The concept of a fuzzy number is expanded to the case of a finite carrier set of partially ordered elements; the set is a lattice, and the membership function of such an expansion also takes values in a lattice. Zadeh's extension principle for determining the degree of membership of a function of fuzzy numbers is changed for this expansion. An analogue of the concept of a mean value is also suggested. The use of partially ordered values in cognitive maps with multiple expert assessments is considered.