@mike,
Thank you for doing some research.
Could you point me to the code for a+=b
and for ++a and for a++?
Then I'll try to fix that.

@John
maybe I do not understand correctly.

Example: I have a class pn (polymorphic numbers)
whatever it is, it comprises double numbers.

I can write
   a  = pn(4);
   a += pn(3);
and then a is 7 (as pn-number)

I just overwrote plus(a,b)
which overwrites not only + as in matlab, but also +=.
So far so good.
It is, as you say, syntactic sugar,
i.e. a+=b is short for a = a + b.
Thus I think it is mandatory,
that plus overwrites not only + but also +=.

Now i think, that ++a is just short for a+=1.
Consequently, i think plus shall affect also ++a operator.
The result should be something like
a+=1, where 1 must be the one-element in the class.
I think ++a should be short for a+=pn(1),
if a has type pn,
i.e. it should be short for a = plus(a,pn(1)).
To use ++, pn(1) must be defined of course.

Yes, i would like to do the implementation.
The usefulness can also be explained:

in matlab, oo allows to overwrite most operations.
Among those also +, -, *, /.
The result is, that these can be used with objects also.

This works as follows:
To these operation are tied functions
plus, minus, mtimes, mrdivide.
Overwriting these functions
results in overwriting the according operations.
So a+b is just a shortcut for plus(a, b).

Unlike Matlab, Octave provides besides the assignment operation =
also the shortcuts +=, -=, *= and /=.
As you know, a += b is just a shortcut for a = a + b
and this in turn for a = plus(a,b).
So to use += in the oo context, i.e. with objects,
one can write a += b only, if this has the meaning of
a = plus(a,b).

Also unlike Matlab, Octave has operator ++,
both prefix and postfix.
++a is just a shortcut for a += 1.
So ++a means nothing but a = plus(a, 1).

But what is 1 in the oo-context? i suggest just cln(1),
where cln is the name of the class and thus of the constructor.
If this is not defined, then adding 1 does not make sense
and I think adding in general does not.

So So ++a means nothing but a = plus(a, cln(1)).

Think of using this in the context of a polynomial
or of defining another kind of arithmetics in octave
like rational arithmetics,
interval arithmetics,
continued fractions or something else
(which is actually what i do).

I see: feature requests are ignored so please close this for me.

In contrast to matlab,
octave provides operators += and ++ (the latter prefix and postfix).
Both are based on the operator + which is in turn defined by the function plus(x,y).

in oo-programming, one can overwrite operators like +
by just overwriting the associated function like plus.
Whereas this automatically overwrites +=, it does not overwrite ++.
I think this is inconsistent.