Взвешенное агрегирование ранжированных объектов по произвольной совокупности других объектов

Предложен универсальный метод распределения ранжированных объектов по меньшему числу других объектов, который можно использовать при проведении экономических, педагогических и других исследовани

The Weighted Aggregation of Ranked Objects by the Arbitrary Totality of Other Objects

The task of distribution of the ranked objects by the smaller number of other objects is set. The first objects are named objects of the first kind, the second objects are the objects of the second kind. The rating of the totality of objects of the first kind, included on the attribute of belonging in the object of the second kind, is suggested to be calculated through the procedure of the weighted aggregation which represents a product of number of the above mentioned objects of the first kind and the average weight coefficient calculated through the average rank (rating) of the totality of the objects of the first kind. An example of such a task is the distribution of ranked universities by the world countries according to one of the global world ratings. The task is extended to the calculation of the integral rank (rating) for an arbitrary number of rankings of different objects of the first kind, distributed on the given number of objects of the second kind

Моделирование взвешенного агрегирования ранжированных объектов по произвольной совокупности других объектов на примере ученых-экономистов и экономических журналов

Алгоритмизирован и апробирован метод взвешенного агрегирования ранжированных объектов, которые названы объектами первого рода, по некоторой меньшей совокупности других объектов, которые названы объектами второго рода. Метод апробирован на примере ранжировок ученых экономистов и научных экономических журналов (объекты первого рода), распределенных по регионам России (объекты второго рода). Разработан универсальный алгоритм и программа на языке C++ для решения такого рода зада

Information-Theoretic-Entropy Based Weight Aggregation Method in Multiple-Attribute Group Decision-Making

Weight aggregation is the key process to solve a multiple-attribute group decision-making (MAGDM) problem. This paper is trying to propose a possible approach to objectivize subjective information and to aggregate information from attribute values themselves and decision-makers’ judgment. An MAGDM problem without information about decision-makers’ and attributes’ weight is considered. In order to define decision-makers’ subjective preference, their utility function is introduced. The attributes value matrix is converted into a subjective attributes value matrix based on their subjective judgment on attribute values. By utilizing the entropy weighting technique, decision-maker’s subjective weight on attributes and objective weight on attributes are determined individually based on the subjective attributes value matrix and attributes value matrix. Based on the principle of minimum cross-entropy, all decision-makers’ subjective weights are integrated into a single weight vector that is closest to all decision-makers’ judgment without any extra information added. Then, by applying the principle of minimum cross-entropy again, a weight aggregation method is proposed to combine the subjective and objective weight of attributes. Finally, an MAGDM example of project choosing is presented to illustrate the procedure of the proposed method