the question of selecting aggregation operator to develop integral students’ academic progress score

The work concerns the problem of selecting an operator of the grade-based rating aggregation in a variety of subjects to develop the integral score of students’ academic achievements based on expert knowledge. The goal is to justify the choice of an aggregation operator and methods of its construction. The possibilities of aggregation of the grade-based rating are mostly defined by selection of the type of an aggregation operator, which aggregates the individual disciplines ratings using the formalized expert preferences.

The paper discusses application options of different aggregation operators in this field, in particular, the arithmetic mean, the weighted arithmetic mean, the Yager's OWA operator. An analysis of the possible use of different operators has shown that the most appropriate in this field is to use the fuzzy measure Choquet integral because this type of aggregation operator complies with all the considered features of the application area. A number of formal mathematical and non-formalized properties of the Choquet integral correspond to these properties. The paper also considers the choice of an appropriate identification method of the fuzzy measure to use the Choquet integral in development of the integral score of students’ academic achievements. It justifies the choice of the identification method based on variance minimization of the fuzzy measure. Other identification methods have properties that militate against their application in the area under consideration.