Progressive Matrix question - straight, round, zigzag lines and arrows

Question

I got the answer correct. It was mostly an intuitive guess though. The horizontal wave appears once on each row and the vertical line (y-axis looking thing) with no arrow head also appears once on each row. Which leaves one possible answer from my standpoint. What's your reasoning on this?

Source: https://www.ijcai.org/Proceedings/15/Papers/132.pdf

Answer 1

The answer is:

E.

Because:

The horizontal elements in each row form the set [wave,curve,arrow]. and the vertical element form the set [line,arrow,wave].

They tell you this in the pdf:

2.3:Example (page 3)
"We illustrate our formulation using the example RPM in Figure 1. In terms of problem representation, the example RPM displays two ternary relations, the union on the shape of the vertical (respectively horizontal) elements across each row yields the constant set {arrow,wave,curve} (respectively {line,arrow,wave})"

Answer 2

The answer is

the frequency of each symbols in each row

For instance;

there are two wave line, one is horizontal, other one is vertical, etc...

so you expect the same thing

for the last row, and see which symbols and shapes are missing for the last part.

and viola!

the answer becomes;

E

but

we ignore the shapes which are used only once in each row for our decision in this methodology.

Here are shapes for the first two rows which are recurring;

1. 2. 3. 4. 5. 6.

Here are shapes only happens once in a row:

1. 2.

so for the last row;

and are not repeating, so it has to have these two at least, which indicates $E$.