摘要：This work is devoted to the development of mathematical models that make it possible to generalize the data obtained in the multicriteria assessment of alternatives when making decisions under certainty conditions. A typical problem in multi-criteria assessment is the integration of particular criteria-based assessments of alternatives into some integral indicator reflecting the degree of attractiveness of alternatives. Traditionally, for these purposes, an additive method was used, which consists in the fact that the final assessment of the alternative is the sum of the assessments by the criteria, possibly multiplied by the weights of the criteria. However, this approach has a number of significant disadvantages, which include the following. When evaluating alternatives, such an indicator of their validity as feasibility is not taken into account, which leads to a distortion of the result due to too simple or difficult criteria. Evaluations of alternatives by qualitative and attributive criteria are subjective, since they are obtained by expert methods, which introduces subjectivity into the integral assessment of the alternative. The integral assessment of an alternative depends on the composition and number of assessed alternatives and on the set of assessment criteria. To eliminate the second drawback, a model for evaluating qualitative alternatives is proposed, which implies the introduction of a certain numerical indicator for a qualitative criterion, which for each alternative have a different meaning, while the attractiveness of the alternative depends on the indicator value. The set of alternatives in relation to the indicator is considered fuzzy, with the belonging function depending on the indicator.
其他摘要：This work is devoted to the development of mathematical models that make it possible to generalize the data obtained in the multicriteria assessment of alternatives when making decisions under certainty conditions. A typical problem in multi-criteria assessment is the integration of particular criteria-based assessments of alternatives into some integral indicator reflecting the degree of attractiveness of alternatives. Traditionally, for these purposes, an additive method was used, which consists in the fact that the final assessment of the alternative is the sum of the assessments by the criteria, possibly multiplied by the weights of the criteria. However, this approach has a number of significant disadvantages, which include the following. When evaluating alternatives, such an indicator of their validity as feasibility is not taken into account, which leads to a distortion of the result due to too simple or difficult criteria. Evaluations of alternatives by qualitative and attributive criteria are subjective, since they are obtained by expert methods, which introduces subjectivity into the integral assessment of the alternative. The integral assessment of an alternative depends on the composition and number of assessed alternatives and on the set of assessment criteria. To eliminate the second drawback, a model for evaluating qualitative alternatives is proposed, which implies the introduction of a certain numerical indicator for a qualitative criterion, which for each alternative have a different meaning, while the attractiveness of the alternative depends on the indicator value. The set of alternatives in relation to the indicator is considered fuzzy, with the belonging function depending on the indicator.
