Numbers and sets

In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.

Prediction of free-stall occupancy rate in dairycattle barns through fuzzy sets

The goal of this study was to develop a fuzzy model to predict the occupancy rate of free-stalls facilities of dairy cattle, aiding to optimize the design of projects. The following input variables were defined for the development of the fuzzy system: dry bulb temperature (Tdb, °C), wet bulb temperature (Twb, °C) and black globe temperature (Tbg, °C). Based on the input variables, the fuzzy system predicts the occupancy rate (OR, %) of dairy cattle in free-stall barns. For the model validation, data collecting were conducted on the facilities of the Intensive System of Milk Production (SIPL), in the Dairy Cattle National Research Center (CNPGL) of Embrapa. The OR values, estimated by the fuzzy system, presented values of average standard deviation of 3.93%, indicating low rate of errors in the simulation. Simulated and measured results were statistically equal (P>0.05, t Test). After validating the proposed model, the average percentage of correct answers for the simulated data was 89.7%. Therefore, the fuzzy system developed for the occupancy rate prediction of free-stalls facilities for dairy cattle allowed a realistic prediction of stalls occupancy rate, allowing the planning and design of free-stall barns.

Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease) and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA) and by fuzzy max-min compositions (fuzzy), and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

Selection of patients for myocardial perfusion scintigraphy based on fuzzy sets theory applied to clinical-epidemiological data and treadmill test results

Coronary artery disease (CAD) is a worldwide leading cause of death. The standard method for evaluating critical partial occlusions is coronary arteriography, a catheterization technique which is invasive, time consuming, and costly. There are noninvasive approaches for the early detection of CAD. The basis for the noninvasive diagnosis of CAD has been laid in a sequential analysis of the risk factors, and the results of the treadmill test and myocardial perfusion scintigraphy (MPS). Many investigators have demonstrated that the diagnostic applications of MPS are appropriate for patients who have an intermediate likelihood of disease. Although this information is useful, it is only partially utilized in clinical practice due to the difficulty to properly classify the patients. Since the seminal work of Lotfi Zadeh, fuzzy logic has been applied in numerous areas. In the present study, we proposed and tested a model to select patients for MPS based on fuzzy sets theory. A group of 1053 patients was used to develop the model and another group of 1045 patients was used to test it. Receiver operating characteristic curves were used to compare the performance of the fuzzy model against expert physician opinions, and showed that the performance of the fuzzy model was equal or superior to that of the physicians. Therefore, we conclude that the fuzzy model could be a useful tool to assist the general practitioner in the selection of patients for MPS.

Agonistic-like responses from the torus semicircularis dorsalis elicited by GABA A blockade in the weakly electric fish Gymnotus carapo

Findings by our group have shown that the dorsolateral telencephalon of Gymnotus carapo sends efferents to the mesencephalic torus semicircularis dorsalis (TSd) and that presumably this connection is involved in the changes in electric organ discharge (EOD) and in skeletomotor responses observed following microinjections of GABA A antagonist bicuculline into this telencephalic region. Other studies have implicated the TSd or its mammalian homologue, the inferior colliculus, in defensive responses. In the present study, we explore the possible involvement of the TSd and of the GABA-ergic system in the modulation of the electric and skeletomotor displays. For this purpose, different doses of bicuculline (0.98, 0.49, 0.245, and 0.015 mM) and muscimol (15.35 mM) were microinjected (0.1 µL) in the TSd of the awake G. carapo. Microinjection of bicuculline induced dose-dependent interruptions of EOD and increased skeletomotor activity resembling defense displays. The effects of the two highest doses showed maximum values at 5 min (4.3 ± 2.7 and 3.8 ± 2.0 Hz, P < 0.05) and persisted until 10 min (11 ± 5.7 and 8.7 ± 5.2 Hz, P < 0.05). Microinjections of muscimol were ineffective. During the interruptions of EOD, the novelty response (increased frequency in response to sensory novelties) induced by an electric stimulus delivered by a pair of electrodes placed in the water of the experimental cuvette was reduced or abolished. These data suggest that the GABA-ergic mechanisms of the TSd inhibit the neural substrate of the defense reaction at this midbrain level.