Analytic network process
The analytic network process (ANP) is a more general form of the analytic hierarchy process (AHP) used in multi-criteria decision analysis. AHP structures a decision problem into a hierarchy with a goal, decision criteria, and alternatives, while the ANP structures it as a network. Both then use a system of pairwise comparisons to measure the weights of the components of the structure, and finally to rank the alternatives in the decision. Hierarchy vs. network. In the AHP, each element in the hierarchy is considered to be independent of all the others—the decision criteria are considered  to be independent of one another, and the alternatives are considered to be independent of the decision criteria and of each other. But in many real-world cases, there is interdependence among the items and the alternatives. ANP does not require independence among elements, so it can be used as an effective tool in these cases. To illustrate this, consider a simple decision about buying an automobile. The decision maker may want to decide among several moderately-priced full-size sedans. He might choose to base his decision on only three factors: purchase price, safety, and comfort. Both the AHP  and ANP would provide useful frameworks to use in making his decision. The AHP would assume that purchase price, safety, and comfort are independent of one another, and would evaluate each of the sedans independently on those criteria. The ANP would allow consideration of the interdependence of price, safety, and comfort. If one could get more safety or comfort by paying more for the automobile (or less by paying less), the ANP could take that into account. Similarly, the ANP could allow the decision criteria to be affected by the traits of the cars under consideration. If, for example, all  the cars are very, very safe, the importance of safety as a decision criterion could appropriately be reduced. Literature and community. Academic articles about ANP appear in journals dealing with the decision sciences, and several books have been written on the subject. There are numerous practical applications of ANP, many of them involving complex decisions about benefits (B), opportunities (O), costs (C) and risks (R). Studying these applications can be very useful in understanding the complexities of the ANP. The literature contains hundreds of elaborately worked out examples of the process, developed by executives, managers, engineers, MBA and Ph.D. students  and others from many countries. About a hundred such uses are illustrated and discussed in The Encyclicon, a dictionary of decisions with dependence and feedback. Academics and practitioners meet biennially at the International Symposium on the Analytic Hierarchy Process (ISAHP), which, despite its name, devotes considerable attention to the ANP. Outline of the steps. Understanding of the ANP is best achieved by using ANP software to work with previously-completed decisions. One of the field's standard texts gives this outline of the steps involved: