The construction and application of variable weight vector

The weighted synthesis is an efficient method in multi-criteria decision-making. Synthesis with constant weight and variable weight is analyzed. A new variable weight vector is proposed according to the original idea of variable weight. The constructed variable weight vector can not only express the relative weightiness of each criterion, but also express the configuration of state values vector. It fulfills the axiomatic definition of variable weight vector and additive standard multifactorial function. The result is compared with the results using constant weighting method and other variable weighting method. It is proved that the result of proposed variable weight synthesis is the weighted mean minus the half of weighted variance.