Weight factors in expert estimates

Conclusions

Thus we have proposed a method of processing of experts' estimates that is based on the use of formulas (3)–(4) and requires for the determination of the “weights” a preliminary interrogation of the experts for the purpose of finding the elements of the matrix A={a _ij}. The elements of this matrix must be subjected to the normalization conditions (8) and also to the conditions (7) or to the stronger conditions (12) or (13). After the interrogation it is necessary to solve a system of linear equations (9), (6) that always has a solution c_i, with c_i≥0 for i=1,..., n. If the matrix A is indecomposable [in particular, if the conditions (12) or (13) hold], this solution will be unique and strictly positive, i.e., c_i≥0 for i=1,..., n. During the solution it is possible to drop one of the equations of system (9) (by virtue of the linear dependence of these equations), and regard the remaining n-1 equations of (9) together with Eq. (6) as a linear algebraic system of n equations with n unknowns c_i.

The determination of the c_i for not too large n does not present any major computational difficulties. If the matrix A is decomposable, it is necessary either to introduce additional information for the determination of c_i, or to repeat the interrogation of the experts by using the conditions (12) or (13), or to change the composition of the group of experts.