that "set much at store" might be characteristic of Indian English, but the GloWbE corpus has no hits for it at all, from India or anywhere else.
The main part of your question: "by improving India's ranking" would seem more natural to me, but "by India's improved ranking" is fine. Both are noun phrases - the one with "improving" is an '-ing' clause, and the other is not a clause, but simply a noun phrase including the pp "improved", used adjectivally.