1. An apparatus comprising: an analytic network process (ANP) storage memory that stores an ANP weighted supermatrix representing an ANP model; and a processor in communication with the ANP storage memory, the processor being configured to facilitate measuring an instantaneous rate of change of alternative scores throughout the ANP model with respect to a fixed node of the ANP model, to determine a marginal influence of the fixed node, the marginal influence indicates how important the fixed node is to the alternative scores; and maintaining a same proportionality in the stored ANP weighted supermatrix, while inducing a family of ANP models formed by row perturbation changes throughout a same row within the ANP supermatrix by predetermined amounts of an ANP-row-family-parameter, as an importance of the fixed node is changed for the measuring of the instantaneous rate of change of the alternative scores throughout the ANP model.