Fuzzy expert system: An example in prostate cancer Maria Jose ´ de Paula Castanho a, * , Lae ´cio Carvalho de Barros b , Akebo Yamakami c , Lae ´rcio Luis Vendite b a Department of Mathematics, Universidade Estadual do Centro-Oeste, 85015-430 Guarapuava, PR, Brazil b Department of Applied Mathematics – IMECC, Universidade Estadual de Campinas, 13083-859 Campinas, SP, Brazil c Department of Telematics – FEEC, Universidade Estadual de Campinas, 13083-970 Campinas, SP, Brazil Abstract Fuzzy set theory has been applied to many fields in which uncertainty is present as, for example, in medical diagnosis. In this paper, we propose a fuzzy expert system as an alternative to predict pathological stage of prostate cancer. Utilizing uncertain variables and approximate reasoning we construct a fuzzy rule-based system. Data of 190 patients submitted to radical prostatectomy were analyzed, seeking the test performance by the receiver operating characteristic (ROC) curve. The fuzzy expert system constructed is an additional tool to predict the pathological stage of prostate cancer and has a performance that is similar to the one presented by probability tables. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Fuzzy rule-based system; Prognosis; Prostatic neoplasms; ROC curve 1. Introduction Medical expert systems have been used to support physicians on their decisions. The process through which a physician uses his knowledge to infer diagnosis based on information presented by patient and test results is complex and characterized by incompleteness and uncertainty. As the fuzzy set theory was developed to deal with uncertainty it is appropriate to base these systems development. The first medical expert system that uses symbolic knowledge in a rule-based format, MYCIN, was devel- oped in the early 1970s [9]. The CADIAG II, described by Adlassnig [2,1], and its successors, CADIAG III and CADIAG IV [8], use the concepts of fuzzy sets to deal with uncertainties inherent to medical knowledge and the reasoning is based on compositional rule of fuzzy inference. In a fuzzy system it is possible to include the knowledge of specialists even if statistics data are not available. It also permits to construct a gradual diagnosis for the patients, facilitating in natural way the classification of the borderline cases. 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.11.055 * Corresponding author. E-mail address: zeza@unicentro.br (M.J. de Paula Castanho). Available online at www.sciencedirect.com Applied Mathematics and Computation 202 (2008) 78–85 www.elsevier.com/locate/amc