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Traditional receiver operating characteristic (ROC) analysis is widely utilized to evaluate diagnostic tests but it is restricted to dichotomous results. The aim of this study is to develop the "fuzzy receiver operating characteristic" methodology combining the fuzzy sets theory and the traditional ROC methodology, and to utilize this new tool to evaluate a diagnostic test. We review traditional ROC analysis in mathematical language that utilizes crisp sets and rewrites it based on fuzzy sets. Fuzzy ROC analysis is used to evaluate a fuzzy-rule-based system (FRBS) developed to predict the pathological stage of a prostate cancer in its ability to discriminate between two states: organ-confined and non-confined. Traditional ROC analysis is insufficient to evaluate this system because the result is given in possibilistic terms. The methodology developed in this work is a generalization of the dichotomous ROC analysis, and appears to better represent the performance of diagnostic tests that include a degree of uncertainty similar to the one presented here.

This paper is a study on the population dynamics of blowflies employing a density-dependent, non-linear mathematical model and a coupled population formalism. In this study, we investigated the coupled population dynamics applying fuzzy subsets to model the population trajectory, analyzing demographic parameters such as fecundity, survival, and migration. The main results suggest different possibilities in terms of dynamic behavior produced by migration in coupled populations between distinct environments and the rescue effect generated by the connection between populations. It was possible to conclude that environmental heterogeneity can play an important role in blowfly metapopulation systems. The implications of these results for population dynamics of blowflies are discussed.

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Resumo. Para decidir o tratamento do câncer de próstataé necessário predizer seu estágio. A literatura urológica dispõe de vários nomogramas baseados na teoria de probabilidade para auxiliar o médico nas predições. Nesse artigo, propomos um sistema baseado em regras fuzzy (SBRF) para realizar essa tarefa. Utilizamos a teoria dos conjuntos fuzzy para desenvolver o modelo, por sua capacidade em lidar com incertezas inerentesàs condutas médicas. O sistema baseado em regras fuzzy fornece resultados em termos de possibilidade do paciente estar em determinado estágio patológico. Simulamos resultados para alguns pacientes e comparamos com as probabilidades fornecidas pelas Tabelas de Partin. Os resultados são consistentes quando se adota probabilidade ou possibilidade para estudar o estágio patológico da doença.