Pobreza multidimensional na região nordeste: uma aplicação da Teoria dos Conjuntos Fuzzy (em 2010)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Interpretação e análise do problema da indução sob uma visão fundamentada em teorias de conjuntos e teoria de probabilidades

The following work is to interpret and analyze the problem of induction under a vision founded on set theory and probability theory as a basis for solution of its negative philosophical implications related to the systems of inductive logic in general. Due to the importance of the problem and the relatively recent developments in these fields of knowledge (early 20th century), as well as the visible relations between them and the process of inductive inference, it has been opened a field of relatively unexplored and promising possibilities. The key point of the study consists in modeling the information acquisition process using concepts of set theory, followed by a treatment using probability theory. Throughout the study it was identified as a major obstacle to the probabilistic justification, both: the problem of defining the concept of probability and that of rationality, as well as the subtle connection between the two. This finding called for a greater care in choosing the criterion of rationality to be considered in order to facilitate the treatment of the problem through such specific situations, but without losing their original characteristics so that the conclusions can be extended to classic cases such as the question about the continuity of the sunrise

Prova automática de satisfatibilidade módulo teoria aplicada ao método B

Este trabalho apresenta uma extensão do provador haRVey destinada à verificação de obrigações de prova originadas de acordo com o método B. O método B de desenvolvimento de software abrange as fases de especificação, projeto e implementação do ciclo de vida do software. No contexto da verificação, destacam-se as ferramentas de prova Prioni, Z/EVES e Atelier-B/Click n Prove. Elas descrevem formalismos com suporte à checagem satisfatibilidade de fórmulas da teoria axiomática dos conjuntos, ou seja, podem ser aplicadas ao método B. A checagem de SMT consiste na checagem de satisfatibilidade de fórmulas da lógica de primeira-ordem livre de quantificadores dada uma teoria decidível. A abordagem de checagem de SMT implementada pelo provador automático de teoremas haRVey é apresentada, adotando-se a teoria dos vetores que não permite expressar todas as construções necessárias às especificações baseadas em conjuntos. Assim, para estender a checagem de SMT para teorias dos conjuntos destacam-se as teorias dos conjuntos de Zermelo-Frankel (ZFC) e de von Neumann-Bernays-Gödel (NBG). Tendo em vista que a abordagem de checagem de SMT implementada no haRVey requer uma teoria finita e pode ser estendida para as teorias nãodecidíveis, a teoria NBG apresenta-se como uma opção adequada para a expansão da capacidade dedutiva do haRVey à teoria dos conjuntos. Assim, através do mapeamento dos operadores de conjunto fornecidos pela linguagem B a classes da teoria NBG, obtem-se uma abordagem alternativa para a checagem de SMT aplicada ao método B

O ensino de matemática no Rio Grande do Norte: trajetória de uma Modernização (1950-1980)

This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses

Uma abordagem híbrida para o problema de seleção de fornecedores em cadeia de suprimentos

This work presents a hybrid approach for the supplier selection problem in Supply Chain Management. We joined decision-making philosophy by researchers from business school and researchers from engineering in order to deal with the problem more extensively. We utilized traditional multicriteria decision-making methods, like AHP and TOPSIS, in order to evaluate alternatives according decision maker s preferences. The both techiniques were modeled by using definitions from the Fuzzy Sets Theory to deal with imprecise data. Additionally, we proposed a multiobjetive GRASP algorithm to perform an order allocation procedure between all pre-selected alternatives. These alternatives must to be pre-qualified on the basis of the AHP and TOPSIS methods before entering the LCR. Our allocation procedure has presented low CPU times for five pseudorandom instances, containing up to 1000 alternatives, as well as good values for all considered objectives. This way, we consider the proposed model as appropriate to solve the supplier selection problem in the SCM context. It can be used to help decision makers in reducing lead times, cost and risks in their supply chain. The proposed model can also improve firm s efficiency in relation to business strategies, according decision makers, even when a large number of alternatives must be considered, differently from classical models in purchasing literature

Probabilidades imprecisas: intervalar, fuzzy e fuzzy intuicionista

The idea of considering imprecision in probabilities is old, beginning with the Booles George work, who in 1854 wanted to reconcile the classical logic, which allows the modeling of complete ignorance, with probabilities. In 1921, John Maynard Keynes in his book made explicit use of intervals to represent the imprecision in probabilities. But only from the work ofWalley in 1991 that were established principles that should be respected by a probability theory that deals with inaccuracies. With the emergence of the theory of fuzzy sets by Lotfi Zadeh in 1965, there is another way of dealing with uncertainty and imprecision of concepts. Quickly, they began to propose several ways to consider the ideas of Zadeh in probabilities, to deal with inaccuracies, either in the events associated with the probabilities or in the values of probabilities. In particular, James Buckley, from 2003 begins to develop a probability theory in which the fuzzy values of the probabilities are fuzzy numbers. This fuzzy probability, follows analogous principles to Walley imprecise probabilities. On the other hand, the uses of real numbers between 0 and 1 as truth degrees, as originally proposed by Zadeh, has the drawback to use very precise values for dealing with uncertainties (as one can distinguish a fairly element satisfies a property with a 0.423 level of something that meets with grade 0.424?). This motivated the development of several extensions of fuzzy set theory which includes some kind of inaccuracy. This work consider the Krassimir Atanassov extension proposed in 1983, which add an extra degree of uncertainty to model the moment of hesitation to assign the membership degree, and therefore a value indicate the degree to which the object belongs to the set while the other, the degree to which it not belongs to the set. In the Zadeh fuzzy set theory, this non membership degree is, by default, the complement of the membership degree. Thus, in this approach the non-membership degree is somehow independent of the membership degree, and this difference between the non-membership degree and the complement of the membership degree reveals the hesitation at the moment to assign a membership degree. This new extension today is called of Atanassov s intuitionistic fuzzy sets theory. It is worth noting that the term intuitionistic here has no relation to the term intuitionistic as known in the context of intuitionistic logic. In this work, will be developed two proposals for interval probability: the restricted interval probability and the unrestricted interval probability, are also introduced two notions of fuzzy probability: the constrained fuzzy probability and the unconstrained fuzzy probability and will eventually be introduced two notions of intuitionistic fuzzy probability: the restricted intuitionistic fuzzy probability and the unrestricted intuitionistic fuzzy probability

Sistema especialista fuzzy para dimensionamento de bombeio mecânico

Despite the emergence of other forms of artificial lift, sucker rod pumping systems remains hegemonic because of its flexibility of operation and lower investment cost compared to other lifting techniques developed. A successful rod pumping sizing necessarily passes through the supply of estimated flow and the controlled wear of pumping equipment used in the mounted configuration. However, the mediation of these elements is particularly challenging, especially for most designers dealing with this work, which still lack the experience needed to get good projects pumping in time. Even with the existence of various computer applications on the market in order to facilitate this task, they must face a grueling process of trial and error until you get the most appropriate combination of equipment for installation in the well. This thesis proposes the creation of an expert system in the design of sucker rod pumping systems. Its mission is to guide a petroleum engineer in the task of selecting a range of equipment appropriate to the context provided by the characteristics of the oil that will be raised to the surface. Features such as the level of gas separation, presence of corrosive elements, possibility of production of sand and waxing are taken into account in selecting the pumping unit, sucker-rod strings and subsurface pump and their operation mode. It is able to approximate the inferente process in the way of human reasoning, which leads to results closer to those obtained by a specialist. For this, their production rules were based on the theory of fuzzy sets, able to model vague concepts typically present in human reasoning. The calculations of operating parameters of the pumping system are made by the API RP 11L method. Based on information input, the system is able to return to the user a set of pumping configurations that meet a given design flow, but without subjecting the selected equipment to an effort beyond that which can bear

Uma aplicação do método fuzzy-electre-topsis para seleção de serviços de computação em nuvem

This work presents an application of a hybrid Fuzzy-ELECTRE-TOPSIS multicriteria approach for a Cloud Computing Service selection problem. The research was exploratory, using a case of study based on the actual requirements of professionals in the field of Cloud Computing. The results were obtained by conducting an experiment aligned with a Case of Study using the distinct profile of three decision makers, for that, we used the Fuzzy-TOPSIS and Fuzzy-ELECTRE-TOPSIS methods to obtain the results and compare them. The solution includes the Fuzzy sets theory, in a way it could support inaccurate or subjective information, thus facilitating the interpretation of the decision maker judgment in the decision-making process. The results show that both methods were able to rank the alternatives from the problem as expected, but the Fuzzy-ELECTRE-TOPSIS method was able to attenuate the compensatory character existing in the Fuzzy-TOPSIS method, resulting in a different alternative ranking. The attenuation of the compensatory character stood out in a positive way at ranking the alternatives, because it prioritized more balanced alternatives than the Fuzzy-TOPSIS method, a factor that has been proven as important at the validation of the Case of Study, since for the composition of a mix of services, balanced alternatives form a more consistent mix when working with restrictions.

Teoria de carteiras e a alocação de parques eólicos offshore

The consumption of energy on the planet is currently based on fossil fuels. They are responsible for adverse effects on the environment. Renewables propose solutions for this scenario, but must face issues related to the capacity of the power supply. Wind energy offshore emerging as a promising alternative. The speed and stability are greater winds over oceans, but the variability of these may cause inconvenience to the generation of electric power fluctuations. To reduce this, a combination of wind farms geographically distributed was proposed. The greater the distance between them, the lower the correlation between the wind velocity, increasing the likelihood that together achieve more stable power system with less fluctuations in power generation. The efficient use of production capacity of the wind park however, depends on their distribution in marine environments. The objective of this research was to analyze the optimal allocation of wind farms offshore on the east coast of the U.S. by Modern Portfolio Theory. The Modern Portfolio Theory was used so that the process of building portfolios of wind energy offshore contemplate the particularity of intermittency of wind, through calculations of return and risk of the production of wind farms. The research was conducted with 25.934 observations of energy produced by wind farms 11 hypothetical offshore, from the installation of 01 simulated ocean turbine with a capacity of 5 MW. The data show hourly time resolution and covers the period between January 1, 1998 until December 31, 2002. Through the Matlab R software, six were calculated minimum variance portfolios, each for a period of time distinct. Given the inequality of the variability of wind over time, set up four strategies rebalancing to evaluate the performance of the related portfolios, which enabled us to identify the most beneficial to the stability of the wind energy production offshore. The results showed that the production of wind energy for 1998, 1999, 2000 and 2001 should be considered by the portfolio weights calculated for the same periods, respectively. Energy data for 2002 should use the weights derived from the portfolio calculated in the previous time period. Finally, the production of wind energy in the period 1998-2002 should also be weighted by 1/11. It follows therefore that the portfolios found failed to show reduced levels of variability when compared to the individual production of wind farms hypothetical offshore

Como vão se formando os professores em física e química: embates entre o ser, o ter e o fazer na formação de licenciandos da UFRN sob a perspectiva da teoria das representações sociais

The purpose of this work is to approach and understand the Social Representations (SR) (MOSCOVICI, 2003) about Physics and Chemistry from people who are major in these courses, as well as their Social Representations about teaching . We took as principle that approaching these representations it would be possible to relate their symbolic contents, in order to show how people who are following the first segments of bachelor degree courses in Physics and Chemistry become teachers, taking into account a psychosocial view. Two source of data was used during this research: Free-association Technique FA (ABRIC, 1994); and Multiple Classification Procedure (MCP) (ROAZZI, 1995). The analytical treatment of the collected data from FA was done according to the proposition of Grize, Vergés and Silem (1987 apud ABRIC, 1994, p. 66). MCP data were analyzed through MSA (Multidimensional Scalogram Analysis) and SSA (Singular Spectrum Analysis) methods associated with the Facet Theory (BILSKY, 2003). The discourses of MCP discussing groups at the moment of explanations were studied by Content Analysis as it was proposed by Bardin (1977) and Franco (2005). Indicative of an approach to the relations with knowledge (CHARLOT, 2000), the connections which aroused from the analyses showed that the group of future majors in Physics thought that this scientific field was based on a rationalist conception, influencing the idealization sense of the phenomena to be explained by Physics. Thus, Physics as school content started to require the student of the fundamental and high school to think abstractly as a cognitive skill of learning. The identifying elements observed in the relations between SR about Physics and Teaching aroused from the antagonism between future majors and their teacher, as well as from the speculation between their fundamental and high school students and themselves, mainly when they had to face the act of teaching due to the obstacles imposed by the own educational system, and by the weakness of the initial preparation. The group of future majors in Chemistry, through its discourses, showed these relations when they conceived empiricist Chemistry and said that teaching was the way of transmission of this knowledge, and didactics of Chemistry teaching was the direction to learning through pedagogic methods in order to lead the students to discoveries. The psychosocial contents which were built and showed from the symbolic relations in the studied SR achieved the relation of identity. This relation revealed identifying elements for these people, resulting from the traffic between their condition as students of Chemistry, and as teachers regarding their work, what placed the current relational contents in the teaching space, named as Knowledge changing and Adaptability . In order to study emerging questions in the discussing environment about formation and teaching professionalization, we focused the psychosocial view on this traffic and managed to observe epistemological practical and pedagogic obstacles that limited a configuration of the teaching work as a professional activity, especially from the particular conditions which led the relations of senses to Physics , Chemistry and Teaching ; and Chemistry and Physics as it was seen in this research. Generally speaking, we noted that these obstacles can denounce such obstacles concerning to the pedagogic doings which mainly impair the learning process of fundamental and high school students

Formação da habilidade de interpretar gráficos cartesianos em licenciandos em química segundo a teoria de P. Ya. Galperin

It has been remarkable among the Science Teaching debates the necessity that students do not learn only theories, laws and concepts, but also develop skills which allows them to act towards a critical citizenship. Therefore, some of the skills for the natural sciences learning must be taught consciously, intentionally and in a planned way, as component of a basic competence. Studies of the last twenty years have shown that students and teachers have plenty of difficulties about skills development and, among several, the skill of interpreting Cartesian graphics, essential for the comprehension of Natural Science. In that sense, the development of that type of professional knowledge during the initial education of future Chemistry teachers has become strategic, not only because they need to know how to use it, but also because they need to know how to teach it. This research has as its general objective the organization, development and study of a process of formation of the skill of interpreting Cartesian graphics as part of the teachers professional knowledge. It has been accomplished through a formative experience with six undergraduate students of the Teaching Degree Course of Chemistry of Universidade Federal do Rio Grande do Norte (UFRN Federal University of Rio Grande do Norte), in Brazil. In order to develop that skill, we have used as reference P. Ya. Galperin s Theory of the Stepwise Formation of Mental Actions and Concepts and its following qualitative indicators: action form, degree of generalization, degree of consciousness, degree of independence and degree of solidness. The research, in a qualitative approach, has prioritized as instruments of data collecting the registering of the activities of the undergraduate students, the observation, the questionnaire and the diagnosis tests. At the first moment, a teaching framework has been planned for the development of the skill of interpreting Cartesian graphics based on the presupposed conceptions and steps of Galperin s Theory. At the second moment, the referred framework has been applied and the process of the skill formation has been studied. The results have shown the possibility of develop the skill conscious about the invariant operation system, with a high degree of generalization and internalized the operational invariant in the mental plane. The students have attested the contributions at that type of formative experience. The research reveals the importance of going deeper about the teaching comprehension of the individualities tied to the process of internalization, according to Galperin s Theory, when the update of abilities as part of the teaching professional knowledge is the issue

O ensino de língua inglesa em um instituto federal : uma análise das recomendações documentais e da perspetiva dos professores

This work aims to understand the teaching of English at the Federal Institute of considering the recommendations of official and technical documents for the integrated secondary school and the perspective of the English teachers settled in one of the campuses of the Institute. It is also an objective of this research to infer as to what extent the perspective of teachers is articulated to the documental recommendations. For this purpose, several official and technical documents (LÜDKE; ANDRÉ, 1986), such as the PCNEMs (BRAZIL, 2000), the OCNEMs (BRAZIL, 2006) and the Political-Pedagogical Project of the Institute (IFRN, in press) were gathered, and a questionnaire was submitted to six teachers of English from one of the campuses of the institution. The theoretical references of the research include, among others, Bakhtin (1997; 1999), Widdowson (1991), Almeida Filho (2011; 2004), Celani (1988; 2009), Hutchinson and Waters (1987) and Dudley-Evans and St. John (1998). The results show that the teaching of English according to the documents predicts the instrumental use of the foreign language, but suggests the development of competences and skills as contextualized social practices, aimed at the education of the student as a professional-citizen. The perspective of teachers, in turn, points to a concern that the teaching of English serves as a tool for improving student life through the instrumental use of language as a means of accessing information and professional training. This finding reveals that the articulation between the documental recommendations and perspective of teachers does not go beyond what refers to the instrumental language teaching, since teachers do not show, when reporting their practices, the teaching of language as social practice, as mentioned in the legal texts

Construções com tópico marcado em cartas pessoais brasileiras dos séculos XVIII, XIX E XX

This dissertation is a research on the marked topic construction (CT) in Brazilian personal letters from eighteenth, nineteenth and twentieth centuries. The goal of our research is to verify if CT are present in the writing of Brazilians born in the centuries in question. Our research focus is based on the assumptions of generative theory (CHOMSKY 1981; 1986), which states that grammar is internalized in the mind / brain of the writers, with the emphasis on studies of grammatical change, as pointed texts by Paixão de Sousa (2004), Carneiro (2005); Galves, Namiuti and Paixão de Sousa (2006) and Martins (2009). Our corpus was extracted from Projeto Para a História do Português Brasileiro (PHPB) and Cartas Brasileiras coletânea de fontes para o estudo do português. We selected forty-six correspondents who should be inserted into the two criteria set out in this research: to be Brazilian and be born in the centuries mentioned above, so that we could find legitimate topic constructions of PB. This work is based on researches by Pontes (1987), Mateus et al. (2003), Araujo (2006, 2009), Berlinck, Duarte and Oliveira (2009), which actively support us in the study of this linguistic phenomenon in Portuguese. The results show that the marked topic construction in our corpus appear on the writing of Brazilians since the second half of the eighteenth century, while the typical constructions in Brazilian Portuguese locative topic, subject topic and copy topic - are already reflected in the I-language of the writers born in the second half of the nineteenth century and the first of the twentieth century

Segmentação fuzzy de imagens e vídeos

Image segmentation is the process of subdiving an image into constituent regions or objects that have similar features. In video segmentation, more than subdividing the frames in object that have similar features, there is a consistency requirement among segmentations of successive frames of the video. Fuzzy segmentation is a region growing technique that assigns to each element in an image (which may have been corrupted by noise and/or shading) a grade of membership between 0 and 1 to an object. In this work we present an application that uses a fuzzy segmentation algorithm to identify and select particles in micrographs and an extension of the algorithm to perform video segmentation. Here, we treat a video shot is treated as a three-dimensional volume with different z slices being occupied by different frames of the video shot. The volume is interactively segmented based on selected seed elements, that will determine the affinity functions based on their motion and color properties. The color information can be extracted from a specific color space or from three channels of a set of color models that are selected based on the correlation of the information from all channels. The motion information is provided into the form of dense optical flows maps. Finally, segmentation of real and synthetic videos and their application in a non-photorealistic rendering (NPR) toll are presented

Contribuições para o processo de verificação de satisfatibilidade módulo teoria em Event-B

Event-B is a formal method for modeling and verification of discrete transition systems. Event-B development yields proof obligations that must be verified (i.e. proved valid) in order to keep the produced models consistent. Satisfiability Modulo Theory solvers are automated theorem provers used to verify the satisfiability of logic formulas considering a background theory (or combination of theories). SMT solvers not only handle large firstorder formulas, but can also generate models and proofs, as well as identify unsatisfiable subsets of hypotheses (unsat-cores). Tool support for Event-B is provided by the Rodin platform: an extensible Eclipse based IDE that combines modeling and proving features. A SMT plug-in for Rodin has been developed intending to integrate alternative, efficient verification techniques to the platform. We implemented a series of complements to the SMT solver plug-in for Rodin, namely improvements to the user interface for when proof obligations are reported as invalid by the plug-in. Additionally, we modified some of the plug-in features, such as support for proof generation and unsat-core extraction, to comply with the SMT-LIB standard for SMT solvers. We undertook tests using applicable proof obligations to demonstrate the new features. The contributions described can potentially affect productivity in a positive manner.