Theory and application of Analytic hierarchy process (AHP) in multi criteria decision making under conditions of risk and uncertainty (individual and group context)

Analytic Hierarchy Process (AHP) is a multi criteria method applicable to structured problems in both individual and group decision-making context. It is in a focus of a scientific community for three decades because it respects important psychological characteristics of the decision maker (DM) and manipulates with ease decision elements given in incommensurate units. The results of a method are intuitively logical and transparent to the DM. AHP is increasingly used to treat risky and conflict decision-making scenarios and situations with uncertain and insufficient information. The subject of research is all known matrix and optimization methods for deriving the weights of decision elements, and theory of their combining within the unique AHP paradigm. The hypothesis is that it is possible to reduce differences between weights’ ratios and judgments, and to propose synthesis procedures that minimize violation of transitive rules as an indicator of the DM’s inconsistency. AHP will be assessed and verified through application for cases of erroneous judgments and different impacts of DMs. Inverse prioritization problem, defined as recognition of semantic judgments given by the DM based on known relative weights of compared elements, will also be assessed; to our best knowledge, this problem has not been treated jet, although it can be extremely important in participative decision-making models in agriculture, water management and forestry.