Big, small and one more - Indian music notation (Sa ri Ga ma) & Western Interval Naming - 2 & 3 note systems

There is a system of Indian music notation where the mapping of notes in Indian notation is exactly like the minor/major system of western interval naming. Then there is a system of naming where there are more than two options for each position in the Indian scale. How does this Carnatic system match with the Western interval notation and why is it useful to have more than two options when it comes to forming scales? Make things easy for you with a clear one to one mapping of the systems and its usefulness.