Computational aspects of establishing universal tables of criterion's importance

In work “How do we digitize the concept of «more important»” the author had proposed an approach towards decision-making in multi-criterial comparison of alternatives that would allow to increase the validity and decrease laboriousness of the process. The method is based on preemptive calculation of universal tables of weight coefficients for linear convolution of criterions. This deems unnecessary calculation of those weights every time a decision is made within the considered system. For every set of criterions, a separate table is made. It contains 2n-1 rows, where n is the number of criterions. Every row corresponds to a unique possible criterions distribution amongst the importance groups. With more criteria, the computational complexity is so great that the computer's power is not enough to get the result in an acceptable time. This paper presents an approach that makes it possible to decrease the calculation complexity of a single table by 2n-1 times. It is made possible due to the observation of so-called “boundary effect”. It shows as repetition of coefficients in different rows of the table. Due to this, a system of linear algebraic equations can be formed, the variables of which are the sought values of the coefficients. The system is easily solved by numerical methods if the coefficients corresponding to one of the rows of the table become known. The proposed approach greatly facilitates the construction of universal tables for a considerably large (several dozen) number of criteria and reduces the amount of memory required from the decision support systems that use this approach. It also allows a deeper understanding of the rational basis of the concept of "more important", used in all areas of human activity.