Mathematical model of independence of alternatives in the theory of ratings

Abstract

This paper considers the alternative theory of measurement - theory of ratings. The axiomatic definition of ranking is based on definitions from category theory. The scope of the rating definition is the set of objects and the set of ordered pairs of objects. The rating is the transformation that maps the set of objects to the set of numeric values and the set of ordered pairs of objects to the difference of the corresponding numeric values. Finding the rating by subjective measurement requires special control of the information received. The method of alternatives can be used to verify the adequacy of experimental data to the axiomatic definition of the rating.

In the paper the definition of the independence of two variables in magnitude is formulated. It is assumed that for independent variables there is an additive or multiplicative representation of the rating. An example of subjective measurement using multi-criteria utility theory (MAUT), hierarchy analysis (AHP) and rating theory is considered. The AHP heuristic method can lead to classification errors. The mathematical model of the utility function in the axiomatic method MAUT is multiplicative or additive and generally corresponds to the rating model with independent variables.