Sigmoid Membership Function Research Articles

Determination Method of Nonlinear Membership Function Based on the Fuzzy Density Means Cluster

Gaussian and Sigmoid membership function are commonly used, both of which have well smoothness, clear physical meaning and have no zeros in their figures. In this paper, fuzzy density means clustering method based on data distance is put forward, by using this method, the initial cluster center is obtained objectively, which has avoided the cluster results falling into a local minimum, finally the parameters used for describe the membership function are got. Through simulation, the membership function of data EB_Da51 in petroleum drilling is determined, which solves the problem that the function is hard to be defined.

Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS

The exact output regulation problem for Takagi-Sugeno (TS) fuzzy models, designed from linear local subsystems, may have a solution if input matrices are the same for every local linear subsystem. Unfortunately, such a condition is difficult to accomplish in general. Therefore, in this work, an adaptive network-based fuzzy inference system (ANFIS) is integrated into the fuzzy controller in order to obtain the optimal fuzzy membership functions yielding adequate combination of the local regulators such that the output regulation error in steady-state is reduced, avoiding in this way the aforementioned condition. In comparison with the steepest descent method employed for tuning fuzzy controllers, ANFIS approximates the mappings between local regulators with membership functions which are not necessary known functions as Gaussian bell (gbell), sigmoidal, and triangular membership functions. Due to the structure of the fuzzy controller, Levenberg-Marquardt method is employed during the training of ANFIS.

Robust classifier learning with fuzzy class labels for large-margin support vector machines

Using class label fuzzification, this study develops the idea of refreshing the attitude of the difficult training examples and gaining a more robust classifier for large-margin support vector machines (SVMs). Fuzzification relaxes the specific hard-limited Lagrangian constraints of the difficult examples, extends the infeasible space of the canonical constraints for optimization, and reconfigures the consequent decision function with a wider margin. With the margin, a classifier capable of achieving a high generalization performance can be more robust. This paper traces the rationale for such a robust performance back to the changes of governing loss function. From the aspect of loss function, the reasons are causally explained. In the study, we also demonstrate a two-stage system for experiments to show the changes corresponding to the label fuzzification. The system first captures the difficult examples in the first-stage preprocessor, and assigns them various fuzzified class labels. Three types of membership functions, including a constant, a linear, and a sigmoidal membership function, are designated in the preprocessor to manipulate the within-class correlations of the difficult examples for reference of the fuzzification. The consequent performance benchmarks confirm the robust and generalized ability due to the label fuzzification. Since the change of yi′ is fundamental, the idea may be transplanted to different prototypes of SVM.

Accuracy Enhancement in a Fuzzy Expert Decision Making System Through Appropriate Determination of Membership Functions and Its Application in a Medical Diagnostic Decision Making System

The paper attempts to improve the accuracy of a fuzzy expert decision making system by tuning the parameters of type-2 sigmoid membership functions of fuzzy input variables and hence determining the most appropriate type-1 membership function. The current work mathematically models the variability of human decision making process using type-2 fuzzy sets. Moreover, an index of accuracy of a fuzzy expert system has been proposed and determined analytically. It has also been ascertained that there exists only one rule in the rule base whose associated mapping for the ith linguistic variable maps to the same value as the maximum value of the membership function for the ith linguistic variable. The improvement in decision making accuracy was successfully verified in a medical diagnostic decision making system for renal diagnostic applications. Based on the accuracy estimations applied over a set of pathophysiological parameters, viz. body mass index, glucose, urea, creatinine, systolic and diastolic blood pressure, appropriate type-1 fuzzy sets of these parameters have been determined assuming normal distribution of type-1 membership function values in type-2 fuzzy sets. The type-1 fuzzy sets so determined have been used to develop an FPGA based smart processor. Using the processor, renal diagnosis of patients has been performed with an accuracy of 98.75%.

A Fuzzy Based Stability Index Using a Right Sigmoid Membership Function

A Fuzzy Based Stability Index Using a Right Sigmoid Membership Function

Remove Noise from Grayscale Digital Images by Traditional and Fuzzy Filters

Image denoising and enhancement is an important field and it is used very much in image processing, where images are corrupted by many kinds of noise, therefore, methods and techniques must be used to remove these noises. In this research seven traditional filters are used to remove noise from digital images corrupted with salt&pepper noise and Gaussian noise. And also adopting principle of fuzzy logic to hybrid between traditional filters and fuzzy logic using double bell shaped membership function and also hybrid with double adjusted sigmoid membership function to create seven fuzzy sigmoidal filters. After applying seven traditional methods, seven fuzzy bell methods and seven fuzzy sigmoidal methods , by using measures of restored image PSNR, MSE, MAE , shows the final methods i.e. seven fuzzy sigmoidal methods are better than other filters i.e. methods that are used in this research after comparing the results.

Adaptive neuro-fuzzy inference systems based approach to nonlinear noise cancellation for images

The adaptive neuro-fuzzy inference system (ANFIS) is an effective tool that can be applied to induct rules from observations, e.g. pattern recognition. In this paper, we extend the nonlinear noise cancellation method using ANFIS from 1-D signals to 2-D counterpart images. First, the image restoration contaminated with Gaussian noise is investigated in nonlinear passage dynamics of order 2. We inspect eight types of membership functions (MF): bell MF, triangle MF, Gaussian MF, two sided Gaussian MF, pi-shaped MF, product of two sigmoidal MFs, difference of two sigmoidal MFs, and trapezoidal MF. In addition, the other parameters, such as the training epochs, the number of MFs for each input, the optimization method, the type of output MFs, and the over-fitting problem, are investigated. For comparison with the noise cancellation using ANFIS, we simulate 22 conventional filtering techniques: spatial filters, optimal Wiener filter, frequency domain filters, wavelet, wavelet packet, 2-D adaptive filters, etc. The quality in terms of mean square error (MSE) of image restoration using the proposed noise cancellation using ANFIS (Pi-shaped MF) is at least 75 times better for Gaussian noise than that derived using any of these conventional filtering techniques.

Uncertainty of Data, Fuzzy Membership Functions, and Multilayer Perceptrons

Probability that a crisp logical rule applied to imprecise input data is true may be computed using fuzzy membership function (MF). All reasonable assumptions about input uncertainty distributions lead to MFs of sigmoidal shape. Convolution of several inputs with uniform uncertainty leads to bell-shaped Gaussian-like uncertainty functions. Relations between input uncertainties and fuzzy rules are systematically explored and several new types of MFs discovered. Multilayered perceptron (MLP) networks are shown to be a particular implementation of hierarchical sets of fuzzy threshold logic rules based on sigmoidal MFs. They are equivalent to crisp logical networks applied to input data with uncertainty. Leaving fuzziness on the input side makes the networks or the rule systems easier to understand. Practical applications of these ideas are presented for analysis of questionnaire data and gene expression data.

Fuzzy Colour Naming Based on Sigmoid Membership Functions

Fuzzy Colour Naming Based on Sigmoid Membership Functions

Adaptive Fuzzy Control of Nonlinear Systems with Sigmoidal Membership Functions

Recently, various adaptive fuzzy control schemes have been proposed to deal with nonlinear systems with poorly understood dynamics by using the parameterized fuzzy approximator. However, all of the adaptive fuzzy control systems have been designed with the Gaussian membership functions so that in such a system there is only one kind of shape of membership function that appears to symmetric bell-shaped curve. Namely, it is unable to specify asymmetric membership functions, which are important in practical applications. In this paper, first, we use the product of two Sigmoidal functions to express membership function, which will refer to as Sigmoidal membership function and is able to specify various shapes of membership function such as asymmetric triangular, trapezoid, either open left or right and so on. Next, by using the first order Taylor's expansion, we present an approximation theorem concerning the properties of the fuzzy approximator with the Sigmoidal membership function so that we can stably tune all parameters, which appear either linearly or nonlinearly in the fuzzy approximator, in our adaptive fuzzy control system. Also it is shown the proposed fuzzy adaptive controller guarantees tracking error, between outputs of considered system and desired values, to be asymptotically in decay.