Time dependent decision-making; dynamic priorities in the analytic hierarchy process/analytic network process: generalizing from points to functions and from real to complex variables

Because good decisions depend on the conditions of the future, and because conditions vary over time, to make a good decision requires judgments of what is more likely or more preferred over different time periods. There are at least three ways to deal with dynamic decisions. One is to include in the structure itself different factors that indicate change in time such as scenarios and different time periods and then carry out paired comparisons with respect to the time periods using the fundamental scale of the AHP. The second is to do paired comparisons as rates of relative change with respect to time. This is done at different points of time as representatives of intervals to which they belong. These intervals can have different lengths. For each representative point one needs to provide a pairwise judgment about the relative rate of change of one alternative over another and derive mathematical functions for that matrix of comparisons for one of the time periods. The third is to do what I proposed in my first book on the AHP and that is to use functions for the paired comparisons and derive functions from them. It is usually difficult to know what functions to use and what they mean. Ideas and examples are presented towards the development of a theory for dynamic decision making.