Review of main classes of order weighted aggregation operators

Abstract

The article discusses the main classes of ordinal weighted aggregation operations, which are widely used due to the presence of a number of numerical characteristics that provide a targeted approach to the organization of the information aggregation procedure in monitoring systems, information and analytical systems, in expert systems and decision support systems, in fuzzy systems and others in which information is processed within the framework of evaluation models. A feature of this type of operators is that before aggregation, the vector evaluation of the object is ordered in non-increasing or non-decreasing order, which allows you to directly take into account the values of the components, and not the importance of information sources, as is done when using weighted averages. Modeling of aggregation operations of this class is reduced to the development of approaches for determining the weight coefficients. By assigning weights in a certain way, it is possible to design an aggregation procedure with certain properties, in particular, a strategy, compensation properties, and a level of uniformity in taking into account the components of a vector assessment. The article discusses various families of operations that implement the technology of ordinal weighted aggregation, their generalizations and modifications, as well as important cases. The connection of these operators with the Sugeno and Choquet integrals is shown, as well as generalized representations based on fuzzy measures. The presented review of foreign publications opens up opportunities for the wide use of aggregation operations from this class in the development of information processing procedures in various application systems, allowing for greater flexibility, multiple alternatives, validity and interpretability.