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The accuracy of the results obtained by using multicriteria evaluation methods largely depends on the determination of the criteria weights. The accuracy of expert evaluation decreases with the increase of the number of criteria. The application of the analytic hierarchy process, based on pairwise comparison of the criteria, or similar methods, may help to solve this problem. However, if the number of the pairs of criteria is large, the same problems, associated with the accuracy of evaluation, arise. In the present paper, a new method of determining the criteria weights, FARE (Factor Relationship), based on the relationships between all the criteria describing the phenomenon considered, is offered. It means that, at the first stage, a minimal amount of the initial data about the relationships between a part of the set of criteria, as well as their strength and direction, is elicited from experts. Then, based on the conditions of functioning and the specific features of the complete set of criteria, the relations between other criteria of the set and their direction are determined analytically in compliance with those established at the first stage. When the total impact of each particular criterion on other criteria of the set or its total dependence on other criteria of a particular set is known, the criteria weights can be determined.