Compute triangular norm (t-norm) from the whole argument, or element-wise.
Usage
minnorm(...)
luknorm(...)
prodnorm(...)
## parallel (element-wise) versions of t-norms:
pminnorm(...)
pluknorm(...)
pprodnorm(...)
Arguments
...
Numeric vectors of values to compute t-norm from.
Value
minnorm, luknorm, and prodnorm return a single value that is the result of
the appropriate t-norm on all values of all arguments.
pminnorm, pluknorm, and pprodnorm return a vector of results after applying
the t-norm on argument in an element-wise (or parallel) way.
Details
minnorm, luknorm, and prodnorm compute the minimum, Lukasiewicz, and
product t-norm from all values in the arguments. If the arguments are vectors they are combined
together firstly so that a single value is returned.
pminnorm, pluknorm, and pprodnorm compute the minimum, Lukasiewicz, and
product t-norms as well but in a element-wise manner. I.e. the first values of the arguments are
combined, then the second values (with recycling the vectors if they do not have the same size)
so that the result is a vector of values.
Let $a$, $b$ be values from the interval $[0, 1]$. Then the t-norms are defined
as follows: