On Fuzzy Implication Classes - Towards Extensions of Fuzzy Rule-Based Systems

Atualmente, há diferentes definições de implicações fuzzy aceitas na literatura. Do ponto de vista teórico, esta falta de consenso demonstra que há discordâncias sobre o real significado de "implicação lógica" nos contextos Booleano e fuzzy. Do ponto de vista prático, isso gera dúvidas a respeito de quais "operadores de implicação" os engenheiros de software devem considerar para implementar um Sistema Baseado em Regras Fuzzy (SBRF). Uma escolha ruim destes operadores pode implicar em SBRF's com menor acurácia e menos apropriados aos seus domínios de aplicação. Uma forma de contornar esta situação e conhecer melhor os conectivos lógicos fuzzy. Para isso se faz necessário saber quais propriedades tais conectivos podem satisfazer. Portanto, a m de corroborar com o significado de implicação fuzzy e corroborar com a implementação de SBRF's mais apropriados, várias leis Booleanas têm sido generalizadas e estudadas como equações ou inequações nas lógicas fuzzy. Tais generalizações são chamadas de leis Boolean-like e elas não são comumente válidas em qualquer semântica fuzzy. Neste cenário, esta dissertação apresenta uma investigação sobre as condições suficientes e necessárias nas quais três leis Booleanlike like — y ≤ I(x, y), I(x, I(y, x)) = 1 e I(x, I(y, z)) = I(I(x, y), I(x, z)) — se mantém válidas no contexto fuzzy, considerando seis classes de implicações fuzzy e implicações geradas por automorfismos. Além disso, ainda no intuito de implementar SBRF's mais apropriados, propomos uma extensão para os mesmos

Segmentação fuzzy de imagens coloridas com características texturais: uma aplicação a rochas sedimentares

Image segmentation is the process of labeling pixels on di erent objects, an important step in many image processing systems. This work proposes a clustering method for the segmentation of color digital images with textural features. This is done by reducing the dimensionality of histograms of color images and using the Skew Divergence to calculate the fuzzy a nity functions. This approach is appropriate for segmenting images that have colorful textural features such as geological, dermoscopic and other natural images, as images containing mountains, grass or forests. Furthermore, experimental results of colored texture clustering using images of aquifers' sedimentary porous rocks are presented and analyzed in terms of precision to verify its e ectiveness.

On fuzzy ideals and fuzzy filters of fuzzy lattices

In the literature there are several proposals of fuzzi cation of lattices and ideals concepts. Chon in (Korean J. Math 17 (2009), No. 4, 361-374), using the notion of fuzzy order relation de ned by Zadeh, introduced a new notion of fuzzy lattice and studied the level sets of fuzzy lattices, but did not de ne a notion of fuzzy ideals for this type of fuzzy lattice. In this thesis, using the fuzzy lattices de ned by Chon, we de ne fuzzy homomorphism between fuzzy lattices, the operations of product, collapsed sum, lifting, opposite, interval and intuitionistic on bounded fuzzy lattices. They are conceived as extensions of their analogous operations on the classical theory by using this de nition of fuzzy lattices and introduce new results from these operators. In addition, we de ne ideals and lters of fuzzy lattices and concepts in the same way as in their characterization in terms of level and support sets. One of the results found here is the connection among ideals, supports and level sets. The reader will also nd the de nition of some kinds of ideals and lters as well as some results with respect to the intersection among their families. Moreover, we introduce a new notion of fuzzy ideals and fuzzy lters for fuzzy lattices de ned by Chon. We de ne types of fuzzy ideals and fuzzy lters that generalize usual types of ideals and lters of lattices, such as principal ideals, proper ideals, prime ideals and maximal ideals. The main idea is verifying that analogous properties in the classical theory on lattices are maintained in this new theory of fuzzy ideals. We also de ne, a fuzzy homomorphism h from fuzzy lattices L and M and prove some results involving fuzzy homomorphism and fuzzy ideals as if h is a fuzzy monomorphism and the fuzzy image of a fuzzy set ~h(I) is a fuzzy ideal, then I is a fuzzy ideal. Similarly, we prove for proper, prime and maximal fuzzy ideals. Finally, we prove that h is a fuzzy homomorphism from fuzzy lattices L into M if the inverse image of all principal fuzzy ideals of M is a fuzzy ideal of L. Lastly, we introduce the notion of -ideals and - lters of fuzzy lattices and characterize it by using its support and its level set. Moreover, we prove some similar properties in the classical theory of - ideals and - lters, such as, the class of -ideals and - lters are closed under intersection. We also de ne fuzzy -ideals of fuzzy lattices, some properties analogous to the classical theory are also proved and characterize a fuzzy -ideal on operation of product between bounded fuzzy lattices L and M and prove some results.

Implementação de uma arquitetura fuzzy neural em hardware com treinamento online

Computational Intelligence Methods have been expanding to industrial applications motivated by their ability to solve problems in engineering. Therefore, the embedded systems follow the same idea of using computational intelligence tools embedded on machines. There are several works in the area of embedded systems and intelligent systems. However, there are a few papers that have joined both areas. The aim of this study was to implement an adaptive fuzzy neural hardware with online training embedded on Field Programmable Gate Array – FPGA. The system adaptation can occur during the execution of a given application, aiming online performance improvement. The proposed system architecture is modular, allowing different configurations of fuzzy neural network topologies with online training. The proposed system was applied to: mathematical function interpolation, pattern classification and selfcompensation of industrial sensors. The proposed system achieves satisfactory performance in both tasks. The experiments results shows the advantages and disadvantages of online training in hardware when performed in parallel and sequentially ways. The sequentially training method provides economy in FPGA area, however, increases the complexity of architecture actions. The parallel training method achieves high performance and reduced processing time, the pipeline technique is used to increase the proposed architecture performance. The study development was based on available tools for FPGA circuits.

Técnica para segmentação automática de imagens microscópicas de componentes sanguíneos e classificação diferencial de leucócitos baseada em lógica fuzzy

Automatic detection of blood components is an important topic in the field of hematology. The segmentation is an important stage because it allows components to be grouped into common areas and processed separately and leukocyte differential classification enables them to be analyzed separately. With the auto-segmentation and differential classification, this work is contributing to the analysis process of blood components by providing tools that reduce the manual labor and increasing its accuracy and efficiency. Using techniques of digital image processing associated with a generic and automatic fuzzy approach, this work proposes two Fuzzy Inference Systems, defined as I and II, for autosegmentation of blood components and leukocyte differential classification, respectively, in microscopic images smears. Using the Fuzzy Inference System I, the proposed technique performs the segmentation of the image in four regions: the leukocyte’s nucleus and cytoplasm, erythrocyte and plasma area and using the Fuzzy Inference System II and the segmented leukocyte (nucleus and cytoplasm) classify them differentially in five types: basophils, eosinophils, lymphocytes, monocytes and neutrophils. Were used for testing 530 images containing microscopic samples of blood smears with different methods. The images were processed and its accuracy indices and Gold Standards were calculated and compared with the manual results and other results found at literature for the same problems. Regarding segmentation, a technique developed showed percentages of accuracy of 97.31% for leukocytes, 95.39% to erythrocytes and 95.06% for blood plasma. As for the differential classification, the percentage varied between 92.98% and 98.39% for the different leukocyte types. In addition to promoting auto-segmentation and differential classification, the proposed technique also contributes to the definition of new descriptors and the construction of an image database using various processes hematological staining

Sistema de contagem com morfologia matemática fuzzy

Mathematical Morphology presents a systematic approach to extract geometric features of binary images, using morphological operators that transform the original image into another by means of a third image called structuring element and came out in 1960 by researchers Jean Serra and George Matheron. Fuzzy mathematical morphology extends the operators towards grayscale and color images and was initially proposed by Goetherian using fuzzy logic. Using this approach it is possible to make a study of fuzzy connectives, which allows some scope for analysis for the construction of morphological operators and their applicability in image processing. In this paper, we propose the development of morphological operators fuzzy using the R-implications for aid and improve image processing, and then to build a system with these operators to count the spores mycorrhizal fungi and red blood cells. It was used as the hypothetical-deductive methodologies for the part formal and incremental-iterative for the experimental part. These operators were applied in digital and microscopic images. The conjunctions and implications of fuzzy morphology mathematical reasoning will be used in order to choose the best adjunction to be applied depending on the problem being approached, i.e., we will use automorphisms on the implications and observe their influence on segmenting images and then on their processing. In order to validate the developed system, it was applied to counting problems in microscopic images, extending to pathological images. It was noted that for the computation of spores the best operator was the erosion of Gödel. It developed three groups of morphological operators fuzzy, Lukasiewicz, And Godel Goguen that can have a variety applications

Segmentação fuzzy de objetos tridimensionais com propriedades texturais

Digital image segmentation is the process of assigning distinct labels to different objects in a digital image, and the fuzzy segmentation algorithm has been used successfully in the segmentation of images from several modalities. However, the traditional fuzzy segmentation algorithm fails to segment objects that are characterized by textures whose patterns cannot be successfully described by simple statistics computed over a very restricted area. In this paper we present an extension of the fuzzy segmentation algorithm that achieves the segmentation of textures by employing adaptive affinity functions as long as we extend the algorithm to tridimensional images. The adaptive affinity functions change the size of the area where they compute the texture descriptors, according to the characteristics of the texture being processed, while three dimensional images can be described as a finite set of two-dimensional images. The algorithm then segments the volume image with an appropriate calculation area for each texture, making it possible to produce good estimates of actual volumes of the target structures of the segmentation process. We will perform experiments with synthetic and real data in applications such as segmentation of medical imaging obtained from magnetic rosonance

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.

Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Fuzzy angel: uma arquitetura distribuída de telemedicina para monitoramento de pacientes com esclerose lateral amiotrófica

The Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease characterized by progressive muscle weakness that leads the patient to death, usually due to respiratory complications. Thus, as the disease progresses the patient will require noninvasive ventilation (NIV) and constant monitoring. This paper presents a distributed architecture for homecare monitoring of nocturnal NIV in patients with ALS. The implementation of this architecture used single board computers and mobile devices placed in patient’s homes, to display alert messages for caregivers and a web server for remote monitoring by the healthcare staff. The architecture used a software based on fuzzy logic and computer vision to capture data from a mechanical ventilator screen and generate alert messages with instructions for caregivers. The monitoring was performed on 29 patients for 7 con-tinuous hours daily during 5 days generating a total of 126000 samples for each variable monitored at a sampling rate of one sample per second. The system was evaluated regarding the rate of hits for character recognition and its correction through an algorithm for the detection and correction of errors. Furthermore, a healthcare team evaluated regarding the time intervals at which the alert messages were generated and the correctness of such messages. Thus, the system showed an average hit rate of 98.72%, and in the worst case 98.39%. As for the message to be generated, the system also agreed 100% to the overall assessment, and there was disagreement in only 2 cases with one of the physician evaluators.

Fuzzy angel: uma arquitetura distribuída de telemedicina para monitoramento de pacientes com esclerose lateral amiotrófica

The Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease characterized by progressive muscle weakness that leads the patient to death, usually due to respiratory complications. Thus, as the disease progresses the patient will require noninvasive ventilation (NIV) and constant monitoring. This paper presents a distributed architecture for homecare monitoring of nocturnal NIV in patients with ALS. The implementation of this architecture used single board computers and mobile devices placed in patient’s homes, to display alert messages for caregivers and a web server for remote monitoring by the healthcare staff. The architecture used a software based on fuzzy logic and computer vision to capture data from a mechanical ventilator screen and generate alert messages with instructions for caregivers. The monitoring was performed on 29 patients for 7 con-tinuous hours daily during 5 days generating a total of 126000 samples for each variable monitored at a sampling rate of one sample per second. The system was evaluated regarding the rate of hits for character recognition and its correction through an algorithm for the detection and correction of errors. Furthermore, a healthcare team evaluated regarding the time intervals at which the alert messages were generated and the correctness of such messages. Thus, the system showed an average hit rate of 98.72%, and in the worst case 98.39%. As for the message to be generated, the system also agreed 100% to the overall assessment, and there was disagreement in only 2 cases with one of the physician evaluators.

Strong primeness in fuzzy environment

The main aim of this investigation is to propose the notion of uniform and strong primeness in fuzzy environment. First, it is proposed and investigated the concept of fuzzy strongly prime and fuzzy uniformly strongly prime ideal. As an additional tool, the concept of t/m systems for fuzzy environment gives an alternative way to deal with primeness in fuzzy. Second, a fuzzy version of correspondence theorem and the radical of a fuzzy ideal are proposed. Finally, it is proposed a new concept of prime ideal for Quantales which enable us to deal with primeness in a noncommutative setting.

Strong primeness in fuzzy environment

The main aim of this investigation is to propose the notion of uniform and strong primeness in fuzzy environment. First, it is proposed and investigated the concept of fuzzy strongly prime and fuzzy uniformly strongly prime ideal. As an additional tool, the concept of t/m systems for fuzzy environment gives an alternative way to deal with primeness in fuzzy. Second, a fuzzy version of correspondence theorem and the radical of a fuzzy ideal are proposed. Finally, it is proposed a new concept of prime ideal for Quantales which enable us to deal with primeness in a noncommutative setting.