Normalises the direct-influence matrix X by the larger of its greatest
row sum and its greatest column sum (the standard DEMATEL normalisation,
which keeps the Neumann series N + N^2 + N^3 + ... convergent), then
solves the total-relation matrix T = N(I - N)^-1 in closed form rather
than by truncating the series. D is each criterion's row sum of T
(how much it influences the others, direct and indirect combined) and R
its column sum (how much it is influenced). Prominence D + R is overall
involvement in the system, while relation D - R is net direction,
positive for a net cause and negative or zero for a net effect. The
threshold is the arithmetic mean of every entry of T: relations at or
above it are considered significant enough to draw in an influence
diagram.
Value
A list with normalised (N), total_relation (T), D, R,
prominence (D + R), relation (D - R), threshold (mean of T), and
role (a character vector, "cause" where relation > 0, else
"effect").
Details
solve() fails outright if I - N is exactly singular, which does not
arise for a matrix normalised this way in ordinary use. No fallback series
truncation is implemented, unlike the harvested source, because a singular
I - N here would signal a malformed matrix rather than a case to work
around silently.