Fuzzy ARTMAP, Slow Learning and Probability Estimation

A nonparametric probability estimation procedure using the fuzzy ARTMAP neural network is here described. Because the procedure does not make a priori assumptions about underlying probability distributions, it yields accurate estimates on a wide variety of prediction tasks. Fuzzy ARTMAP is used to perform probability estimation in two different modes. In a 'slow-learning' mode, input-output associations change slowly, with the strength of each association computing a conditional probability estimate. In 'max-nodes' mode, a fixed number of categories are coded during an initial fast learning interval, and weights are then tuned by slow learning. Simulations illustrate system performance on tasks in which various numbers of clusters in the set of input vectors mapped to a given class.

Towards Possibilistic Fuzzy Answer Set Programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers.

Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Design of a Takagi-Sugeno Fuzzy Regulator for a Set of Operation Points

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

Fuzzy community structure detection by particle competition and cooperation

Identification and classification of overlapping nodes in networks are important topics in data mining. In this paper, a network-based (graph-based) semi-supervised learning method is proposed. It is based on competition and cooperation among walking particles in a network to uncover overlapping nodes by generating continuous-valued outputs (soft labels), corresponding to the levels of membership from the nodes to each of the communities. Moreover, the proposed method can be applied to detect overlapping data items in a data set of general form, such as a vector-based data set, once it is transformed to a network. Usually, label propagation involves risks of error amplification. In order to avoid this problem, the proposed method offers a mechanism to identify outliers among the labeled data items, and consequently prevents error propagation from such outliers. Computer simulations carried out for synthetic and real-world data sets provide a numeric quantification of the performance of the method. © 2012 Springer-Verlag.

Metodologia baseada em sistema fuzzy intervalar do tipo-2 para detecção e identificação de faltas de incipientes em motores de indução

Desde a incorporação da automação no processo produtivo, a busca por sistemas mais eficientes, objetivando o aumento da produtividade e da qualidade dos produtos e serviços, direcionou os estudos para o planejamento de estratégias que permitissem o monitoramento de sistemas com o intuito principal de torna-los mais autônomos e robustos. Por esse motivo, as pesquisas envolvendo o diagnóstico de faltas em sistemas industriais tornaram-se mais intensivas, visto a necessidade da incorporação de técnicas para monitoramente detalhado de sistemas. Tais técnicas permitem a verificação de perturbações, falta ou mesmo falhas. Em vista disso, essa trabalho investiga técnicas de detecção e diagnostico de faltas e sua aplicação em motores de indução trifásicos, delimitando o seu estudo em duas situações: sistemas livre de faltas, e sobre atuação da falta incipiente do tipo curto-circuitoparcial nas espiras do enrolamento do estator. Para a detecção de faltas, utilizou-se analise paramétrica dos parâmetros de um modelo de tempo discreto, de primeira ordem, na estrutura autoregressivo com entradas exógenas (ARX). Os parâmetros do modelo ARX, que trazem informação sobre a dinâmica dominante do sistema, são obtidos recursivamente pela técnica dos mínimos quadrados recursivos (MQR). Para avaliação da falta, foi desenvolvido um sistema de inferência fuzzy (SIF) intervala do tipo-2, cuja mancha de incerteza ou footprint of uncertainty (FOU), características de sistema fuzzy tipo-2, é ideal como forma de representar ruídos inerentes a sistemas reais e erros numéricos provenientes do processo de estimação paramétrica. Os parâmetros do modelo ARX são entradas para o SIF. Algoritmos genéricos (AG’s) foram utilizados para otimização dos SIF intervalares tipo-2, objetivando reduzir o erro de diagnóstico da falta identificada na saída desses sistemas. Os resultados obtidos em teste de simulação computacional demonstram a efetividade da metodologia proposta.

Fuzzy min-max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes.

Two Consistent Many-Valued Logics for Paraconsistent Phenomena

In this reviewing paper, we recall the main results of our papers [24, 31] where we introduced two paraconsistent semantics for Pavelka style fuzzy logic. Each logic formula a is associated with a 2 x 2 matrix called evidence matrix. The two semantics are consistent if they are seen from 'outside'; the structure of the set of the evidence matrices M is an MV-algebra and there is nothing paraconsistent there. However, seen from "inside,' that is, in the construction of a single evidence matrix paraconsistency comes in, truth and falsehood are not each others complements and there is also contradiction and lack of information (unknown) involved. Moreover, we discuss the possible applications of the two logics in real-world phenomena.

A new fuzzy additive model for determining the common set of weights in Data Envelopment Analysis

The main advantage of Data Envelopment Analysis (DEA) is that it does not require any priori weights for inputs and outputs and allows individual DMUs to evaluate their efficiencies with the input and output weights that are only most favorable weights for calculating their efficiency. It can be argued that if DMUs are experiencing similar circumstances, then the pricing of inputs and outputs should apply uniformly across all DMUs. That is using of different weights for DMUs makes their efficiencies unable to be compared and not possible to rank them on the same basis. This is a significant drawback of DEA; however literature observed many solutions including the use of common set of weights (CSW). Besides, the conventional DEA methods require accurate measurement of both the inputs and outputs; however, crisp input and output data may not relevant be available in real world applications. This paper develops a new model for the calculation of CSW in fuzzy environments using fuzzy DEA. Further, a numerical example is used to show the validity and efficacy of the proposed model and to compare the results with previous models available in the literature.

An overall profit Malmquist productivity index with fuzzy and interval data

Although crisp data are fundamentally indispensable for determining the profit Malmquist productivity index (MPI), the observed values in real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized with fuzzy and interval methods. In this paper, we reformulate the conventional profit MPI problem as an imprecise data envelopment analysis (DEA) problem, and propose two novel methods for measuring the overall profit MPI when the inputs, outputs, and price vectors are fuzzy or vary in intervals. We develop a fuzzy version of the conventional MPI model by using a ranking method, and solve the model with a commercial off-the-shelf DEA software package. In addition, we define an interval for the overall profit MPI of each decision-making unit (DMU) and divide the DMUs into six groups according to the intervals obtained for their overall profit efficiency and MPIs. We also present two numerical examples to demonstrate the applicability of the two proposed models and exhibit the efficacy of the procedures and algorithms. © 2011 Elsevier Ltd.

Dense Continuity and Selections of Set-Valued Mappings

∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.