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The ambiguous information in multi-criteria decision-making (MCDM) and the vagueness of decision-makers for qualitative judgments necessitate accurate tools to overcome uncertainties and generate reliable solutions. As one of the latest and most powerful MCDM methods for obtaining criteria weight, the best-worst method (BWM) has been developed. Compared to other MCDM methods, such as the analytic hierarchy process, the BWM requires fewer pairwise comparisons and produces more consistent results. Consequently, the main objective of this study is to develop an extension of BWM using spherical fuzzy sets (SFS) to address MCDM problems under uncertain conditions. Hesitancy, non-membership, and membership degrees are three-dimensional functions included in the SFS. The presence of three defined degrees allows decision-makers to express their judgments more accurately. An optimization model based on nonlinear constraints is used to determine optimal spherical fuzzy weight coefficients (SF-BWM). Additionally, a consistency ratio is proposed for the SF-BWM to assess the reliability of the proposed method in comparison to other versions of BWM. SF-BWM is examined using two numerical decision-making problems. The results show that the proposed method based on the SF-BWM provided the criteria weights with the same priority as the BWM and fuzzy BWM. However, there are differences in the criteria weight values based on the SF-BWM that indicate the accuracy and reliability of the obtained results. The main advantage of using SF-BWM is providing a better consistency ratio. Based on the comparative analysis, the consistency ratio obtained for SF-BWM is threefold better than the BWM and fuzzy BWM methods, which leads to more accurate results than BWM and fuzzy BWM.

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The classifier selection problem in Assistive Technology Adoption refers to selecting the classification algorithms that have the best performance in predicting the adoption of technology, and is often addressed through measuring different single performance indicators. Satisfactory classifier selection can help in reducing time and costs involved in the technology adoption process. As there are multiple criteria from different domains and several candidate classification algorithms, the classifier selection process is now a problem that can be addressed using Multiple-Criteria Decision-Making (MCDM) methods. This paper proposes a novel approach to address the classifier selection problem by integrating Intuitionistic Fuzzy Sets (IFS), Decision Making Trial and Evaluation Laboratory (DEMATEL), and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The step-by-step procedure behind this application is as follows. First, IF-DEMATEL was used for estimating the criteria and sub-criteria weights considering uncertainty. This method was also employed to evaluate the interrelations among classifier selection criteria. Finally, a modified TOPSIS was applied to generate an overall suitability index per classifier so that the most effective ones can be selected. The proposed approach was validated using a real-world case study concerning the adoption of a mobile-based reminding solution by People with Dementia (PwD). The outputs allow public health managers to accurately identify whether PwD can adopt an assistive technology which results in (i) reduced cost overruns due to wrong classification, (ii) improved quality of life of adopters, and (iii) rapid deployment of intervention alternatives for non-adopters.

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BACKGROUND: The national health and nutrition survey allows to know the state of health of the Mexican population, it provides data for the analysis of different factors and / or indicators of health, diseases and nutritional conditions, such as chronic degenerative diseases and depressive symptoms, which, in turn, if both occur simultaneously, they will have a negative impact on health. This article studies the four factors involved in the overall health of the population in Mexico: excess weight, diabetes, high blood pressure, and depressive symptoms, which are used to conduct a multidimensional characterization and analysis. METHODS: Two methodological resources are applied, a descriptive statistical characterization and the construction of a multidimensional health index with the use of fuzzy sets, through the National Health and Nutrition Survey (ENSANUT 2018-19 - for its acronym in Spanish) in Mexico. RESULTS: The results reveal a growing percentage of individuals who experience detriments to their health, that is, the factors being studied have had a negative impact and tend to follow international projections. The construction of a multidimensional index enables the interaction between the factors being studied, thus allowing for an adequate modeling for the identification of health in Mexico. CONCLUSION: This study aims to elucidate the current state of health throughout the population in Mexico by using the most current data provided by the autonomous public body of statistics and geography to build a multidimensional panorama using four elementary public health indicators (diabetes, obesity, high blood pressure, and depressive symptoms).

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Ecological literature offers a myriad of methods for quantifying ß diversity. One such method is determining BDtotal (BD), which, unlike other methods, can be decomposed into meaningful components that indicate how unique a sampling unit is regarding its composition (local contribution) and how unique a species is regarding its occurrence in the community (species contribution). Despite this advantage, the original formulation of the BD metric only assesses taxonomic variation and neglects other important dimensions of biodiversity. We expanded the original formulation of BD to capture variation in the functional and phylogenetic dimensions of community data by computing two new metrics-BDFun and BDPhy -as well as their respective components that represent the local and species contribution. We tested the statistical performance of these new metrics for capturing variation in functional and phylogenetic composition through simulated communities and illustrated the potential use of these new metrics by analyzing ß diversity of stream fish communities. Our results demonstrated that BDPhy and BDFun have acceptable type I error and great power to detect the effect of deep evolutionary relationships and attributes mediating patterns of ß diversity. The empirical example illustrated how BDPhy and BDFun reveal complementary aspects of ß diversity relative to the original BD metric. These new metrics can be used to identify local communities that are of conservation importance because they represent unique functional, phylogenetic, and taxonomic compositions. We conclude that BDPhy and BDFun are important tools for providing complementary information in the investigation of the structure of biological communities.

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Clinical decision support systems (CDSS) have been designed, implemented, and validated to help clinicians and practitioners for decision-making about diagnosing some diseases. Within the CDSSs, we can find Fuzzy inference systems. For the reasons above, the objective of this study was to design, to implement, and to validate a methodology for developing data-driven Mamdani-type fuzzy clinical decision support systems using clusters and pivot tables. For validating the proposed methodology, we applied our algorithms on five public datasets including Wisconsin, Coimbra breast cancer, wart treatment (Immunotherapy and cryotherapy), and caesarian section, and compared them with other related works (Literature). The results show that the Kappa Statistics and accuracies were close to 1.0% and 100%, respectively for each output variable, which shows better accuracy than some literature results. The proposed framework could be considered as a deep learning technique because it is composed of various processing layers to learn representations of data with multiple levels of abstraction.

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A type-2 fuzzy edge detection method is presented in this paper. The general process consists of first obtaining the image gradients in the four directions-horizontal, vertical, and the two diagonals-and this technique is known as the morphological gradient. After that, the general type-2 fuzzy Sugeno integral (GT2 FSI) is used to integrate the four image gradients. In this second step, the GT2 FSI establishes criteria to determine at which level the obtained image gradient belongs to an edge during the process; this is calculated assigning different general type-2 fuzzy densities, and these fuzzy gradients are aggregated using the meet and join operators. The gradient integration using the GT2 FSI provides a methodology for achieving more robust edge detection, even more if we are working with blurry images. The experimental evaluations are performed on synthetic and real images, and the accuracy is quantified using Pratt's Figure of Merit. The results values demonstrate that the proposed edge detection method outperforms other existing algorithms.

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A hybrid approach composed by different types of fuzzy systems, such as the Type-1 Fuzzy Logic System (T1FLS), Interval Type-2 Fuzzy Logic System (IT2FLS) and Generalized Type-2 Fuzzy Logic System (GT2FLS) for the dynamic adaptation of the alpha and beta parameters of a Bee Colony Optimization (BCO) algorithm is presented. The objective of the work is to focus on the BCO technique to find the optimal distribution of the membership functions in the design of fuzzy controllers. We use BCO specifically for tuning membership functions of the fuzzy controller for trajectory stability in an autonomous mobile robot. We add two types of perturbations in the model for the Generalized Type-2 Fuzzy Logic System to better analyze its behavior under uncertainty and this shows better results when compared to the original BCO. We implemented various performance indices; ITAE, IAE, ISE, ITSE, RMSE and MSE to measure the performance of the controller. The experimental results show better performances using GT2FLS then by IT2FLS and T1FLS in the dynamic adaptation the parameters for the BCO algorithm.

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Cloacal temperature (CT) of broiler chickens is an important parameter to classify its comfort status; therefore its prediction can be used as decision support to turn on acclimatization systems. The aim of this research was to develop and validate a system using the fuzzy set theory for CT prediction of broiler chickens. The fuzzy system was developed based on three input variables: air temperature (T), relative humidity (RH) and air velocity (V). The output variable was the CT. The fuzzy inference system was performed via Mamdani's method which consisted in 48 rules. The defuzzification was done using center of gravity method. The fuzzy system was developed using MAPLE® 8. Experimental results, used for validation, showed that the average standard deviation between simulated and measured values of CT was 0.13°C. The proposed fuzzy system was found to satisfactorily predict CT based on climatic variables. Thus, it could be used as a decision support system on broiler chicken growth.

A temperatura cloacal (TC) de frangos de corte é um importante parâmetro para classificar a sua condição de conforto, portanto, a sua predição pode ser usada no suporte à decisão de acionamento de sistemas de climatização. Objetivou-se com a presente pesquisa desenvolver e validar um sistema, utilizando a teoria dos conjuntos fuzzy para predição da TC de frangos de corte. O sistema fuzzy foi desenvolvido com base em três variáveis de entrada: temperatura do ar (T), umidade relativa (UR) e velocidade do ar (V), tendo, como variável de saída, a TC. A inferência fuzzy foi realizada por meio do método tipo Mamdani, que consistiu na elaboração de 48 regras e a defuzzificação por meio do método do Centro de Gravidade. O sistema fuzzy foi desenvolvido no ambiente computacional MAPLE® 8. Resultados experimentais, usados para a validação, mostraram que o desvio padrão médio entre os valores simulados e medidos de TC foi de 0,13°C. O sistema fuzzy proposto prediz satisfatoriamente a TC com base nas variáveis climáticas, podendo ser utilizado como suporte à decisão em sistemas de criação de frangos de corte.

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Cloacal temperature (CT) of broiler chickens is an important parameter to classify its comfort status; therefore its prediction can be used as decision support to turn on acclimatization systems. The aim of this research was to develop and validate a system using the fuzzy set theory for CT prediction of broiler chickens. The fuzzy system was developed based on three input variables: air temperature (T), relative humidity (RH) and air velocity (V). The output variable was the CT. The fuzzy inference system was performed via Mamdani's method which consisted in 48 rules. The defuzzification was done using center of gravity method. The fuzzy system was developed using MAPLE® 8. Experimental results, used for validation, showed that the average standard deviation between simulated and measured values of CT was 0.13°C. The proposed fuzzy system was found to satisfactorily predict CT based on climatic variables. Thus, it could be used as a decision support system on broiler chicken growth.

A temperatura cloacal (TC) de frangos de corte é um importante parâmetro para classificar a sua condição de conforto, portanto, a sua predição pode ser usada no suporte à decisão de acionamento de sistemas de climatização. Objetivou-se com a presente pesquisa desenvolver e validar um sistema, utilizando a teoria dos conjuntos fuzzy para predição da TC de frangos de corte. O sistema fuzzy foi desenvolvido com base em três variáveis de entrada: temperatura do ar (T), umidade relativa (UR) e velocidade do ar (V), tendo, como variável de saída, a TC. A inferência fuzzy foi realizada por meio do método tipo Mamdani, que consistiu na elaboração de 48 regras e a defuzzificação por meio do método do Centro de Gravidade. O sistema fuzzy foi desenvolvido no ambiente computacional MAPLE® 8. Resultados experimentais, usados para a validação, mostraram que o desvio padrão médio entre os valores simulados e medidos de TC foi de 0,13°C. O sistema fuzzy proposto prediz satisfatoriamente a TC com base nas variáveis climáticas, podendo ser utilizado como suporte à decisão em sistemas de criação de frangos de corte.

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OBJECTIVE: This study proposes a new approach that considers uncertainty in predicting and quantifying the presence and severity of diabetic peripheral neuropathy. METHODS: A rule-based fuzzy expert system was designed by four experts in diabetic neuropathy. The model variables were used to classify neuropathy in diabetic patients, defining it as mild, moderate, or severe. System performance was evaluated by means of the Kappa agreement measure, comparing the results of the model with those generated by the experts in an assessment of 50 patients. Accuracy was evaluated by an ROC curve analysis obtained based on 50 other cases; the results of those clinical assessments were considered to be the gold standard. RESULTS: According to the Kappa analysis, the model was in moderate agreement with expert opinions. The ROC analysis (evaluation of accuracy) determined an area under the curve equal to 0.91, demonstrating very good consistency in classifying patients with diabetic neuropathy. CONCLUSION: The model efficiently classified diabetic patients with different degrees of neuropathy severity. In addition, the model provides a way to quantify diabetic neuropathy severity and allows a more accurate patient condition assessment.

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Cloacal temperature (CT) of broiler chickens is an important parameter to classify its comfort status; therefore its prediction can be used as decision support to turn on acclimatization systems. The aim of this research was to develop and validate a system using the fuzzy set theory for CT prediction of broiler chickens. The fuzzy system was developed based on three input variables: air temperature (T), relative humidity (RH) and air velocity (V). The output variable was the CT. The fuzzy inference system was performed via Mamdani's method which consisted in 48 rules. The defuzzification was done using center of gravity method. The fuzzy system was developed using MAPLE® 8. Experimental results, used for validation, showed that the average standard deviation between simulated and measured values of CT was 0.13°C. The proposed fuzzy system was found to satisfactorily predict CT based on climatic variables. Thus, it could be used as a decision support system on broiler chicken growth.

A temperatura cloacal (TC) de frangos de corte é um importante parâmetro para classificar a sua condição de conforto, portanto, a sua predição pode ser usada no suporte à decisão de acionamento de sistemas de climatização. Objetivou-se com a presente pesquisa desenvolver e validar um sistema, utilizando a teoria dos conjuntos fuzzy para predição da TC de frangos de corte. O sistema fuzzy foi desenvolvido com base em três variáveis de entrada: temperatura do ar (T), umidade relativa (UR) e velocidade do ar (V), tendo, como variável de saída, a TC. A inferência fuzzy foi realizada por meio do método tipo Mamdani, que consistiu na elaboração de 48 regras e a defuzzificação por meio do método do Centro de Gravidade. O sistema fuzzy foi desenvolvido no ambiente computacional MAPLE® 8. Resultados experimentais, usados para a validação, mostraram que o desvio padrão médio entre os valores simulados e medidos de TC foi de 0,13°C. O sistema fuzzy proposto prediz satisfatoriamente a TC com base nas variáveis climáticas, podendo ser utilizado como suporte à decisão em sistemas de criação de frangos de corte.

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La evidencia disponible indica que existe fuerte asociación entre dolor lumbar y manejo manual de carga. Atendiendo a la naturaleza de la carga manipulada, se pueden distinguir dos grandes grupos de trabajadoras: las que realizan manejo de materiales y aquellas que realizan fundamentalmente manejo de pacientes. En ambos sectores se han identificado factores de riesgo de naturaleza física, organizacional y psicosocial que estarían asociados a ese diagnóstico, pero a pesar de los esfuerzos en prevención, este problema sigue siendo importante. La evidencia sugiere que el problema sería más crítico en el sector de la salud. Los autores de la presente investigación proponen que es necesario ocupar herramientas que pertenecen al ámbito de la Ingeniería Cognitiva para explorar las causas de esta tendencia. Esta investigación fue llevada a cabo en una muestra de trabajadoras que pertenecen al sector industrial y al sector de la salud con el objetivo de determinar si existe diferencia significativa asociada a distintas categorías de percepción de la carga manipulada (ej., moderada, pesada,máxima, etc.). Los resultados demuestran que existe diferencia en la percepción del esfuerzo entre ambos grupos de trabajadoras. Esencialmente, esto implica que ambas poblaciones deberían ser estudiadas en forma separada y, en particular, las iniciativas de prevención de los trastornos músculoesqueléticos vinculadas al manejo manual de carga deberían incorporar también elementos propios del proceso cognitivo que gobierna la percepción de la carga de trabajo. Esto sería especialmente importante en las investigaciones desarrolladas con el propósito de establecer límites de peso seguros para la población laboral femenina nacional.

The available evidence indicates that there is a strong association between low back pain and manual load handling. According to the type of load, two large groups of workers can be distinguished: those handling materials and those handling mainly patients. Among bothof these groups, physical, organizational and psychosocial risk factors, probably related to this diagnosis, have been identified. In spite of efforts to prevent it, this situation remains relevant. Evidence suggests that this problem is more critical in the health sector. Authors of the present study propose the use of tools pertaining to Cognitive Engineering and thus to explore the causes of this tendency. This research was carried out in a sample of workers from the industry and health sectors. The study’s goal was to determine ifthere is a significant difference associated to different perception categories of load heaviness (e.g. moderate, heavy, very heavy, etc.). Results show a difference in effort perception between groups. Essentially, this implies that both populations should be studied separately and initiatives intended to prevent musculoskeletaldisorder related to load handling should also include elements which are characteristic of the cognitive process controlling the perception of load heaviness. All of this would be especially important in studies conducted with the purpose of establishing safe weight limits for the nation’s female workers.

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O método Grade of Membership (GoM) tem sido cada vez mais utilizado por demógrafos brasileiros e tem a vantagem de possuir um parâmetro que mensura a heterogeneidade individual, com base nas correlações não-observáveis entre as categorias de resposta das variáveis de interesse, gerando um medida do grau de pertencimento de cada indivíduo a perfis extremos. Alguns autores, contudo, chamam atenção para questões importantes na calibragem dos modelos finais que utilizam o programa GoM versão 3.4, como o problema de identificabilidade - soluções múltiplas para parâmetros estimados. Neste artigo, é sugerido um procedimento capaz de identificar um modelo final com solução única que descreva os tipos puros mais fidedignos à base de dados, em uma tentativa de otimização. Para ilustrar esse processo, utilizou-se uma base de dados correspondente a um levantamento econômico e sociodemográfico de uma população de pequenos agricultores residentes ao longo da Rodovia Transamazônica, no Estado do Pará. Também identificou-se a existência de instabilidade nos parâmetros estimados pelo programa GoM 3.4, sendo proposto um método de estabilização de seus valores. Com esses procedimentos combinados, os usuários do programa GoM 3.4 poderão descrever sua base de dados de forma mais adequada e responder às críticas sobre questões de identificabilidade e estabilidade dos modelos resultantes. Essas soluções empíricas são relevantes por afetarem cálculos de prevalência e de incidência de eventos de interesse, além de trazerem consequências importantes sobre o ponto e o momento corretos para intervenções de políticas públicas ou de planejamento prospectivo em análises de projeção.

The Grade of Membership (GoM) method has been increasingly employed by Brazilian demographers, and has the advantage of including a parameter that measures individual heterogeneousness on the basis of non-observable correlations among the categories of responses to variables of interest. The parameter shows each individual's degree of membership to extreme profiles. Several authors, however, have called attention to important issues in adjusting the final models that use 3.4 Version of the GoM Program, such as the problem of identifiability - multiple solutions for estimated parameters. In this article a procedure is discussed that is able to identify a final model with a single solution that describes the pure types that are the most reliable for the database, in an attempt at streamlining. To illustrate this process, a database was used with data corresponding to an economic and sociodemographic study of a population of small farmers living along the TransAmazon Highway, in the northern State of Pará, Brazil. The existence of instability in the parameters estimated by the GoM 3.4 Program was also identified and a method of stabilization of its values was proposed. With these combined procedures, users of the GoM 3.4 Program will be able to describe their databases more adequately and respond to criticisms regarding the identifiability and stability of the resulting models. These empirical solutions are significant. Not only do they affect calculations of prevalence and incidence of events of interest, they also bring about important consequences at the correct point and correct moment for interventions of public policies or of prospective planning in projection analyses.

El método Grade of Membership (GoM) ha sido cada vez más utilizado por los demógrafos brasileños y tiene la ventaja de poseer un parámetro que mide la heterogeneidad individual, sobre la base de las correlaciones no observables entre las categorías de respuesta de las variables de interés, generando una medida del grado de pertenencia de cada individuo a perfiles extremos. Algunos autores, sin embargo, destacan cuestiones importantes en la calibración de los modelos finales que utiliza el programa GoM versión 3.4, como el problema de identificabilidad - soluciones múltiples para parámetros estimados. En este artículo, se sugiere un procedimiento capaz de identificar un modelo final con una solución única que describa los tipos puros de mayor fidelidad con respecto a la base de datos, con una intención de optimización. Para ilustrar este proceso, se utilizó una base de dados correspondiente a un relevamiento económico y socio-demográfico de una población de pequeños agricultores residentes a lo largo de la Autopista Transamazônica, en el Estado de Pará. También se identificó la existencia de inestabilidad en los parámetros estimados por el programa GoM 3.4, y se propuso un método de estabilización de sus valores. Con esos procedimientos combinados, los usuarios del programa GoM 3.4 podrán describir su base de dados en forma más adecuada y responder a las críticas sobre cuestiones de identificabilidad y estabilidad de los modelos resultantes. Estas soluciones empíricas son relevantes porque afectan cálculos de superioridad y de incidencia de eventos de interés, además de traer consecuencias importantes sobre el punto y el momento correctos para las intervenciones de políticas públicas o de planificación prospectiva en análisis de proyección.

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Nos últimos anos o aumento da incidência de casos de câncer de próstata configura-se como um importante problema de saúde pública e um desafio para a ciência médica. O objetivo deste trabalho é a avaliação do desempenho de um modelo matemático, desenvolvido por Silveira (2007) para predizer o estadiamento patológico do câncer de próstata, por meio da metodologia ROC (Receiver Operating Characteristic). O modelo consiste num sistema baseado em regras fuzzy (SBRF), que combina os dados pré-cirúrgicos – estado clínico, nível de PSA e grau de Gleason – acionando um conjunto de regras linguísticas, elaboradas com base nas informações presentes nos nomogramas já existentes. A saída do sistema fornece as possibilidades do indivíduo, com determinado quadro clínico, se enquadrar em cada um dos estádios de extensão do tumor: localizado, localmente avançado e metastático. Para a análise do poder discriminatório do modelo fuzzy como um teste de diagnóstico, foi construída, a partir das medidas de sensibilidade e especificidade, a curva ROC e calculada a área total sob a curva, como medida de desempenho. Além disso, foram obtidos (de duas maneiras distintas) os pontos de corte mais “adequados”, isto é, um limiar de decisão entre a doença estar totalmente localizada no interior da glândula prostática ou não. Dados reais de pacientes do Hospital de Clínicas da UNICAMP foram usados nos cálculos e a cirurgia– prostatectomia radical – foi adotada como padrão-ouro. Os resultados alcançados mostraram que o modelo fuzzy em questão pode vir a ser utilizado para discriminar câncer de próstata localizado.

In recent years, the increase in the incidence of prostate cancer has become a major public health problem and a challenge for medical science. The goal of this work is assessing the performance of a mathematical model, developed by Silveira (2007) to predict the pathological stage of the prostate cancer, through ROC methodology (Receiver Operating Characteristic). The model is a fuzzy rule based system, that combines pre-surgical data – clinical stage, PSA level and Gleason score – availing of a set of linguistic rules made with base on information of the existents nomograms. The output of the system provides the possibilities of the individual, with certain clinical features, be in each stage of the tumor extension: localized, advanced locally and metastatic. To analyze the discriminatory power of the fuzzy model as a diagnosis test, was constructed from the measures of sensitivity and specificity, the ROC curve and calculated the total area under the curve, as measure of performance. Moreover, were obtained (in two different ways) the cutoff points most “appropriate”, that is a threshold for deciding between the disease is fully localized within the prostate gland or not. Real data of patients from the Clinics Hospital of UNICAMP were used in the calculations and the surgery – radical prostatectomy – was used as gold standard. The results showed that the fuzzy model in question can be used to discriminate localized prostate cancer.

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O objetivo desta pesquisa é a análise de modelos de aprendizagem, utilizando diferentes operações aritméticas aplicadas de Sistemas Neuro-Fuzzy (NFS)...

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This work discusses basic information about fundamental concepts in the theory of fuzzy sets, and presents a new view point of things existing in various specific studies in the areas of topology, vector space measurement and integration, statistics, etc. The objectives were: 1. Compare these new concepts with tradicional ones in the classical theory of sets and 2. Try, in the teaching form, to interpret this mathematical model which reflects, in a clearer way, on human behavior.  

  O presente trabalho pretende ser uma divulgação básica dos conceitos fundamentais da Teoria de Conjuntos Fuzzy, como uma forma de mostrar um novo enfoque de Matemática, da qual já existem estudos específicos no terreno da Topologia, Espaços Vetoriais, Medida e Integração, Estatística, etc. Tem os seguintes objetivos: lo. comparar estes novos conceitos com os conceitos tradicionais da teoria de conjuntos clássica e; 2o. tentar de forma didática, interpretar este novo modelo matemático, que reflete, de maneira mais clara, o comportamento humano.    

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This work discusses basic information about fundamental concepts in the theory of fuzzy sets, and presents a new view point of things existing in various specific studies in the areas of topology, vector space measurement and integration, statistics, etc. The objectives were: 1. Compare these new concepts with tradicional ones in the classical theory of sets and 2. Try, in the teaching form, to interpret this mathematical model which reflects, in a clearer way, on human behavior.

O presente trabalho pretende ser uma divulgação básica dos conceitos fundamentais da Teoria de Conjuntos Fuzzy, como uma forma de mostrar um novo enfoque de Matemática, da qual já existem estudos específicos no terreno da Topologia, Espaços Vetoriais, Medida e Integração, Estatística, etc. Tem os seguintes objetivos: lo. comparar estes novos conceitos com os conceitos tradicionais da teoria de conjuntos clássica e; 2o. tentar de forma didática, interpretar este novo modelo matemático, que reflete, de maneira mais clara, o comportamento humano.