The interesting feature of the ordered weighted
average is that it is possible to control the degree of
ANDORness and trade-off between factors within
limits. For example, using order weights of [1 0 0]
yields the minimum operator of fuzzy sets, with full
ANDness and no trade-off. Using order weights of
[0 0 1] yields the maximum operator of fuzzy sets
with full ORness and no trade-off. Using weights of
[0.33 0.33 0.33] yields the traditional averaging
operator of MCE with intermediate ANDness and
ORness, and full trade-off. Trade-off is thus
controlled by the degree of dispersion in the weights
while ANDness or ORness is governed by the
amount of skew. For example, order weights of
[0 1 0] would yield an operator with intermediate
ANDness and ORness, but no trade-off, while the
original example with order weights of [0.5 0.3 0.2]
would yield an operator with substantial trade-off
and a moderate degree of ANDness.