Applying fuzzy logic to comparative distribution modelling: a case study with two sympatric amphibians.

We modelled the distributions of two toads (Bufo bufo and Epidalea calamita) in the Iberian Peninsula using the favourability function, which makes predictions directly comparable for different species and allows fuzzy logic operations to relate different models. The fuzzy intersection between individual models, representing favourability for the presence of both species simultaneously, was compared with another favourability model built on the presences shared by both species. The fuzzy union between individual models, representing favourability for the presence of any of the two species, was compared with another favourabilitymodel based on the presences of either or both of them. The fuzzy intersections between favourability for each species and the complementary of favourability for the other (corresponding to the logical operation “A and not B”) were compared with models of exclusive presence of one species versus the exclusive presence of the other. The results of modelling combined species data were highly similar to those of fuzzy logic operations between individual models, proving fuzzy logic and the favourability function valuable for comparative distribution modelling. We highlight several advantages of fuzzy logic over other forms of combining distribution models, including the possibility to combine multiple species models for management and conservation planning.

Fuzzy ART

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP synthesize fuzzy logic and ART networks by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic: intersection (∩) with the fuzzy intersection (∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric: theory in which the fuzzy inter:>ec:tion and the fuzzy union (∨), or component-wise maximum, play complementary roles. Complement coding preserves individual feature amplitudes while normalizing the input vector, and prevents a potential category proliferation problem. Adaptive weights :otart equal to one and can only decrease in time. A geometric interpretation of fuzzy AHT represents each category as a box that increases in size as weights decrease. A matching criterion controls search, determining how close an input and a learned representation must be for a category to accept the input as a new exemplar. A vigilance parameter (p) sets the matching criterion and determines how finely or coarsely an ART system will partition inputs. High vigilance creates fine categories, represented by small boxes. Learning stops when boxes cover the input space. With fast learning, fixed vigilance, and an arbitrary input set, learning stabilizes after just one presentation of each input. A fast-commit slow-recode option allows rapid learning of rare events yet buffers memories against recoding by noisy inputs. Fuzzy ARTMAP unites two fuzzy ART networks to solve supervised learning and prediction problems. A Minimax Learning Rule controls ARTMAP category structure, conjointly minimizing predictive error and maximizing code compression. Low vigilance maximizes compression but may therefore cause very different inputs to make the same prediction. When this coarse grouping strategy causes a predictive error, an internal match tracking control process increases vigilance just enough to correct the error. ARTMAP automatically constructs a minimal number of recognition categories, or "hidden units," to meet accuracy criteria. An ARTMAP voting strategy improves prediction by training the system several times using different orderings of the input set. Voting assigns confidence estimates to competing predictions given small, noisy, or incomplete training sets. ARPA benchmark simulations illustrate fuzzy ARTMAP dynamics. The chapter also compares fuzzy ARTMAP to Salzberg's Nested Generalized Exemplar (NGE) and to Simpson's Fuzzy Min-Max Classifier (FMMC); and concludes with a summary of ART and ARTMAP applications.

Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.

Application of adaptive neuro-fuzzy inference for wind power short-term forecasting

The increased integration of wind power into the electric grid, as nowadays occurs in Portugal, poses new challenges due to its intermittency and volatility. Hence, good forecasting tools play a key role in tackling these challenges. In this paper, an adaptive neuro-fuzzy inference approach is proposed for short-term wind power forecasting. Results from a real-world case study are presented. A thorough comparison is carried out, taking into account the results obtained with other approaches. Numerical results are presented and conclusions are duly drawn. (C) 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Fuzzy FMEA with a guided rules reduction system for prioritization of failures

Purpose – To propose a generic method to simplify the fuzzy logic-based failure mode and effect analysis (FMEA) methodology by reducing the number of rules that needs to be provided by FMEA users for the fuzzy risk priority number (RPN) modeling process.

Design/methodology/approach – The fuzzy RPN approach typically requires a large number of rules, and it is a tedious task to obtain a full set of rules. The larger the number of rules provided by the users, the better the prediction accuracy of the fuzzy RPN model. As the number of rules required increases, ease of use of the model decreases since the users have to provide a lot of information/rules for the modeling process. A guided rules reduction system (GRRS) is thus proposed to regulate the number of rules required during the fuzzy RPN modeling process. The effectiveness of the proposed GRRS is investigated using three real-world case studies in a semiconductor manufacturing process.

Findings – In this paper, we argued that not all the rules are actually required in the fuzzy RPN model. Eliminating some of the rules does not necessarily lead to a significant change in the model output. However, some of the rules are vitally important and cannot be ignored. The proposed GRRS is able to provide guidelines to the users which rules are required and which can be eliminated. By employing the GRRS, the users do not need to provide all the rules, but only the important ones when constructing the fuzzy RPN model. The results obtained from the case studies demonstrate that the proposed GRRS is able to reduce the number of rules required and, at the same time, to maintain the ability of the Fuzzy RPN model to produce predictions that are in agreement with experts' knowledge in risk evaluation, ranking, and prioritization tasks.

Research limitations/implications – The proposed GRRS is limited to FMEA systems that utilize the fuzzy RPN model.

Practical implications – The proposed GRRS is able to simplify the fuzzy logic-based FMEA methodology and make it possible to be implemented in real environments.

Originality/value – The value of the current paper is on the proposal of a GRRS for rule reduction to enhance the practical use of the fuzzy RPN model in real environments.

Neural network and interval type-2 fuzzy system for stock price forecasting

Stock price forecast has long been received special attention of investors and financial institutions. As stock prices are changeable over time and increasingly uncertain in modern financial markets, their forecasting becomes more important than ever before. A hybrid approach consisting of two components, a neural network and a fuzzy logic system, is proposed in this paper for stock price prediction. The first component of the hybrid, i.e. a feedforward neural network (FFNN), is used to select inputs that are highly relevant to the dependent variables. An interval type-2 fuzzy logic system (IT2 FLS) is employed as the second component of the hybrid forecasting method. The IT2 FLS’s parameters are initialized through deployment of the k-means clustering method and they are adjusted by the genetic algorithm. Experimental results demonstrate the efficiency of the FFNN input selection approach as it reduces the complexity and increase the accuracy of the forecasting models. In addition, IT2 FLS outperforms the widely used type-1 FLS and FFNN models in stock price forecasting. The combination of the FFNN and the IT2 FLS produces dominant forecasting accuracy compared to employing only the IT2 FLSs without the FFNN input selection.

Mass spectrometry-based proteomic data for cancer diagnosis using interval type-2 fuzzy system

An interval type-2 fuzzy logic system is introduced for cancer diagnosis using mass spectrometry-based proteomic data. The fuzzy system is incorporated with a feature extraction procedure that combines wavelet transform and Wilcoxon ranking test. The proposed feature extraction generates feature sets that serve as inputs to the type-2 fuzzy classifier. Uncertainty, noise and outliers that are common in the proteomic data motivate the use of type-2 fuzzy system. Tabu search is applied for structure learning of the fuzzy classifier. Experiments are performed using two benchmark proteomic datasets for the prediction of ovarian and pancreatic cancer. The dominance of the suggested feature extraction as well as type-2 fuzzy classifier against their competing methods is showcased through experimental results. The proposed approach therefore is helpful to clinicians and practitioners as it can be implemented as a medical decision support system in practice.

Previsão de carga multinodal usando a rede neural ART-ARTMAP fuzzy

Pós-graduação em Engenharia Elétrica - FEIS

Desenvolvimento de aplicações em medicina e agronomia utilizando lógica fuzzy e neuro fuzzy

Pós-graduação em Engenharia Elétrica - FEIS

Estimativa da produtividade de trigo em função da adubação nitrogenada utilizando modelagem neuro fuzzy

Currently new techniques for data processing, such as neural networks, fuzzy logic and hybrid systems are used to develop predictive models of complex systems and to estimate the desired parameters. In this article the use of an adaptive neuro fuzzy inference system was investigated to estimate the productivity of wheat, using a database of combination of the following treatments: five N doses (0, 50, 100, 150 and 200 kg ha(-1)), three sources (Entec, ammonium sulfate and urea), two application times of N (at sowing or at side-dressing) and two wheat cultivars (IAC 370 and E21), that were evaluated during two years in Selviria, Mato Grosso do Sul, Brazil. Through the input and output data, the system of adaptive neuro fuzzy inference learns, and then can estimate a new value of wheat yield with different N doses. The productivity prediciton error of wheat in function of five N doses, using a neuro fuzzy system, was smaller than that one obtained with a quadratic approximation. The results show that the neuro fuzzy system is a viable prediction model for estimating the wheat yield in function of N doses.

Modelagem fuzzy de dados climáticos estimados por modelo matemático - CCATT-BRAMS

Pós-graduação em Engenharia Mecânica - FEG