Números complexos graduados e avaliação de desempenho de classificadores

Abstract

Evaluate the performance of classification algorithms is not an easy task to be performed when considering several different criteria and the absolute numerical values are very close. Recently, in order to obtain more flexibility, a linguistic approach based in Fuzzy Complex Numbers for the multi-criteria evaluation of classification algorithms was proposed. However, when the absolute values are very close, this approach suggests a ranking with a large number of ties. In order to solve this problem, this work introduces the concept of Gradual Complex Number and proposes a new linguistic approach. Gradual Complex Numbers are built upon the definitions of: gradual element, gradual set and gradual number. They are pairs of real gradual real numbers and their algebraic and polar forms are developed in such a way that they have the same structure of usual complex numbers. A notion of distance for such numbers is also developed. This work also provides a way to recover the notion of Fuzzy Complex Numbers. Finally the work provides an application of such number in the classifiers performance multi-criteria evaluation.