Modification of 3d Balance Model for Bi-Polar Aggregation Operators Visualisation

Abstract

Aggregation operators provide an overall assessment of an object or a process which is described with several quantitative criteria. An aggregation operator is constructed on the basis of expert knowledge and can take into account the types of criteria interdependencies, the partial order of criteria importance, the desired overall scores for distinct sets of the criteria values provided by an expert. However, in practice the aggregation operator construction process and its result appear to be difficult to perceive and understand by an expert. There is a balance model method for visualizing the aggregation operators in order to simplify evaluation of their conformity to expert preferences. This method allows visualizing an aggregation operator in an intuitively clear way as a mechanical system of weights on a rod. One limitation of the balance model method is that the weights can overlap each other on a rod which makes it difficult to perceive the aggregation result by the expert. A three-dimensional balance model overcomes this limitation but it can visualize unipolar aggregation operators only. This paper extends the existing three-dimensional balance model for bipolar aggregation operators. The extended model allows visualizing the aggregation operators of the criteria defined on bipolar scales of three different types: symmetric bipolar scales, homogeneous bivariate bipolar scales, heterogeneous bipolar scales. The model plane rotation angle constraints were updated to visualize the bipolar aggregation operators. The implementation of the extended model in the Unity game engine is presented. The application of the extended model is illustrated in a case study of the energy storage technology selection considering a trade-off between its performance and its environmental impact.