Aggregation Operators Visualization Using 3d Cognitive Graphics

To solve social dilemmas in multi-agent reinforcement learning it is necessary to formalize the corresponding reward functions in the form of aggregation operators. Such formalization encounters difficulties associated with the lack of an intuitive vision of the aggregation process among many practitioners. Various visualization methods have been proposed to overcome these difficulties. The proposed methods have disadvantages that prevent their wide application. The method proposed in the article differs from the existing ones by the use of a three-dimensional cognitive image which corresponds to a physical object with a well-developed intuitive spatial and physical perception. This method is based on the use of 3D cognitive graphics. The properties of the aggregation operator are directly related to the properties of the physical object which has a well-developed intuitive representation. An absolutely solid plane fixed on the support line by springs acts as such an object. The result of aggregation corresponds to the angle of deviation of the plane from the horizon. By placing loads that meet the criteria and indices of their interaction on this plane it is possible to simulate the corresponding operator including by means of virtual reality. A preliminary asessment of the formal properties of the proposed method was carried out in comparison with existing visualization methods using the example of the Choquet integral of the 2nd order. Based on the results of this assessment conclusions were drawn about the advantages of a three-dimensional balance model over existing visualization methods and the feasibility of continuing work in this direction.