Why can an increase in inflation rate, increase interest rates?
In a free currency exchanges market, the central bank defined goal, in the general case, is to maintain price stability and inflation rate restrained, that is to keep inflation positive but at a low rate, 
In order to encourage economic activity

Inflation can be manipulated by the amount of money - more money in the system, the lower its value, and higher prices respectively, and vice-versa.

The amount of money is manipulated by the central using interest rates: higher interest rates encourages deposits in banks and discourages taking loans, both actions leading to less money in the system, and vice-versa