Optimization and choice based on ratio-scales

The classical choice theory considers three alternative approaches to the individual choice problem: a criterion language, a binary relation language and a language of choice functions. These approaches provide equivalent descriptions of choice function classes. The framework of rational choice is strongly based on the assumption that criteria are ordinal scales. For instance, two scalar criteria generate the same choice functions if and only if they are equivalent ordinal scales. Hence, the classical framework is not able to distinguish choices based on cardinal scales. The aim of this paper is to present a theory of choice for ratio-scales. It turns out that fuzzy set theory provides a sufficient basis for constructing pair-dominant mechanisms of choice and a choice function language which give an adequate description of choice for ratio-scales. Scalar and vector criterion choice mechanisms are studied in detail in the paper.