A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Selecting the individual numerical scale and prioritization method in the analytic hierarchy process : a 2-tuple fuzzy linguistic approach

The validity of the priority vector used in the analytic hierarchy process (AHP) relies on two factors: the selection of a numerical scale and the selection of a prioritization method. The traditional AHP selects only one numerical scale (e.g., the Saaty scale) and one prioritization method (e.g., the eigenvector method) for each particular problem. For this traditional selection approach, there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector. In fact, the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the AHP decision makers. By defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices (LPCMs) of the priority vector and by using LPCMs to unify the format of the input and output of AHP, this paper extends the AHP prioritization process under the 2-tuple fuzzy linguistic model. Based on the extended AHP prioritization process, we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods. We also use the performance measure criteria to develop a 2-tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different LPCMs. In this paper, we call this type of selection the individual selection of the numerical scale and prioritization method. We also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection.

A guided rule reduction system for prioritization of failures in fuzzy FMEA

Traditional Failure Mode and Effect Analysis (FMEA) utilizes the Risk Priority Number (RPN) ranking system to evaluate the risk level of failures, to rank failures, and to prioritize actions. Although this method is simple, it suffers from several shortcomings. In this paper, use of fuzzy inference techniques for RPN determination in an attempt to overcome the weaknesses associated with the traditional RPN ranking system is investigated. However, the fuzzy RPN model, suffers from the combinatorial rule explosion problem. As a result, a generic rule reduction approach, i.e. the Guided Rule Reduction System (GRRS), is proposed to reduce the number of rules that need to be provided by users during the fuzzy RPN modeling process. The proposed approach is evaluated using real-world case studies pertaining to semiconductor manufacturing. The results are analyzed, and implications of the proposed approach are discussed.

Fuzzy rule base assessment models : theoretical analyses and a case study

An assessment model is usually a mathematical model that produces a measuring index, in the form of a numerical score to a situation/object, with respect to the subject of measure. To allow a valid and useful comparison among various situations/objects according to their associated numerical scores to be made, two important properties, i.e., the monotone output property and output resolution properties, are essential in fuzzy inference-based assessment problems. In this paper, the conditions for a fuzzy assessment model to fulfill the monotone output property is investigated using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to the input, whereby the derivative should be greater than a minimum resolution. Based on the derivative, improvements to the output resolution property by refining the fuzzy production rules are suggested. A case study on the Bowles fuzzy RPN model to demonstrate the effectiveness of the properties is also included.

Enhancing the failure mode and effect analysis methodology with fuzzy inference techniques

Traditional Failure Mode and Effect Analysis (FMEA) adopts the Risk Priority Number (RPN) ranking model to evaluate failure risks, to rank failures, as well as to prioritize actions. Although this approach is simple, it suffers from several shortcomings. In this paper, we investigate a number of fuzzy inference techniques for determining the RPN scores, in an attempt to overcome the weaknesses associated with the traditional RPN model. The main objective is to examine the possibility of using fuzzy rule interpolation and reduction techniques to design new fuzzy RPN models. The performance of the fuzzy RPN models is evaluated using a real-world case study pertaining to the test handler process in a semiconductor manufacturing plant. The FMEA procedure for the test handler is performed, and a fuzzy RPN model is developed. In addition, improvement to the fuzzy RPN model is proposed by refining the weights of the fuzzy production rules, hence a new weighted fuzzy RPN model. The ability of the weighted fuzzy RPN model in failure risk evaluation with a reduced rule base is also demonstrated.

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.

On the use of fuzzy inference techniques in assessment models : part I — theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.

On the use of fuzzy inference techniques in assessment models : part II : industrial applications

In this paper, we study the applicability of the monotone output property and the output resolution property in fuzzy assessment models to two industrial Failure Mode and Effect Analysis (FMEA) problems. First, the effectiveness of the monotone output property in a single-input fuzzy assessment model is demonstrated with a proposed fuzzy occurrence model. Then, the usefulness of the two properties to a multi-input fuzzy assessment model, i.e., the Bowles fuzzy Risk Priority Number (RPN) model, is assessed. The experimental results indicate that both the fuzzy occurrence model and Bowles fuzzy RPN model are able to fulfill the monotone output property, with the derived conditions (in Part I) satisfied. In addition, the proposed rule refinement technique is able to improve the output resolution property of the Bowles fuzzy RPN model.

Análise da estabilidade de sistemas fuzzy Takagi-Sugeno utilizando as desigualdades de Lyapunov-Metzler

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Desenvolvimento de um modelo fuzzy para otimização da energia gerada por um sistema híbrido (solar-fotovoltaico e eólico)

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Estimação do número de internações por doenças respiratórias utilizando lógica fuzzy tipo-2 intervalar

In this work was developed a fuzzy computational model type-2 predictive interval, using the software of the type-2 fuzzy MATLAB toolbox, the final idea is to estimate the number of hospitalizations of patients with respiratory diseases. The interest in the creation of this model is to assist in decision makeshift hospital environment, where there are no medical or professional equipment available to provide the care that the population need. It began working with the study of fuzzy logic, the fuzzy inference system and fuzzy toolbox. Through a real database provided by the Departamento de Informática do Sistema Único de Saúde (DATASUS) and Companhia de Tecnologia de Saneamento Básico (CETESB), was possible to start the model. The analyzed database is composed of the number of patients admitted with respiratory diseases a day for the public hospital in São José dos Campos, during the year 2009 and by factors such as PM10, SO2, wind and humidity. These factors were analyzed as input variables and, through these, is possible to get the number of admissions a day, which is the output variable of the model. For data analysis we used the fuzzy control method type-2 Mamdani. In the following steps the performance developed in this work was compared with the performance of the same model using fuzzy logic type-1. Finally, the validity of the models was estimated by the ROC curve

Modelo fuzzy estimando tempo de internação por doenças cardiovasculares

Abstract A fuzzy linguistic model based on the Mamdani method with input variables, particulate matter, sulfur dioxide, temperature and wind obtained from CETESB with two membership functions each was built to predict the average hospitalization time due to cardiovascular diseases related to exposure to air pollutants in São José dos Campos in the State of São Paulo in 2009. The output variable is the average length of hospitalization obtained from DATASUS with six membership functions. The average time given by the model was compared to actual data using lags of 0 to 4 days. This model was built using the Matlab v. 7.5 fuzzy toolbox. Its accuracy was assessed with the ROC curve. Hospitalizations with a mean time of 7.9 days (SD = 4.9) were recorded in 1119 cases. The data provided revealed a significant correlation with the actual data according to the lags of 0 to 4 days. The pollutant that showed the greatest accuracy was sulfur dioxide. This model can be used as the basis of a specialized system to assist the city health authority in assessing the risk of hospitalizations due to air pollutants.

Novas condições de estabilidade de sistemas não lineares utilizando funções de Lyapunov fuzzy

Pós-graduação em Engenharia Elétrica - FEIS

Aplicação da teoria fuzzy no controle de sistemas de geração de energias alternativas

This paper presents the application and use of a methodology based on fuzzy theory and simulates its use in intelligent control of a hybrid system for generating electricity, using solar energy, photovoltaic and wind. When using a fuzzy control system, it reached the point of maximum generation of energy, thus shifting all energy generated from the alternative sources-solar photovoltaic and wind, cargo and / or batteries when its use not immediately. The model uses three variables used for entry, which are: wind speed, solar radiation and loading the bank of batteries. For output variable has to choose which of the batteries of the battery bank is charged. For the simulations of this work is used MATLAB software. In this environment mathematical computational are analyzed and simulated all mathematical modeling, rules and other variables in the system described fuzzy. This model can be used in a system of control of hybrid systems for generating energy, providing the best use of energy sources, sun and wind, so we can extract the maximum energy possible these alternative sources without any prejudice to the environment.

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

Pós-graduação em Engenharia Mecânica - FEG