On applicability of mathematical scaling and normalization in applied problem solving

Introduction. The applicability of mathematical scaling and normalization in solving various applied problems is analyzed. The best known formulas often used along the theoretical and experimental studies are considered. The purpose of this work is to identify the properties of mathematical scaling and rationing. Materials and Methods. The errors obtained under using the mathematical scaling and normalization formulas are considered via specific computational examples. Based on a comparative evaluation of the ratio of the degree of magnitude of the initial and resulting values (as well as the ratio of the degree of difference of these values), the correctness of the results obtained which significantly effects the final values is estimated. Research Results. The analysis leads to the conclusion that some known mathematical scaling and normalization formulas possess properties that are ignored in theory and practice. Discussion and Conclusions. The results obtained allow avoiding erroneous decisions caused by the use of invalid scaling and normalization formulas under solving problems in theory and practice of economics, administrative management, medicine, and plenty of other fields.