On an Approach to Forming Two-Level Model “State-Probability of Action” on the Base of Pairwise Comparisons on the and Analytic Hierarchy Process

An approach to modeling non-deterministic and probabilistic decision making on the base of the model “state-probability of choice” is being developed in the paper. A way to forming a specific type of such a model on the base of pairwise comparisons and the Analytic Hierarchy Process is suggested.The regarded case is that an agent is to choose one of two available alternatives, but this choice depends on different criteria. Some systems of states connected to the hierarchy are suggested. The first-level system is the basis one, states of which correspond to probabilities of choosing the two options. Each second-level system corresponds to a separate criterion which may affect the final choice.For forming systems of states, applying pairwise comparisons is suggested. Each state corresponds to a certain grade of preference between alternatives – either in general or by separate criterion; transitive scales for quantifying preference values are used. Within the framework of the model “state-probability of action” that actually corresponds to the following rule of making decisions: “if an alternative has the preference over some other alternative with respect to a separate criteria then it has an overall preference over that alternative”.Decisions made by separate criteria probably shall contradict to each other. The suggested way to getting a combined decision is based on pairwise comparisons among the criteria like the approach common to the two-level Analytic Hierarchy Process. Weighting coefficients reflecting degrees of importance for each criterion are being found as the Perronian, i.e. the normalized eigenvectors of the pairwise comparison matrix though there are some other approaches.An illustrative example involving two alternatives and three criteria is provided. This example illustrates both a situation of equilibrium between alternatives and breaking it by means of changing the matrix of pairwise comparisons among criteria.Some ways of developing the suggested approach as well as some arising problems are discussed. This includes but is not limited to possible using of fuzzy estimations, non-linear transformations of grading scales, different way of treating different types of inconsistencies in PCMs etc.