Titlebook: Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems; Inversion, Displacem Irik Z. Mukhametzyanov Book 2023 T

Anticlimax

Linear Methods for Multivariate Normalization,ess invariance. A meaningful interpretation of linear normalized scales is given. Using the invariant properties of linear normalization methods often eliminates simple problems and avoids obvious errors when solving MCDM problems.

deviate

Significant Difference of the Performance Indicator of Alternatives, are proposed, and numerical algorithms for estimating the magnitude of the relative error are proposed, which determine a significant difference in ratings with variations in the initial data and variations in normalization methods. Based on this analysis, it is possible to determine the aggregation methods that have the best ranking resolution.

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Non-linear Multivariate Normalization Methods,o a dimensionless form based on linear normalization methods. A non-linear transformation allows you to redefine proportions (distances) between attribute values for different alternatives. Therefore, the entire chain of transformations can be defined as a non-linear normalization.

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Book 2023hods and ways to eliminate them. ..The invariant properties of the linear normalization methods presented here can be used to eliminate simple problems and avoid obvious errors when choosing a normalization method. The book introduces valuable, novel techniques for the multistep normalization of mul

遗传

The MCDM Rank Model,y aggregating normalized attribute values. Aggregation of normalized attribute values transforms the original multi-criteria decision-making problem with different-sized and differently directed criteria to a one-dimensional problem of ranking alternatives in descending or ascending integrated perfo

想象

Normalization and MCDM Rank Model,lated. This is the preservation of order and proportions between natural and normalized values on separate scales. General approaches of goal inversion for cost criteria are given. A description of anisotropic scaling in the transition to conditionally general normalized scales is given. The use of

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Inversion of Normalized Values: ReS-Algorithm,classification is presented. A detailed description of the problems of attribute value inversion is given. A universal method for inverting normalized values based on the Reverse Sorting Algorithm (ReS-algorithm) is presented. The ReS-algorithm preserves the dispositions of natural and normalized va