Методы многокритериальной стратификации и их экспериментальное сравнение
Математические методы анализа решений в экономике, бизнесе и политике. WP7. Издательский дом ВШЭ, 2013. № WP7/2013/06.
At multivariate ranking, one may concentrate not on the problem of strict ordering of the objects but rather on tying them up in groups of more or less similar entities. Following Sociology and Mineralogy, such tied groups can be referred to as strata. A popular “univariate” ABC-classification problem, in fact, partitions the set in three strata. This work proposes two novel algorithms for automatic stratification with a prespecified number of strata. One of our algorithms chooses criteria weights in such a way that the objects within each single stratum are located on the axis of the aggregate criterion as close to each other as possible. The other, in contrast, takes all the criteria to be incomparable, so that the strata approximate Pareto boundaries of the vector preference relation. These methods are experimentally compared with a set of known ranking methods, for which we propose some strata generation mechanisms.