A concept of multi-valued cognitive maps is introduced in this paper. The
concept expands the fuzzy one. However, all variables and weights are not
linearly ordered in the concept, but are only partially-ordered. Such an ap-
proach allows us to operate in cognitive maps with partially-ordered linguis-
tic variables directly, without vague fuzzication/defuzzication methods.
Hence, we may consider more subtle differences in degrees of experts' uncer-
tainty, than in the fuzzy case. We prove the convergence of such cognitive
maps and give a simple computational example which demonstrates using
such a partially-ordered uncertainty degree scale.