Two types of fuzzy linear programming i.e. fuzzy number linear programming and interval number linear programming are used for optimization problems. In interval form of linear programming we convert the inequalities from the feasible region, containing intervals as coefficients, to two groups of inequalities characterized by real, exact coefficients values. Then classical programming has been used to achieve an optimal solution in the feasible region. In fuzzy number linear programming, α‐cuts and LR forms of fuzzy numbers as coefficients have been used to find optimal solution in the feasible region. Finally the numerical examples and their solutions are attached to provide explanations of procedures.

Thesis (Ph. D.)--University of Alabama at Birmingham, 2007. / Additional advisors: Ian Knowles, Kevin D. Reilly, Peter Slarter, Wei-Shen Hsia. Description based on contents viewed June 10, 2008; title from title screen. Includes bibliographical references.

As imagens digitais são frequentemente corrompidas por ruídos ou distorcidas pelo processo de aquisição. A teoria dos conjuntos fuzzy e a lógica fuzzy constituem uma alternativa mais adequada para lidar com tais incertezas, em comparação com os sistemas convencionais, baseados na lógica tradicional (crisp). Este trabalho propõe uma nova metodologia para análise de micropadrões de imagens digitais baseada em números fuzzy. Um micropadrão é uma estrutura de níveis de cinza dos pixels de uma vizinhança e pode descrever o contexto espacial da imagem, como borda, textura, linha, canto e padrões mais complexos. Na literatura de visão computacional, algumas abordagens foram desenvolvidas para extrair estas características, tais como Texture Unit (TU), Local Binary Pattern (LBP) e Fuzzy Number Edge Detector (FUNED). O trabalho apresenta um novo método que modela a distribuição dos níveis de cinza de um micropadrão como um conjunto fuzzy, e com base nas funções de pertinência usadas gera códigos-fuzzy que representam o grau de pertinência de cada pixel vizinho com nível de cinza próximo do pixel central. A metodologia proposta é chamada de Local Fuzzy Pattern (LFP) e é aplicada na análise de textura usando a função sigmoide (LFP-s), a função triangular e simétrica (LFP-t) e a função gaussiana (LFP-g) para calcular o grau de pertinência do pixel central em relação à sua vizinhança. Para avaliar o desempenho da técnica proposta foram usados bases de texturas, cujas imagens foram amostradas aleatoriamente. Após processá-las pelas abordagens LFP-s, LFP-t, LFP-g e LBP, foram comparadas as taxas de acertos alcançadas usando a distância Chi-quadrado. Nos experimentos realizados também é avaliado o esforço computacional do LFP, comparando-o com o descritor LBP. Os resultados mostram que o LFP é eficaz na descrição de textura e que supera o LBP nos diferentes testes realizados. Neste trabalho também é demonstrado que a formulação do LFP é uma generalização de técnicas previamente publicadas, como Texture Unit, Local Binary Pattern e FUNED. / Digital images are often corrupted by noise and distorted by the acquisition process. The fuzzy set theory and fuzzy logic are an alternative more appropriate to deal with these uncertainties, in comparison with conventional treatment based on traditional logic (crisp). This work proposes a new methodology for the analysis of micro-patterns of digital images based on fuzzy numbers. A micro-pattern is the structure of the gray-level pixels within a neighborhood and can describe the spatial context of the image, such as edge, texture, line, corner and more complex patterns. In the literature of computer vision, some approaches have been developed to extract these features, such as Texture Unit (TU), Local Binary Pattern (LBP) and Fuzzy Number Edge Detector (FUNED). This work presents a new method that models the distribution of the gray levels of a micro-pattern as a fuzzy set, and based on the membership functions used generates fuzzy-codes that represent the membership degree of each neighbor pixel neighbor with gray-levels near of the central pixel. The proposed methodology is called Local Fuzzy Pattern (LFP) and is applied in the texture analysis by using a sigmoid (LFP-s), a symmetrical triangular (LFP-t) function and Gaussian function (LFP-g) for calculating the membership degree of a central pixel of a neighborhood. To evaluate the performance of the proposed technique were used two database, whose images were randomly sampled. After processing these images by the LFP-s, LFP-t, LFP-g and LBP approaches, it was compared the hit-rate reached by using the Chi-square distance. In the experiments also evaluated the computational effort of the LFP and surpasses the LBP that the different tests. The results show that the LFP-s is efficient to describe texture and that it surpasses the LBP in different tests. This work also demonstrates that the proposed formulation for the LFP is a generalization of previously published techniques such as Texture Unit, LBP and FUNED.

As imagens digitais são frequentemente corrompidas por ruídos ou distorcidas pelo processo de aquisição. A teoria dos conjuntos fuzzy e a lógica fuzzy constituem uma alternativa mais adequada para lidar com tais incertezas, em comparação com os sistemas convencionais, baseados na lógica tradicional (crisp). Este trabalho propõe uma nova metodologia para análise de micropadrões de imagens digitais baseada em números fuzzy. Um micropadrão é uma estrutura de níveis de cinza dos pixels de uma vizinhança e pode descrever o contexto espacial da imagem, como borda, textura, linha, canto e padrões mais complexos. Na literatura de visão computacional, algumas abordagens foram desenvolvidas para extrair estas características, tais como Texture Unit (TU), Local Binary Pattern (LBP) e Fuzzy Number Edge Detector (FUNED). O trabalho apresenta um novo método que modela a distribuição dos níveis de cinza de um micropadrão como um conjunto fuzzy, e com base nas funções de pertinência usadas gera códigos-fuzzy que representam o grau de pertinência de cada pixel vizinho com nível de cinza próximo do pixel central. A metodologia proposta é chamada de Local Fuzzy Pattern (LFP) e é aplicada na análise de textura usando a função sigmoide (LFP-s), a função triangular e simétrica (LFP-t) e a função gaussiana (LFP-g) para calcular o grau de pertinência do pixel central em relação à sua vizinhança. Para avaliar o desempenho da técnica proposta foram usados bases de texturas, cujas imagens foram amostradas aleatoriamente. Após processá-las pelas abordagens LFP-s, LFP-t, LFP-g e LBP, foram comparadas as taxas de acertos alcançadas usando a distância Chi-quadrado. Nos experimentos realizados também é avaliado o esforço computacional do LFP, comparando-o com o descritor LBP. Os resultados mostram que o LFP é eficaz na descrição de textura e que supera o LBP nos diferentes testes realizados. Neste trabalho também é demonstrado que a formulação do LFP é uma generalização de técnicas previamente publicadas, como Texture Unit, Local Binary Pattern e FUNED. / Digital images are often corrupted by noise and distorted by the acquisition process. The fuzzy set theory and fuzzy logic are an alternative more appropriate to deal with these uncertainties, in comparison with conventional treatment based on traditional logic (crisp). This work proposes a new methodology for the analysis of micro-patterns of digital images based on fuzzy numbers. A micro-pattern is the structure of the gray-level pixels within a neighborhood and can describe the spatial context of the image, such as edge, texture, line, corner and more complex patterns. In the literature of computer vision, some approaches have been developed to extract these features, such as Texture Unit (TU), Local Binary Pattern (LBP) and Fuzzy Number Edge Detector (FUNED). This work presents a new method that models the distribution of the gray levels of a micro-pattern as a fuzzy set, and based on the membership functions used generates fuzzy-codes that represent the membership degree of each neighbor pixel neighbor with gray-levels near of the central pixel. The proposed methodology is called Local Fuzzy Pattern (LFP) and is applied in the texture analysis by using a sigmoid (LFP-s), a symmetrical triangular (LFP-t) function and Gaussian function (LFP-g) for calculating the membership degree of a central pixel of a neighborhood. To evaluate the performance of the proposed technique were used two database, whose images were randomly sampled. After processing these images by the LFP-s, LFP-t, LFP-g and LBP approaches, it was compared the hit-rate reached by using the Chi-square distance. In the experiments also evaluated the computational effort of the LFP and surpasses the LBP that the different tests. The results show that the LFP-s is efficient to describe texture and that it surpasses the LBP in different tests. This work also demonstrates that the proposed formulation for the LFP is a generalization of previously published techniques such as Texture Unit, LBP and FUNED.

Kokybiška mokomoji medžiaga yra viena svarbiausių mokymo(-si) kokybės veiksnių, todėl mokomųjų objektų (toliau – MO) daugkartinio panaudojamumo kokybės vertinimas yra viena opiausių švietimo problemų. Problema yra aktuali visiems švietimo dalyviams – švietimo įstaigoms (pvz., mokykloms), kurios turi išrinkti kokybišką mokomąją medžiagą (MO) savo tikslams pasiekti, švietimo politikams, kuriems reikia aiškių kokybės kriterijų vykdant MO viešuosius pirkimus, mokomosios medžiagos autoriams (pvz., leidykloms), kurie turi žinoti kokybės reikalavimus, remdamiesi kuriais jie kurs MO, ir pan. Disertacinis darbas skirtas pasiūlyti ir išbandyti MO daugkartinio panaudojamumo kokybės vertinimo metodiką: kokybės modelį ir paprastus bei efektyvius ekspertinio kokybės vertinimo metodus (t.y., pagerinti edukologinių uždavinių sprendimo galimybes naudojant informatikos inžinerijos metodus). Tam analizuojamos MO daugkartinio panaudojamumo ir ekspertinio kokybės vertinimo sąvokos, kokybės modelio sudarymo principai, galimi paprasti ir efektyvūs kokybės ekspertinio vertinimo metodai. Darbe yra pateiktas sukurtas mokomųjų objektų daugkartinio panaudojamumo kokybės modelis ir vertinimo metodas. Mokomųjų objektų kokybės modelį sudaro devyni trijų grupių (technologiniai, pedagoginiai, intelektinių teisių) kokybės kriterijai, kurie atspindi visapusišką kokybės kriterijų sistemą, kurioje yra svarbūs ne tik patys kriterijai, bet ir jų tarpusavio sąryšiai. Mokomųjų objektų daugkartinio panaudojamumo... [toliau žr. visą tekstą] / Qualitative learning material (or Learning Objects – LOs) is one of the main factors of learning quality. Therefore, evaluation of LOs quality is one of the most relevant education problems. The problem is relevant for all participants of the educational sector – for educational institutions (e.g. schools) that have to select qualitative learning material for their needs, for education policy makers who need clear quality criteria while implementing LOs tenders, for authors of learning material (e.g. publishers) who need to know quality requirements to create LOs etc. The research work is aimed to propose and pilot LOs reusability and quality evaluation methodology, i.e., quality model, and simple and effective expert evaluation methods, thus improving solution of educational tasks using informatics engineering methods. To reach this aim, we have to analyse the notions of LOs reusability and expert evaluation of quality, principles of creating LOs reusability and quality model, and possible simple and effective methods for the expert evaluation of LOs quality and reusability. Both LO quality and reusability model and evaluation method are presented in the work. LO quality model created consists of 9 quality criteria divided into 3 groups i.e. technological, pedagogical, and IPR criteria. This model is comprehensive and matches scientific principles of creating a model. The following methods are selected and consecutively applied in the research while evaluating LOs quality... [to full text]

Qualitative learning material (or Learning Objects – LOs) is one of the main factors of learning quality. Therefore, evaluation of LOs quality is one of the most relevant education problems. The problem is relevant for all participants of the educational sector – for educational institutions (e.g. schools) that have to select qualitative learning material for their needs, for education policy makers who need clear quality criteria while implementing LOs tenders, for authors of learning material (e.g. publishers) who need to know quality requirements to create LOs etc. The research work is aimed to propose and pilot LOs reusability and quality evaluation methodology, i.e., quality model, and simple and effective expert evaluation methods, thus improving solution of educational tasks using informatics engineering methods. To reach this aim, we have to analyse the notions of LOs reusability and expert evaluation of quality, principles of creating LOs reusability and quality model, and possible simple and effective methods for the expert evaluation of LOs quality and reusability. Both LO quality and reusability model and evaluation method are presented in the work. LO quality model created consists of 9 quality criteria divided into 3 groups i.e. technological, pedagogical, and IPR criteria. This model is comprehensive and matches scientific principles of creating a model. The following methods are selected and consecutively applied in the research while evaluating LOs quality... [to full text] / Kokybiška mokomoji medžiaga yra viena svarbiausių mokymo(-si) kokybės veiksnių, todėl mokomųjų objektų (toliau – MO) daugkartinio panaudojamumo kokybės vertinimas yra viena opiausių švietimo problemų. Problema yra aktuali visiems švietimo dalyviams – švietimo įstaigoms (pvz., mokykloms), kurios turi išrinkti kokybišką mokomąją medžiagą (MO) savo tikslams pasiekti, švietimo politikams, kuriems reikia aiškių kokybės kriterijų vykdant MO viešuosius pirkimus, mokomosios medžiagos autoriams (pvz., leidykloms), kurie turi žinoti kokybės reikalavimus, remdamiesi kuriais jie kurs MO, ir pan. Disertacinis darbas skirtas pasiūlyti ir išbandyti MO daugkartinio panaudojamumo kokybės vertinimo metodiką: kokybės modelį ir paprastus bei efektyvius ekspertinio kokybės vertinimo metodus (t.y., pagerinti edukologinių uždavinių sprendimo galimybes naudojant informatikos inžinerijos metodus). Tam analizuojamos MO daugkartinio panaudojamumo ir ekspertinio kokybės vertinimo sąvokos, kokybės modelio sudarymo principai, galimi paprasti ir efektyvūs kokybės ekspertinio vertinimo metodai. Darbe yra pateiktas sukurtas mokomųjų objektų daugkartinio panaudojamumo kokybės modelis ir vertinimo metodas. Mokomųjų objektų kokybės modelį sudaro devyni trijų grupių (technologiniai, pedagoginiai, intelektinių teisių) kokybės kriterijai, kurie atspindi visapusišką kokybės kriterijų sistemą, kurioje yra svarbūs ne tik patys kriterijai, bet ir jų tarpusavio sąryšiai. Mokomųjų objektų daugkartinio panaudojamumo... [toliau žr. visą tekstą]

Orientador: Laécio Carvalho de Barros / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T12:45:04Z (GMT). No. of bitstreams: 1 Cabral_ValtemirMartins_D.pdf: 2169233 bytes, checksum: c4051eaa1a73354d7ada77be53b8fd51 (MD5) Previous issue date: 2011 / Resumo: Neste trabalho estudamos as equações diferenciais fuzzy (EDF) que possuem coeficientes e/ou condições iniciais incertas e modeladas por conjuntos fuzzy interativos. São estudadas duas formas de interatividade: via t-normas e pelo conceito de números fuzzy completamente correlacionados. As EDF são tratadas de duas formas distintas: Via inclusão diferencial e via princípio de extensão. Provamos que os conjuntos atingíveis através da família de inclusões diferenciais coincidem com as soluções estendidas, via extensão do sistema determinístico associado. Quando a interatividade é definida a partir das t-normas básicas, são gerados 4 problemas de valor inicial com parâmetro fuzzy. Para estes problemas, mostramos que os diâmetros das soluções satisfazem uma relação de inclusão. Quando a interatividade é dada por conjuntos fuzzy completamente correlacionados verificamos que a solução da EDF associada possui diâmetro contido na solução da EDF com parâmetros não interativos. Além disso, mostramos que neste ambiente o Teorema de Nguyen permanece válido. Propomos um modelo SI com parâmetros completamente correlacionados e um modelo para a dinâmica HIV com retardo e taxa de mortalidade do vírus completamente correlacionados. Para o modelo HIV apresentamos uma solução fuzzy e a comparamos com solução obtida por Jafelice et al [36] na qual os parâmetros da equação diferencial fuzzy são não interativos / Abstract: In this work we study the fuzzy differential equations (EDF) that have coefficients and/or initial conditions uncertain and modeled by interactive fuzzy sets. Are studied two forms of interactivity: via t-norms and the concept of completely correlated fuzzy numbers. The EDF are treated of two different forms: Via differential inclusion and extension principle. We prove that the sets attainable through the family of differential inclusions coincide with the extended solutions, via extension of the associated deterministic system. When the interactivity is defined from the basic 4 t- norm, are generated 4 initial value problems with fuzzy parameters. For these problems, we show that the diameters of the solutions satisfy a relation of inclusion. When the interactivity is given by completely correlated fuzzy sets, we verified the solution of the EDF associated have diameters contained in the solution of the EDF with noninteractive parameters. Furthermore we show that this environment the Nguyen's Theorem remain valid. We propose a model SI with completely correlated parameters and a model for HIV dynamics with delay and mortality rate of the virus completely correlated. For the HIV we present a fuzzy solution and we compared it with the solution obtained by Jafelice et al [36] in which the parameters of fuzzy differential equation are not interactive / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

El objetivo en esta Memoría ha sido el análisis de eficiencia de un determinado sector empresarial, teniendo en cuenta dos problemas casi siempre presentes, y de naturaleza muy diferente, por una parte, que los datos que se manejan pueden ser imprecisos y, por tanto, afectar al resultado de cualquier estudio de eficiencia y, por otra parte, el deseo de ordenar las empresas (Unidades De Toma de Decisión) atendiendo a la medición de su eficiencia. Para la medición de la eficiencia se ha recurrido a la metodología no paramétrica del Análisis Envolvente de datos (DEA) aplicandola a empresas del sector textil muy cercanas a nosotros. Ahora bien, dado que consideramos que siempre existe alguna incertidumbre o un posible error en la medición de algunos datos (inputs y outputs), introducimos la limitación de la certeza con el tratamiento fuzzy de los datos, métodos que no requieren conocer ni aplicar hipótesis sobre distribuciones de probabilidad de esos datos, que dicho sea de paso, podría no ser fáctible bajo determinados supuestos de incertidumbre. Pero además de la medir la eficiencia pretendemos proporcionar más información que la mera separación dicotómica entre empresas eficientes o no eficientes. Para ello desarrollamos y aplicamos los modelos de super-efficiencyfuzzy y cross-efficiency-fuzzy, que nos permiten establecer una ordenación bajo incertidumbre. Con este trabajo hemos realizado un estudio amplio de la eficiencia bajo incertidumbre. Se observa que los resultados obtenidos aplicando los distintos métodos son similares. Además, estos métodos proporcionan más información sobre las unidades estudiadas que las que proporciona un solo índice de eficiencia. Estos métodos pueden ser aplicables a otros tipos de empresas, aportando nueva información que puede ayudar u orientar en la toma de decisiones de sus gestores / Pla Ferrando, ML. (2013). Modelos flexibles para la valoración de la eficiencia [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/31521 / TESIS

Yes / Fuzzy data-driven reliability analysis has been used in different safety-critical domains for risk assessment and decision-making where precise failure data is non-existent. Expert judgements and fuzzy set theory have been combined with different variants of fault trees as part of fuzzy data-driven reliability analysis studies. In such fuzzy fault tree analyses, different people represented failure data using different membership functions for the fuzzy set, and different parameters were set differently in the expert opinion elicitation process. Due to the availability of a wide variety of options, it is possible to obtain different outcomes when choosing one option over another. This article performed an analysis in the context of fuzzy data-based temporal fault tree analysis to investigate the effect of choosing different membership functions on the estimated system reliability and criticality ranking of different failure events. Moreover, the effect of using different values for the relaxation factor, a parameter set during the expert elicitation process, was studied on the system reliability and criticality evaluation. The experiments on the fuel distribution system case study show system reliability did not vary when triangular and trapezoidal fuzzy numbers were used with the same upper and lower bounds. However, it was seen that the criticality rankings of a couple of events were changed due to choosing different membership functions and different values of relaxation factor

Software effort estimation by analogy is a viable alternative method to other estimation techniques, and in many cases, researchers found it outperformed other estimation methods in terms of accuracy and practitioners' acceptance. However, the overall performance of analogy based estimation depends on two major factors: similarity measure and attribute selection & weighting. Current similarity measures such as nearest neighborhood techniques have been criticized that have some inadequacies related to attributes relevancy, noise and uncertainty in addition to the problem of using categorical attributes. This research focuses on improving the efficiency and flexibility of analogy-based estimation to overcome the abovementioned inadequacies. Particularly, this thesis proposes two new approaches to model and handle uncertainty in similarity measurement method and most importantly to reflect the structure of dataset on similarity measurement using Fuzzy modeling based Fuzzy C-means algorithm. The first proposed approach called Fuzzy Grey Relational Analysis method employs combined techniques of Fuzzy set theory and Grey Relational Analysis to improve local and global similarity measure and tolerate imprecision associated with using different data types (Continuous and Categorical). The second proposed approach presents the use of Fuzzy numbers and its concepts to develop a practical yet efficient approach to support analogy-based systems especially at early phase of software development. Specifically, we propose a new similarity measure and adaptation technique based on Fuzzy numbers. We also propose a new attribute subset selection algorithm and attribute weighting technique based on the hypothesis of analogy-based estimation that assumes projects that are similar in terms of attribute value are also similar in terms of effort values, using row-wise Kendall rank correlation between similarity matrix based project effort values and similarity matrix based project attribute values. A literature review of related software engineering studies revealed that the existing attribute selection techniques (such as brute-force, heuristic algorithms) are restricted to the choice of performance indicators such as (Mean of Magnitude Relative Error and Prediction Performance Indicator) and computationally far more intensive. The proposed algorithms provide sound statistical basis and justification for their procedures. The performance figures of the proposed approaches have been evaluated using real industrial datasets. Results and conclusions from a series of comparative studies with conventional estimation by analogy approach using the available datasets are presented. The studies were also carried out to statistically investigate the significant differences between predictions generated by our approaches and those generated by the most popular techniques such as: conventional analogy estimation, neural network and stepwise regression. The results and conclusions indicate that the two proposed approaches have potential to deliver comparable, if not better, accuracy than the compared techniques. The results also found that Grey Relational Analysis tolerates the uncertainty associated with using different data types. As well as the original contributions within the thesis, a number of directions for further research are presented. Most chapters in this thesis have been disseminated in international journals and highly refereed conference proceedings.