The modern science of multicriteria decision making and its practical applications: the AHP/ANP approach.

*(English)*Zbl 1291.90110Summary: This paper presents a summary of the discrete mathematical part of my work, the Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP), for measuring tangible and intangible factors, particularly as applied to decision making. The factors of the decision are arranged in hierarchical or network structures and judgments are then made by the decision maker, or by an expert, about the dominant element for each pair with respect to a common property. From simple judgments on two elements at a time with respect to a common property, priority vectors are obtained that are combined throughout the structure to give the best outcome for a decision. The judgments may be inconsistent, and there is a mathematical way to measure inconsistency so that the outlying judgments may be revised by the decision maker in an acceptable way or a decision may be delayed until more consistent information is obtained. In practical applications using either hierarchical or network structures, decisions are often analyzed in separate parts for their benefits, opportunities, costs, and risks, and the results are then combined in an appropriate way into an overall synthesis of those priorities. The mathematics has been generalized in the literature to the Neural Network Process (NNP), the continuous case for modeling how the brain synthesizes signals. There has been a diversity of applications over the past 30 to 40 years, and some of these are reported here. A brief mention is made of other methods of decision making and how AHP/ANP may compare with them.

##### MSC:

90B50 | Management decision making, including multiple objectives |