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

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.

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

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On extension of Fuzzy connectives

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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

Algoritmos de agrupamentos fuzzy intervalares e índice de validação para agrupamento de dados simbólicos do tipo intervalo

Symbolic Data Analysis (SDA) main aims to provide tools for reducing large databases to extract knowledge and provide techniques to describe the unit of such data in complex units, as such, interval or histogram. The objective of this work is to extend classical clustering methods for symbolic interval data based on interval-based distance. The main advantage of using an interval-based distance for interval-based data lies on the fact that it preserves the underlying imprecision on intervals which is usually lost when real-valued distances are applied. This work includes an approach allow existing indices to be adapted to interval context. The proposed methods with interval-based distances are compared with distances punctual existing literature through experiments with simulated data and real data interval

Detecção de interface em tanques de petróleo usando transmissores de nível e controladores Fuzzy

This work presents a proposal to detect interface in atmospheric oil tanks by installing a differential pressure level transmitter to infer the oil-water interface. The main goal of this project is to maximize the quantity of free water that is delivered to the drainage line by controlling the interface. A Fuzzy Controller has been implemented by using the interface transmitter as the Process Variable. Two ladder routine was generated to perform the control. One routine was developed to calculate the error and error variation. The other was generate to develop the fuzzy controller itself. By using rules, the fuzzy controller uses these variables to set the output. The output is the position variation of the drainage valve. Although the ladder routine was implemented into an Allen Bradley PLC, Control Logix family it can be implemented into any brand of PLCs

Técnicas de inteligência artificial para a geração dinâmica de set points para uma coluna de destilação

Artificial Intelligence techniques are applied to improve performance of a simulated oil distillation system. The chosen system was a debutanizer column. At this process, the feed, which comes to the column, is segmented by heating. The lightest components become steams, by forming the LPG (Liquefied Petroleum Gas). The others components, C5+, continue liquid. In the composition of the LPG, ideally, we have only propane and butanes, but, in practice, there are contaminants, for example, pentanes. The objective of this work is to control pentane amount in LPG, by means of intelligent set points (SP s) determination for PID controllers that are present in original instrumentation (regulatory control) of the column. A fuzzy system will be responsible for adjusting the SP's, driven by the comparison between the molar fraction of the pentane present in the output of the plant (LPG) and the desired amount. However, the molar fraction of pentane is difficult to measure on-line, due to constraints such as: long intervals of measurement, high reliability and low cost. Therefore, an inference system was used, based on a multilayer neural network, to infer the pentane molar fraction through secondary variables of the column. Finally, the results shown that the proposed control system were able to control the value of pentane molar fraction under different operational situations

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

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

The Interval Constructor on classes of ML-algebras

Monoidal logic, ML for short, which formalized the fuzzy logics of continuous t-norms and their residua, has arisen great interest, since it has been applied to fuzzy mathematics, artificial intelligence, and other areas. It is clear that fuzzy logics basically try to represent imperfect or fuzzy information aiming to model the natural human reasoning. On the other hand, in order to deal with imprecision in the computational representation of real numbers, the use of intervals have been proposed, as it can guarantee that the results of numerical computation are in a bounded interval, controlling, in this way, the numerical errors produced by successive roundings. There are several ways to connect both areas; the most usual one is to consider interval membership degrees. The algebraic counterpart of ML is ML-algebra, an interesting structure due to the fact that by adding some properties it is possible to reach different classes of residuated lattices. We propose to apply an interval constructor to ML-algebras and some of their subclasses, to verify some properties within these algebras, in addition to the analysis of the algebraic aspects of them

Lógica BDI fuzzy

Intendding to understand how the human mind operates, some philosophers and psycologists began to study about rationality. Theories were built from those studies and nowadays that interest have been extended to many other areas such as computing engineering and computing science, but with a minimal distinction at its goal: to understand the mind operational proccess and apply it on agents modelling to become possible the implementation (of softwares or hardwares) with the agent-oriented paradigm where agents are able to deliberate their own plans of actions. In computing science, the sub-area of multiagents systems has progressed using several works concerning artificial intelligence, computational logic, distributed systems, games theory and even philosophy and psycology. This present work hopes to show how it can be get a logical formalisation extention of a rational agents architecture model called BDI (based in a philosophic Bratman s Theory) in which agents are capable to deliberate actions from its beliefs, desires and intentions. The formalisation of this model is called BDI logic and it is a modal logic (in general it is a branching time logic) with three access relations: B, D and I. And here, it will show two possible extentions that tranform BDI logic in a modal-fuzzy logic where the formulae and the access relations can be evaluated by values from the interval [0,1]

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

Novos métodos determinísticos para gerar centros iniciais dos grupos no algoritmo fuzzy C-Means e variantes

Data clustering is applied to various fields such as data mining, image processing and pattern recognition technique. Clustering algorithms splits a data set into clusters such that elements within the same cluster have a high degree of similarity, while elements belonging to different clusters have a high degree of dissimilarity. The Fuzzy C-Means Algorithm (FCM) is a fuzzy clustering algorithm most used and discussed in the literature. The performance of the FCM is strongly affected by the selection of the initial centers of the clusters. Therefore, the choice of a good set of initial cluster centers is very important for the performance of the algorithm. However, in FCM, the choice of initial centers is made randomly, making it difficult to find a good set. This paper proposes three new methods to obtain initial cluster centers, deterministically, the FCM algorithm, and can also be used in variants of the FCM. In this work these initialization methods were applied in variant ckMeans.With the proposed methods, we intend to obtain a set of initial centers which are close to the real cluster centers. With these new approaches startup if you want to reduce the number of iterations to converge these algorithms and processing time without affecting the quality of the cluster or even improve the quality in some cases. Accordingly, cluster validation indices were used to measure the quality of the clusters obtained by the modified FCM and ckMeans algorithms with the proposed initialization methods when applied to various data sets

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