Modeling deviations of object quality indicators from the norm

The concept of a norm on the scale of an object's quality indicator in the context of determining the most preferable object or its state is explored. The notions of permissible and maximum permissible deviations from the norm are utilized, with maximum permissible deviations defining the boundaries of the indicator scale. The fundamental version of the norm is represented as a segment on the indicator scale that excludes these boundaries. Point and semi-interval norms (“no more”, “no less”) are considered special cases of the interval norm, where the semi-interval norm reflects the alignment of the original interval norm's boundary with the indicator scale's boundary. For certain indicators, deviation in one direction from the norm is not only acceptable but also beneficial. An indicator satisfying this condition is termed optimized, while an indicator with undesirable deviations from both ends of the norm is termed neutral. In the model of belonging to the norm, three classes are distinguished: “norm”, “no more” and “no less” than the norm. Piecewise linear and nonlinear membership functions for these classes are proposed. In the nonlinear model, the boundaries of the interval norm are expanded to acceptable limits, leading to the intersection of membership functions of adjacent classes. Classification into these three classes is conducted separately for neutral and optimized indicators. Interpreting deviations from the norm, both unacceptable and acceptable, necessitates introducing two fictitious classes: “worse than the norm” and “better than the norm.” These classes are formed from the “not less than” and “not more than” classes. To calculate the membership function for each class across all indicators, a weighted average function is employed. Aggregated indices of belonging to the classes “norm,” “better than norm,” and “worse than norm” across all indicators are referred to as indices of stability, development, and deterioration of an object, respectively. These indices are used for a comprehensive assessment of the object, termed an indicator of its condition. An example of analyzing deviations from the norm, implemented in the modified SVIR-M selection and ranking system, is provided.