Ideal point method modernization

Аuthors

Terent'ev V. B.^*, Terent'eva A. V.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: tvb-21@yandex.ru
**e-mail: tav-21@mail.ru

Abstract

When solving the problem of objects' multicriterion selection and seriation, modern mathematical modeling technologies can employ various methods, including simple aggregate weighing (SAW) and “ideal point” (TOPSIS) methods.

When comparing alternative objects of research by their effectiveness, the necessity occurs to account for not only positive or negative indicators, but estimate the objects by the degree of proximity to a specified value, i. e. to the criterion. It should be noted, that the criterion value could lay in the middle of the range of the considered indicators. Besides, the object's effectiveness, as a rule, has non-linear dependency from the change of the indicator value. Inasmuch as the existing algorithms of SAW and TOPSIS methods do not allow perform such task, a certain modernization of the TOPSIS method is required. This method is top-of-the-line with respect to the ranking procedure.

In general, when the case in hand is the indicator's degree of proximity to the specified value, the attainability function is used. In multicriterion analysis, it is called the utility function. It allows realize transformation of the initial “decision matrix” system into normalized matrix, with account for the proximity to the specified values of the criteria. This operation is close in its meaning to linear (nonlinear) normalization. It is performed in the SAW method (determines the degree of the maximum or minimum attaining), and replaces the rationing using the TOPSIS method.

Earlier, the TOPSIS method could be applied, when a monotonic-increasing utility function existed for each criterion. In other cases, one had to apply the more simplified SAW method.

The presented TOPSIS method modernization gives, firstly, practically a comprehensive agreement of the computational results with the above said methods for positive indicators, and, secondly, a slight difference with the SAW method while using positive and negative indicators, when the unknown function of the relationship between efficiency and indicators is non-linear (linear and non-linear normalizing).

Thus, the proposed modernized version of TOPSIS method allows extend the scope of this method in the case of the specified criteria values (positive and negative), located within or outside the range of the indicators variation.

Keywords:

object efficiency, ranking procedure, probability density, criteria, attainability function

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