Open AccessAn approach to calculate the weighting factors of the local criteria is considered for a decision maker (DM). As an additive, multiplicative, mini-max, non-linear, or combined convolution, these criteria are part of the integral criteria used for comparative assessment of the alternatives, their ranking, and choosing the best option. The approach is based on the method of custom arithmetic progression and on the principles of customizable assessment of criteria preference and arithmetic progression of interrelations between weight indicators of criteria.
An assessment of criteria preference uses the classical method for pairwise comparison of criteria and their ranking, taking into consideration the calculated values of weight levels of these criteria. Thus, the paper discusses options both for full and for partial order of criteria priorities, whereby the same weight level of criteria is possible. In ranking all the criteria are divided into the weight groups.
In the case of complete ranking each group includes only one criterion, in the case of a partial ranking the group includes the same criteria in terms of weight. In the case of customizable assessment of criteria preference a DM specifies a key figure to differentiate weighting factors of the boundary groups, i.e. a coefficient to show the superiority level of criteria weights of the most weighting group in comparison with criteria weights of the less weighting group. Thus, the criteria weighting factors of the ranked groups are members of decreasing arithmetic progression.
The simple analytical expressions to calculate weighting factors of criteria that are part of the ranked series are obtained.
A DM has a large set of control parameters, namely: the number of criteria, the number of criteria groups, the number of criteria in each group, the level of difference in criterion weightings of the boundary groups. These parameters allow us to conduct research activities and make recommendations on the selection of the most appropriate set of weighting factors of the local criteria.
The paper gives examples to show that it is easy to use the proposed analytical expressions for calculating the weighting factors of criteria to solve practical problems.