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

Identificação não linear usando uma rede fuzzy wavelet neural network modificada

In last decades, neural networks have been established as a major tool for the identification of nonlinear systems. Among the various types of networks used in identification, one that can be highlighted is the wavelet neural network (WNN). This network combines the characteristics of wavelet multiresolution theory with learning ability and generalization of neural networks usually, providing more accurate models than those ones obtained by traditional networks. An extension of WNN networks is to combine the neuro-fuzzy ANFIS (Adaptive Network Based Fuzzy Inference System) structure with wavelets, leading to generate the Fuzzy Wavelet Neural Network - FWNN structure. This network is very similar to ANFIS networks, with the difference that traditional polynomials present in consequent of this network are replaced by WNN networks. This paper proposes the identification of nonlinear dynamical systems from a network FWNN modified. In the proposed structure, functions only wavelets are used in the consequent. Thus, it is possible to obtain a simplification of the structure, reducing the number of adjustable parameters of the network. To evaluate the performance of network FWNN with this modification, an analysis of network performance is made, verifying advantages, disadvantages and cost effectiveness when compared to other existing FWNN structures in literature. The evaluations are carried out via the identification of two simulated systems traditionally found in the literature and a real nonlinear system, consisting of a nonlinear multi section tank. Finally, the network is used to infer values of temperature and humidity inside of a neonatal incubator. The execution of such analyzes is based on various criteria, like: mean squared error, number of training epochs, number of adjustable parameters, the variation of the mean square error, among others. The results found show the generalization ability of the modified structure, despite the simplification performed

Ambiente para desenvolvimento de aplicações fuzzy industriais

This paper describes the design, implementation and enforcement of a system for industrial process control based on fuzzy logic and developed using Java, with support for industrial communication protocol through the OPC (Ole for Process Control). Besides the java framework, the software is completely independent from other platforms. It provides friendly and functional tools for modeling, construction and editing of complex fuzzy inference systems, and uses these logical systems in control of a wide variety of industrial processes. The main requirements of the developed system should be flexibility, robustness, reliability and ease of expansion

Técnicas inteligentes hídridas para o controle de sistemas não lineares

A neuro-fuzzy system consists of two or more control techniques in only one structure. The main characteristic of this structure is joining one or more good aspects from each technique to make a hybrid controller. This controller can be based in Fuzzy systems, artificial Neural Networks, Genetics Algorithms or rein forced learning techniques. Neuro-fuzzy systems have been shown as a promising technique in industrial applications. Two models of neuro-fuzzy systems were developed, an ANFIS model and a NEFCON model. Both models were applied to control a ball and beam system and they had their results and needed changes commented. Choose of inputs to controllers and the algorithms used to learning, among other information about the hybrid systems, were commented. The results show the changes in structure after learning and the conditions to use each one controller based on theirs characteristics

Arquitetura de controladores fuzzy em redes foundation fieldbus

Foundation Fieldbus Industrial networks are the high standard technology which allows users to create complex control logic and totally decentralized. Although being so advanced, they still have some limitations imposed by their own technology. Attempting to solve one of these limitations, this paper describes how to design a Fuzzy controller in a Foundation Fieldbus network using their basic elements of programming, the functional blocks, so that the network remains fully independent of other devices other than the same instruments that constitute it. Moreover, in this work was developed a tool that aids this process of building the Fuzzy controller, setting the internal parameters of functional blocks and informing how many and which blocks should be used for a given structure. The biggest challenge in creating this controller is exactly the choice of blocks and how to arrange them in order to effectuate the same functions of a Fuzzy controller implemented in other kind of environment. The methodology adopted was to divide each one of the phases of a traditional Fuzzy controller and then create simple structures with the functional blocks to implement them. At the end of the work, the developed controller is compared with a Fuzzy controller implemented in a mathematical program that it has a proper tool for the development and implementation of Fuzzy controllers, obtaining comparatives graphics of performance between both

Lógica Fuzzy para Controle de pH em um Processo Petrolífero

This work proposes the design, the performance evaluation and a methodology for tuning the initial MFs parameters of output of a function based Takagi-Sugeno-Kang Fuzzy-PI controller to neutralize the pH in a stirred-tank reactor. The controller is designed to perform pH neutralization of industrial plants, mainly in units found in oil refineries where it is strongly required to mitigate uncertainties and nonlinearities. In addition, it adjusts the changes in pH regulating process, avoiding or reducing the need for retuning to maintain the desired performance. Based on the Hammerstein model, the system emulates a real plant that fits the changes in pH neutralization process of avoiding or reducing the need to retune. The controller performance is evaluated by overshoots, stabilization times, indices Integral of the Absolute Error (IAE) and Integral of the Absolute Value of the Error-weighted Time (ITAE), and using a metric developed by that takes into account both the error information and the control signal. The Fuzzy-PI controller is compared with PI and gain schedule PI controllers previously used in the testing plant, whose results can be found in the literature.

Sistema automatizado para o aproveitamento de água cinza e azul, com controle de PH utilizando lógica fuzzy

Every day, water scarcity becomes a more serious problem and, directly affects global society. Studies are directed in order to raise awareness of the rational use of this natural asset that is essential to our survival. Only 0.007% of the water available in the world have easy access and can be consumed by humans, it can be found in rivers, lakes, etc... To better take advantage of the water used in homes and small businesses, reuse projects are often implemented, resulting in savings for customers of water utilities. The reuse projects involve several areas of engineering, like Environmental, Chemical, Electrical and Computer Engineering. The last two are responsible for the control of the process, which aims to make gray water (soapy water), and clear blue water (rain water), ideal for consumption, or for use in watering gardens, flushing, among others applications. Water has several features that should be taken into consideration when it comes to working its reuse. Some of the features are, turbidity, temperature, electrical conductivity and, pH. In this document there is a proposal to control the pH (potential Hydrogen) through a microcontroller, using the fuzzy logic as strategy of control. The controller was developed in the fuzzy toolbox of Matlab®

Sistema para detecção e diagnóstico de falhas em motores elétricos de indução utilizando lógica fuzzy

Induction motors are one of the most important equipment of modern industry. However, in many situations, are subject to inadequate conditions as high temperatures and pressures, load variations and constant vibrations, for example. Such conditions, leaving them more susceptible to failures, either external or internal in nature, unwanted in the industrial process. In this context, predictive maintenance plays an important role, where the detection and diagnosis of faults in a timely manner enables the increase of time of the engine and the possibiity of reducing costs, caused mainly by stopping the production and corrective maintenance the motor itself. In this juncture, this work proposes the design of a system that is able to detect and diagnose faults in induction motors, from the collection of electrical line voltage and current, and also the measurement of engine speed. This information will use as input to a fuzzy inference system based on rules that find and classify a failure from the variation of thess quantities

Estratégia de escalonamento de controladores PID baseado em regras Fuzzy para redes industriais foundation fieldbus usando blocos padrões

The main objective of work is to show procedures to implement intelligent control strategies. This strategies are based on fuzzy scheduling of PID controllers, by using only standard function blocks of this technology. Then, the standardization of Foundation Fieldbus is kept. It was developed an environment to do the necessary tests, it validates the propose. This environment is hybrid, it has a real module (the fieldbus) and a simulated module (the process), although the control signals and measurement are real. Then, it is possible to develop controllers projects. In this work, a fuzzy supervisor was developed to schedule a network of PID controller for a non-linear plant. Analyzing its performance results to the control and regulation problem

Controle fuzzy espacialmente diferenciado para um sistema de irrigação

Traditional irrigation projects do not locally determine the water availability in the soil. Then, irregular irrigation cycles may occur: some with insufficient amount that leads to water deficit, other with excessive watering that causes lack of oxygen in plants. Due to the nonlinear nature of this problem and the multivariable context of irrigation processes, fuzzy logic is suggested to replace commercial ON-OFF irrigation system with predefined timing. Other limitation of commercial solutions is that irrigation processes either consider the different watering needs throughout plant growth cycles or the climate changes. In order to fulfill location based agricultural needs, it is indicated to monitor environmental data using wireless sensors connected to an intelligent control system. This is more evident in applications as precision agriculture. This work presents the theoretical and experimental development of a fuzzy system to implement a spatially differentiated control of an irrigation system, based on soil moisture measurement with wireless sensor nodes. The control system architecture is modular: a fuzzy supervisor determines the soil moisture set point of each sensor node area (according to the soil-plant set) and another fuzzy system, embedded in the sensor node, does the local control and actuates in the irrigation system. The fuzzy control system was simulated with SIMULINK® programming tool and was experimentally built embedded in mobile device SunSPOTTM operating in ZigBee. Controller models were designed and evaluated in different combinations of input variables and inference rules base

Controle de Temperatura do Sistema de Refrigeração a água de uma tocha plasmática Indutiva Utilizando Lógica fuzzy

Este projeto propõe desenvolver e implementar um controlador para o sistema de refrigeração da tocha indutiva a plasma térmico. Este processo é feito a partir da medição da temperatura através de um sensor do sistema de refrigeração. O sinal produzido será enviado para uma entrada analógica do microcontrolador da família PIC, que utilizando os conceitos de lógica fuzzy, controla a velocidade de um motor bomba. Este é responsável por diminuir ou aumentar o fluxo circulante de água que passa pela bobina, pelo corpo da tocha e pelo flange de fixação, deixando-os na temperatura desejada. A velocidade desta bomba será controlada por um inversor de frequência. O microcontrolador, também, acionará um ventilador caso exceda a temperatura de referência. A proposta inicial foi o desenvolvimento do controle da temperatura da bobina de uma tocha indutiva a plasma, mas com algumas adequações, foi possível também aplicar no corpo da tocha. Essa tocha será utilizada em uma planta de tratamento de resíduos industriais e efluentes petroquímicos. O controle proposto visa garantir as condições físicas necessárias para tocha de plasma, mantendo a temperatura da água em um determinado nível que permita o resfriamento sem comprometer, no entanto, o rendimento do sistema. No projeto será utilizada uma tocha de plasma com acoplamento indutivo (ICPT), por ter a vantagem de não possuir eletrodos metálicos internos sendo erodidos pelo jato de plasma, evitando uma possível contaminação, e também devido à possibilidade do reaproveitamento energético através da cogeração de energia. O desenvolvimento da tecnologia a plasma na indústria de tratamento de resíduos vem obtendo bons resultados. Aplicações com essa tecnologia têm se tornado cada vez mais importantes por reduzir, em muitos casos, a produção de resíduos e o consumo de energia em vários processos industriais

Utilização da lógica difusa no controle inteligente de sistemas eletro-hidráulicos

Electro-hydraulic servo-systems are widely employed in industrial applications such as robotic manipulators, active suspensions, precision machine tools and aerospace systems. They provide many advantages over electric motors, including high force to weight ratio, fast response time and compact size. However, precise control of electro-hydraulic systems, due to their inherent nonlinear characteristics, cannot be easily obtained with conventional linear controllers. Most flow control valves can also exhibit some hard nonlinearities such as deadzone due to valve spool overlap on the passage´s orifice of the fluid. This work describes the development of a nonlinear controller based on the feedback linearization method and including a fuzzy compensation scheme for an electro-hydraulic actuated system with unknown dead-band. Numerical results are presented in order to demonstrate the control system performance

Controle por modos deslizantes com compensação difusa aplicado a sistemas com descontinuidade

The development of non-linear controllers gained space in the theoretical ambit and of practical applications on the moment that the arising of digital computers enabled the implementation of these methodologies. In comparison with the linear controllers more utilized, the non -linear controllers present the advantage of not requiring the linearity of the system to determine the parameters of control, which permits a more efficient control especially when the system presents a high level of non-linearity. Another additional advantage is the reduction of costs, since to obtain the efficient control through linear controllers it is necessary the utilization of sensors and more refined actuators than when it is utilized a non-linear controller. Among the non-linear theories of control, the method of control by gliding ways is detached for being a method that presents more robustness, before uncertainties. It is already confirmed that the adoption of compensation on the region of residual error permits to improve better the performance of these controllers. So, in this work it is described the development of a non-linear controller that looks for an association of strategy of control by gliding ways, with the fuzzy compensation technique. Through the implementation of some strategies of fuzzy compensation, it was searched the one which provided the biggest efficiency before a system with high level of nonlinearities and uncertainties. The electrohydraulic actuator was utilized as an example of research, and the results appoint to two configurations of compensation that permit a bigger reduction of the residual error

Uma nova forma de calcular os centros dos Clusters em algoritmos de agrupamento tipo fuzzy c-means

Clustering data is a very important task in data mining, image processing and pattern recognition problems. One of the most popular clustering algorithms is the Fuzzy C-Means (FCM). This thesis proposes to implement a new way of calculating the cluster centers in the procedure of FCM algorithm which are called ckMeans, and in some variants of FCM, in particular, here we apply it for those variants that use other distances. The goal of this change is to reduce the number of iterations and processing time of these algorithms without affecting the quality of the partition, or even to improve the number of correct classifications in some cases. Also, we developed an algorithm based on ckMeans to manipulate interval data considering interval membership degrees. This algorithm allows the representation of data without converting interval data into punctual ones, as it happens to other extensions of FCM that deal with interval data. In order to validate the proposed methodologies it was made a comparison between a clustering for ckMeans, K-Means and FCM algorithms (since the algorithm proposed in this paper to calculate the centers is similar to the K-Means) considering three different distances. We used several known databases. In this case, the results of Interval ckMeans were compared with the results of other clustering algorithms when applied to an interval database with minimum and maximum temperature of the month for a given year, referring to 37 cities distributed across continents

On extension of Fuzzy connectives

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