Measurement by the method of rating

• Main Author: V. M. Romanchak
• Format: Article
• Language: Russian
• Published: The United Institute of Informatics Problems of the National Academy of Sciences of Belarus 2019-06-01
• Series: Informatika
• Subjects: expert estimates; rating; fechner's law; stevens law; utility function
• Online Access: https://inf.grid.by/jour/article/view/473

The definition of rating is given and mathematical model of finding the values of object quantity by means of rating is specified. With the help of the rating it is possible to consider both objective and subjective measurements from a single point of view. If, as example, some sequence of objects is sorted by a varying uniformly magnitude an object number in the sequence could be considered as the rating.The axiomatic definition of the rating is based on a mathematical model of measurement. The formalization of the process of measuring an arbitrary value begins with a clarification of the concept of measurement. During the measurement, the sizes of objects are compared, the matrix of paired comparisons is axiomatically determined, on the basis of this matrix the rating is located. Knowing the rating you can find the value. Then by means of a rating the laws of Fechner and Stevens are analyzed. The equivalence of Fechner and Stevens laws is a confirmation of the algorithm for determining the values of the measured value based on the rating.The subjective method of finding the rating requires a special method of checking the reliability of the information received. Verification of the reliability of the subjective measurement is proposed to perform the method of alternatives. In the alternatives method, each object is compared twice, and different objects are selected as the object for comparison. The criterion of reliability of subjective measurement is the statistical coincidence of rating values obtained by alternative methods of comparison.