The concept of a fuzzy number is generalized to the case of a finite carrier
set of partially ordered elements, more precisely, a lattice, when a membership
function also takes values in a partially ordered set (a lattice). Zadeh's
extension principle for determining the degree of membership of a function of
fuzzy numbers is corrected for this generalization. An analogue of the concept
of mean value is also suggested. The use of partially ordered values in
cognitive maps with comparison of expert assessments is considered.