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 approach allows us to operate in cognitive maps with partially-ordered linguistic variables directly, without vague fuzzification/defuzzification methods. Hence, we may consider more subtle differences in degrees of experts' uncertainty, than in the fuzzy case. We prove the convergence of such cognitive maps and give two simple computational examples which demonstrate using such a partially-ordered uncertainty degree scale compared to the fuzzy case.