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 extension of Fuzzy connectives

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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.

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

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

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.

Automação da detecção de fraudes em sistemas de medição de energia elétrica utilizando lógica fuzzy em ambiente SCADA

This works presents a proposal to make automatic the identification of energy thefts in the meter systems through Fuzzy Logic and supervisory like SCADA. The solution we find by to collect datas from meters at customers units: voltage, current, power demand, angles conditions of phasors diagrams of voltages and currents, and taking these datas by fuzzy logic with expert knowledge into a fuzzy system. The parameters collected are computed by fuzzy logic, in engineering alghorithm, and the output shows to user if the customer researched may be consuming electrical energy without to pay for it, and these feedbacks have its own membership grades. The value of this solution is a need for reduce the losses that already sets more than twenty per cent. In such a way that it is an expert system that looks for decision make with assertivity, and it looks forward to find which problems there are on site and then it wont happen problems of relationship among the utility and the customer unit. The database of an electrical company was utilized and the datas from it were worked by the fuzzy proposal and algorithm developed and the result was confirmed

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]

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

What is a Fuzzy Bi-implication?

In order to make this document self-contained, we first present all the necessary theory as a background. Then we study several definitions that extended the classic bi-implication in to the domain of well stablished fuzzy logics, namely, into the [0; 1] interval. Those approaches of the fuzzy bi-implication can be summarized as follows: two axiomatized definitions, which we proved that represent the same class of functions, four defining standard (two of them proposed by us), which varied by the number of different compound operators and what restrictions they had to satisfy. We proved that those defining standard represent only two classes of functions, having one as a proper subclass of the other, yet being both a subclass of the class represented by the axiomatized definitions. Since those three clases satisfy some contraints that we judge unnecessary, we proposed a new defining standard free of those restrictions and that represents a class of functions that intersects with the class represented by the axiomatized definitions. By this dissertation we are aiming to settle the groundwork for future research on this operator.