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** (.):** the expert methods, ranking of alternatives, decomposition, genetic algorithms

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** (.):** The problem is considered of expert ranking of alternatives, which can be matched to elements of an N-dimensional space. To solve this problem we propose decomposition methods, which help to significantly increase the number of alternatives reliably ranked by experts as compared to traditional expert procedures. To eliminate possible expert contradictions we propose the genetic algorithm to solve the problem of matrix triangulation.

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