Selecting Methods of the Weighting Factors of Local Criteria

Abstract

The paper considers calculation methods of weight coefficients of local criteria for the person to make decision (PMD). Methods can be used by a decision-maker to form the integrated criteria in the form of the additive, multiplicative, minimax, nonlinear or combined convolution of local criteria, different in degree of importance, as well as to carry out a comparative assessment of the studied alternative options on their basis, range these options, and choose the best option among them. The paper classifies the calculation methods of weight coefficients of criteria and distinguishes three groups, namely: methods based on the paired comparison of criteria, methods based on the analytical interrelation of indicators of criteria preference, and methods based on the formalistic approach. Among the methods based on paired comparison of criteria the following ones are distinguished: a classical method of paired comparison of criteria, and methods of paired comparison of criteria based on the fixed, floating, and exponential floating preferences of criteria. The last two methods of criteria comparison are respectively basic for the practical use of both a method of hierarchy analysis and a multiplicative method of hierarchy analysis. The paper considers in detail calculation methods of weight coefficients of criteria using analytical dependences of interrelation between the indicators of criteria importance based on an arithmetic and geometrical progression. The considered formal methods include the method of consecutive comparison of criteria known as a Cherchmen's method – Akoffa, method and a method of basic criterion. It is shown that when using methods of paired comparison of criteria or methods based on the interrelation of weight coefficients of criteria obeyed to an analytical or geometrical progression with the strictly ranging criteria K K K ......K K 1 2 3 n-1 n , a difference in weight coefficients of the most important and least important criteria is strictly the fixed number of times  which depends on the used method and the number of the considered criteria n . So when using a classical method of paired comparison of criteria and a method based on the use of an arithmetic progression,   n, and when using a geometrical progression,   n , and it sharply increases with growing n. To eliminate noted shortcomings in considered calculation methods of weight coefficients of criteria, methods of the adjusted assessment of criteria preference are developed and offered for a practical use: a method of paired comparison on the basis of the adjusted fixed preference of criteria; a method on the basis of the adjusted decreasing arithmetic progression, and a method on the basis of the adjusted decreasing geometrical progression. The offered methods allow a decision-maker in case of strictly ranging criteria, as basic data, to set both the number of criteria, and the value - coefficient of superiority of the most important criterion in comparison with the least important criterion and have a pronounced practical focus.