Visualizing the multidimensional Pareto frontier using 3D cognitive graphics

In many multicriteria decision-making problems, it is assumed that the decision maker is presented with a Pareto frontier in one form or another for analysis and decision making. To facilitate the perception of this frontier by a person, various approaches to its visualization are used. These approaches have limitations associated with the insufficient use of human capabilities. Therefore, the problem of expanding the existing approaches to visualizing the Pareto frontier is relevant. One of the directions for solving this problem is the use of three-dimensional cognitive graphics. The purpose of the work is to expand human-machine interaction in the field of decision making using the Pareto frontier. This expansion consists in developing an approach to visualizing the Pareto frontier based on the use of three-dimensional cognitive graphics. The proposed approach will provide the decision maker with the opportunity to see an intuitively clear picture of the effect of changes in the value of one criterion on the values of other criteria when moving along the Pareto frontier. Thanks to this vision, the decision maker will be able to interactively exclude from consideration combinations of criterion values that are undesirable from his point of view, leaving as a result the selected values that are on the Pareto frontier. A comparative assessment of the formal properties of the cognitive image used in the proposed approach to visualizing the Pareto frontier was carried out, which showed the advantages of the approach compared to existing visualizations of the Pareto frontier. The results of the study can be used in the design of decision support systems. In many multicriteria decision-making problems, it is assumed that the decision maker is presented with a Pareto frontier in one form or another for analysis and decision making. To facilitate the perception of this frontier by a person, approaches to visualizing the Pareto frontier are developed. These approaches have limitations associated with the insufficient use of human capabilities. The article proposes an approach to visualizing the Pareto frontier based on the use of an intuitive three-dimensional cognitive image. This image is represented by a virtual dashboard, the controls on which correspond to the criteria. The user can see how exactly a change in the value of one criterion affects the values of other criteria when moving along the Pareto frontier. Thanks to this vision, he will be able to interactively exclude from consideration combinations of criterion values ​​that are undesirable from his point of view, leaving as a result the selected values located on the Pareto frontier. An assessment of the formal properties of the proposed visualization showed its advantages over existing visualizations of the Pareto frontier and the prospects for continuing work in this direction.