The operation of increase-key or decrease-key is for updating a key within a max- or min-heap, respectively.
Why doesn't a max-heap have a decrease-key operation, and a min-heap a increase-key operation?
This have been discussed before here. To sum up, these operations can easily be implemented in
O(log(n)) but usually aren't provided because they have little interest from a pure algorithmic perspective.
On the contrary, decrease-key on a min heap have an existing
O(1) implementation in a Fibonacci Heap and has an application, for example in a Dijkstra path-finding.