Solving Leontief Input-Output Model with Trapezoidal Fuzzy Numbers and Gauss-Seidel Algorithm

In this work a fuzzy linear system is used to solve Leontief input-output model with fuzzy entries. For solving this model, we assume that the consumption matrix from di erent sectors of the economy and demand are known. These assumptions heavily depend on the information obtained from the industries. Hence uncertainties are involved in this information. The aim of this work is to model these uncertainties and to address them by fuzzy entries such as fuzzy numbers and LR-type fuzzy numbers (triangular and trapezoidal). Fuzzy linear system has been developed using fuzzy data and it is solved using Gauss-Seidel algorithm. Numerical examples show the e ciency of this algorithm. The famous example from Prof. Leontief, where he solved the production levels for U.S. economy in 1958, is also further analyzed.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Cognitive Functions After Traumatic Brain Injury. A 30-year Follow-up Study

Many cognitive deficits after TBI (traumatic brain injury) are well known, such as memory and concentration problems, as well as reduced information-processing speed. What happens to patients and cognitive functioning after immediate recovery is poorly known. Cognitive functioning is flexible and may be influenced by genetic, psychological and environmental factors decades after TBI. The general aim of this thesis was to describe the long-term cognitive course after TBI, to find variables that may contribute to it, and how the cognitive functions after TBI are associated with specific medical factors and reduced survival. The original study group consisted of 192 patients with TBI who were originally assessed with the Mild Deterioration Battery (MDB) on average two years after the injury, during the years 1966 – 1972. During a 30-year follow-up, we studied the risks for reduced survival, and the mortality of the patients was compared with the general population using the Standardized Mortality Ratio (SMR). Sixty-one patients were re-assessed during 1998-2000. These patients were evaluated with the MDB, computerized testing, and with various other neuropsychological methods for attention and executive functions. Apolipoprotein-E (ApoE) genotyping and magnetic resonance imaging (MRI) based on volumetric analysis of the hippocampus and lateral ventricles were performed. Depressive symptoms were evaluated with the short form of the Beck depression inventory. The cognitive performance at follow-up was compared with a control group that was similar to the study group in regard to age and education. The cognitive outcome of the patients with TBI varied after three decades. The majority of the patients showed a decline in their cognitive level, the rest either improved or stayed at the same level. Male gender and higher age at injury were significant risk factors for the decline. Whereas most cognitive domains declined during the follow-up, semantic memory behaved in the opposite way, showing recovery after TBI. In the follow-up assessment, the memory decline and impairments in the set-shifting domain of executive functions were associated with MRI-volumetric measures, whereas reduction in information-processing speed was not associated with the MRI measures. The presence of local contusions was only weakly associated with cognitive functions. Only few cognitive methods for attention were capable of discriminating TBI patients with and without depressive symptoms. On the other hand, most complex attentional tests were sensitive enough to discriminate TBI patients (non-depressive) from controls. This means that complex attention functions, mediated by the frontal lobes, are relatively independent of depressive symptoms post-TBI. The presence of ApoE4 was associated with different kinds of memory processes including verbal and visual episodic memory, semantic memory and verbal working memory, depending on the length of time since TBI. Many other cognitive processes were not affected by the presence of ApoE4. Age at injury and poor vocational outcome were independent risk factors for reduced survival in the multivariate analysis. Late mortality was higher among younger subjects (age < 40 years at death) compared with the general population which should be borne in mind when assessing the need for rehabilitation services and long-term follow-up after TBI.

NADPH-Dependent Thioredoxin System In Regulation of Chloroplast Functions

Photosynthesis, the process in which carbon dioxide is converted into sugars using the energy of sunlight, is vital for heterotrophic life on Earth. In plants, photosynthesis takes place in specific organelles called chloroplasts. During chloroplast biogenesis, light is a prerequisite for the development of functional photosynthetic structures. In addition to photosynthesis, a number of other metabolic processes such as nitrogen assimilation, the biosynthesis of fatty acids, amino acids, vitamins, and hormones are localized to plant chloroplasts. The biosynthetic pathways in chloroplasts are tightly regulated, and especially the reduction/oxidation (redox) signals play important roles in controlling many developmental and metabolic processes in chloroplasts. Thioredoxins are universal regulatory proteins that mediate redox signals in chloroplasts. They are able to modify the structure and function of their target proteins by reduction of disulfide bonds. Oxidized thioredoxins are restored via the action of thioredoxin reductases. Two thioredoxin reductase systems exist in plant chloroplasts, the NADPHdependent thioredoxin reductase C (NTRC) and ferredoxin-thioredoxin reductase (FTR). The ferredoxin-thioredoxin system that is linked to photosynthetic light reactions is involved in light-activation of chloroplast proteins. NADPH can be produced via both the photosynthetic electron transfer reactions in light, and in darkness via the pentose phosphate pathway. These different pathways of NADPH production enable the regulation of diverse metabolic pathways in chloroplasts by the NADPH-dependent thioredoxin system. In this thesis, the role of NADPH-dependent thioredoxin system in the redox-control of chloroplast development and metabolism was studied by characterization of Arabidopsis thaliana T-DNA insertion lines of NTRC gene (ntrc) and by identification of chloroplast proteins regulated by NTRC. The ntrc plants showed the strongest visible phenotypes when grown under short 8-h photoperiod. This indicates that i) chloroplast NADPH-dependent thioredoxin system is non-redundant to ferredoxinthioredoxin system and that ii) NTRC particularly controls the chloroplast processes that are easily imbalanced in daily light/dark rhythms with short day and long night. I identified four processes and the redox-regulated proteins therein that are potentially regulated by NTRC; i) chloroplast development, ii) starch biosynthesis, iii) aromatic amino acid biosynthesis and iv) detoxification of H₂O₂. Such regulation can be achieved directly by modulating the redox state of intramolecular or intermolecular disulfide bridges of enzymes, or by protecting enzymes from oxidation in conjunction with 2-cysteine peroxiredoxins. This thesis work also demonstrated that the enzymatic antioxidant systems in chloroplasts, ascorbate peroxidases, superoxide dismutase and NTRC-dependent 2-cysteine peroxiredoxins are tightly linked up to prevent the detrimental accumulation of reactive oxygen species in plants.

A quantitative view on fuzzy numbers

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

Estimativa das condições de conforto térmico para avicultura de postura usando a teoria dos conjuntos Fuzzy

Neste trabalho, foi utilizada uma ferramenta matemática promissora na análise de sistemas e/ou processos, particularmente na área de produção animal. Essa ferramenta é a desenvolvida segundo a abordagem da teoria dos Conjuntos Fuzzy e, neste caso específico, permitiu a análise da composição das variáveis climáticas independentes, como temperatura de bulbo seco e umidade relativa do ar, que influenciam na variável dependente denominada conforto térmico das aves. Foi realizada a construção de regras baseadas na intuição humana, segundo o conhecimento de especialistas da área, a partir do que é possível simular cenários distintos para o suporte à decisão de construção de galpões para abrigo a animais. Neste trabalho, foi estimado o conforto térmico para alojamento de aves poedeiras em produção. Os resultados foram analisados, usando-se o ambiente de computação científica MATLAB 6.5, o que pode ser realizado iterativamente a cada cenário gerado. Com base nos resultados obtidos, pode-se analisar as condições de conforto para distintas composições das variáveis de entrada.

Uso da lógica fuzzy na caracterização do ambiente produtivo para matrizes gestantes

O objetivo desta pesquisa consistiu na avaliação do ambiente de alojamento, estimando as condições favoráveis ao melhor desempenho de matrizes gestantes. O experimento foi realizado no período compreendido entre 4-1 e 11-3-2005, em propriedade de produção industrial de suínos, localizada no município de Elias Fausto - SP. A pesquisa foi desenvolvida no setor de gestação, com 24 matrizes primíparas, 12 fêmeas alojadas em baias individuais (T1) e 12 em baias coletivas (T2). O trabalho foi dividido em duas etapas, em função da forma de avaliação dos dados: análise bioclimática e da qualidade do ar, e estimativa dos padrões de conforto térmico ambiental. As variáveis bioclimáticas T (ºC), UR (%), Tgn (ºC) e fisiológicas, taxa respiratória (mov min-1) e temperatura retal (ºC) apontam o sistema de confinamento em baias coletivas como o que possibilitou melhor condicionamento térmico natural às matrizes em gestação. O uso da teoria dos conjuntos fuzzy permitiu que se fizesse inferência entre os dados resultantes do trabalho experimental com os estabelecidos pela literatura, por intermédio de base de regras, para a determinação do conforto ambiental aplicado a matrizes na fase de gestação.

Sistema fuzzy para estimativa do bem-estar de matrizes pesadas

Entender o comportamento e suas pequenas variações decorrentes das mudanças do ambiente térmico e desenvolver modelos que simulem o bem-estar a partir de respostas das aves ao ambiente constituem o primeiro passo para a criação de um sistema de monitoramento digital de aves em galpões de produção. Neste trabalho, foi desenvolvido um sistema de suporte à decisão com base na teoria dos conjuntos fuzzy para a estimativa do bem-estar de matrizes pesadas em função de frequências e duração dos comportamentos expressos pelas aves. O desenvolvimento do sistema passou por cinco etapas distintas: 1) organização dos dados experimentais; 2) apresentação dos vídeos em entrevista com "especialista"; 3) criação das funções de pertinência com base nas entrevistas e na revisão da literatura; 4) simulação de frequências de ocorrências e tempos médios de expressão dos comportamentos classificados como indicadores de bem-estar utilizando equações de regressão obtidas na literatura, e 5) construção das regras, simulação e validação do sistema. O sistema fuzzy desenvolvido estimou satisfatoriamente o bem-estar de matrizes pesadas, tendo na sua última versão, com maior número de regras, acertado 77,8% dos dados experimentais, comparados com as respostas esperadas por um especialista. O sistema pode ser utilizado como instrumento matemático-computacional para apoiar decisões em galpões de produção de matrizes pesadas.

Índice fuzzy de conforto térmico para frangos de corte

A estimativa de conforto térmico na avicultura moderna é importante para que sistemas de climatização possam ser acionados no tempo correto, diminuindo perdas e aumentando rendimentos. Embora a literatura corrente apresente alguns índices de conforto térmico, que são aplicados para essa estimativa, estes são baseados apenas em condições do ambiente térmico e não consideram fatores importantes inerentes aos animais, tais como genética e capacidade de aclimatação, provendo, geralmente, uma estimativa inadequada do conforto térmico das aves. Este trabalho desenvolveu o Índice Fuzzy de Conforto Térmico (IFCT), com o intuito de estimar o conforto térmico de frangos de corte, considerando que o mecanismo usado pelas aves para perda de calor em ambientes fora da zona termoneutra é a vasodilatação periférica, que aumenta a temperatura superficial, e que pode ser usada como indicador do estado de conforto. O IFCT foi desenvolvido a partir de dois experimentos, que proporcionaram 108 cenários ambientais diferentes. Foram usadas imagens termográficas infravermelhas, para o registro dos dados de temperaturas superficiais das penas e da pele, e o grau de empenamento das aves. Para os mesmos cenários de ambiente térmico observados nos experimentos, foram comparados os resultados obtidos usando o IFCT e o Índice de Temperatura e Umidade (ITU). Os resultados validaram o IFCT para a estimativa do conforto térmico de frangos de corte, sendo específico na estimativa de condições de perigo térmico, usual em alojamentos em países de clima tropical. Essa característica é desejável em modelos que estimem o bem-estar térmico de frangos de corte, pois situações classificadas como perigo acarretam no dispêndio de recursos para evitar perdas produtivas.

Application of fuzzy logic for the evaluation of livestock slaughtering

The fuzzy logic admits infinite intermediate logical values between false and true. With this principle, it developed in this study a system based on fuzzy rules, which indicates the body mass index of ruminant animals in order to obtain the best time to slaughter. The controller developed has as input the variables weight and height, and as output a new body mass index, called Fuzzy Body Mass Index (Fuzzy BMI), which may serve as a detection system at the time of livestock slaughtering, comparing one another by the linguistic variables "Very Low", "Low", "Average ", "High" and "Very High". For demonstrating the use application of this fuzzy system, an analysis was made with 147 Nellore beeves to determine Fuzzy BMI values for each animal and indicate the location of body mass of any herd. The performance validation of the system was based on a statistical analysis using the Pearson correlation coefficient of 0.923, representing a high positive correlation, indicating that the proposed method is appropriate. Thus, this method allows the evaluation of the herd comparing each animal within the group, thus providing a quantitative method of farmer decision. It was concluded that this study established a computational method based on fuzzy logic that mimics part of human reasoning and interprets the body mass index of any bovine species and in any region of the country.

Procedimento fuzzy aplicado à avaliação da insalubridade em atividades agrícolas

Diante do alto grau de mecanização a que as atividades agrícolas estão sendo submetidas, objetivou-se, com esta pesquisa, desenvolver um modelo fuzzy capaz de avaliar e classificar o nível de insalubridade em diversos ambientes de trabalho. O modelo desenvolvido tem como variáveis de entrada: o índice de bulbo úmido e temperatura de globo (IBUTG, °C), o nível de ruído (dBA), a taxa de metabolismo (W m-2) e o tempo de descanso (%) e, como variável de saída, o índice de bem-estar humano (IBEH). O método de inferência utilizado foi o de Mandani e, na defuzificacão, utilizou-se o método do centro de gravidade. O sistema de regras foi desenvolvido com base nas combinações das variáveis de entrada. Foram definidas 400 regras com pesos iguais a 1, sendo que, na elaboração das regras, um especialista da área foi consultado. Foram utilizados dados de campo visando a testar o sistema desenvolvido, e os resultados mostraram que a modelagem proposta é uma ferramenta promissora na determinação do IBEH, apresentando tempo de descanso ideal variando de 64,2% (motosserra, próximo ao ouvido do operador) até 25% (derriçadora, 20 m de distância do operador), sendo que, diante de um cenário predefinido do ambiente térmico e acústico, foi possível determinar o grau de bem-estar humano e o tempo de descanso ideal para cada equipamento avaliado.

Sistema fuzzy para predição do desempenho produtivo de frangos de corte de 1 a 21 dias de idade

Um sistema de inferência fuzzy foi desenvolvido baseado em dados da literatura para predição do consumo de ração, ganho de peso e conversão alimentar de frangos de corte com idade variando de 1 a 21, dias submetidos a diferentes condições térmicas. O sistema fuzzy foi estruturado com base em três variáveis de entrada: idade das aves (semanas), temperatura (°C) e umidade relativa (%) ambientes, sendo que as variáveis de saída consideradas foram: ganho de peso, consumo de ração e conversão alimentar. A inferência foi realizada por meio do método de Mamdani, que consistiu na elaboração de 45 regras e a defuzzificação por meio do método do Centro de Gravidade. Com base nos resultados, ao se compararem os dados da literatura com os obtidos pelo sistema fuzzy proposto, verificou-se desempenho satisfatório na predição das variáveis respostas, com R² da ordem de 0,995; 0,998 e 0,976, respectivamente. O ganho de peso predito pela lógica fuzzy foi validado com dados experimentais de campo, no qual se obteve R² = 0,975, apresentando grande potencial de uso em sistemas de climatização automatizado.

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.

Fuzzy rule-based system for evaluation of uncertainty transaction in cassava chain

A fuzzy ruled-based system was developed in this study and resulted in an index indicating the level of uncertainty related to commercial transactions between cassava growers and their dealers. The fuzzy system was developed based on Transaction Cost Economics approach. The fuzzy system was developed from input variables regarding information sharing between grower and dealer on “Demand/purchase Forecasting”, “Production Forecasting” and “Production Innovation”. The output variable is the level of uncertainty regarding the transaction between seller and buyer agent, which may serve as a system for detecting inefficiencies. Evidences from 27 cassava growers registered in the Regional Development Offices of Tupa and Assis, São Paulo, Brazil, and 48 of their dealers supported the development of the system. The mathematical model indicated that 55% of the growers present a Very High level of uncertainty, 33% present Medium or High. The others present Low or Very Low level of uncertainty. From the model, simulations of external interferences can be implemented in order to improve the degree of uncertainty and, thus, lower transaction costs.

Management zones using fuzzy clustering based on spatial-temporal variability of soil and corn yield

Clustering soil and crop data can be used as a basis for the definition of management zones because the data are grouped into clusters based on the similar interaction of these variables. Therefore, the objective of this study was to identify management zones using fuzzy c-means clustering analysis based on the spatial and temporal variability of soil attributes and corn yield. The study site (18 by 250-m in size) was located in Jaboticabal, São Paulo/Brazil. Corn yield was measured in one hundred 4.5 by 10-m cells along four parallel transects (25 observations per transect) over five growing seasons between 2001 and 2010. Soil chemical and physical attributes were measured. SAS procedure MIXED was used to identify which variable(s) most influenced the spatial variability of corn yield over the five study years. Basis saturation (BS) was the variable that better related to corn yield, thus, semivariograms models were fitted for BS and corn yield and then, data values were krigged. Management Zone Analyst software was used to carry out the fuzzy c-means clustering algorithm. The optimum number of management zones can change over time, as well as the degree of agreement between the BS and corn yield management zone maps. Thus, it is very important take into account the temporal variability of crop yield and soil attributes to delineate management zones accurately.