RE: Boolean valued and relational operations
Arnold may have a point, but irrespective of whether we can select
reasonable unique operations, we should probably treat this the same way
as several folks proposed to treat modal intervals and other stuff:
* to pass the standard easier, let us keep the contents to the necessary
minimum (so let us not include modal intervals and fuzzy at this stage)
but
* let us design the standard in such away that future extensions are
possible.
Chenyi, if there are any additional operations that would help in
implementing fuzzy stuff we can discuss that. From my reading, I do not
see any such need but I may be missing something here.
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Chenyi
Hu
Sent: Tuesday, November 18, 2008 8:06 AM
To: Sylvain Pion; Arnold Neumaier
Cc: stds-1788@xxxxxxxxxxxxxxxxx
Subject: Boolean valued and relational operations
In addition to Boolean valued operations, interval relational operations
<, <=, >, >= are useful in decision making. Since intervals are not
comparable in binary logic, we have developed fuzzy order relations for
intervals to deal with interval valued matrix game and interval weighted
graph. I would suggest the committee to consider include fuzzy order
relational operations.
References can be found in our recent book "Knowledge Processing with
Interval and Soft Computing" (Springer, 2008) pp. 149-152 and 168-172.
Chenyi
> - 4.2 (Boolean valued operations) : comparisons should also mention ==
> and !=.
> Moreover, you mention 3-valued return value, but it may be desirable
to
> have
> a 4-valued return value. This is what we did for the C++ proposal
where
> interval comparisons return std::bool_set which stands for "true",
"false"
> "true or false" and "neither true nor false". In practice, the last
value
> is returned when you compare against the empty interval. You get
more
> information out of the comparison (the empty interval propagates :)
),
> and there is no significant added cost.