Gaussian Fuzzy Membership Function Research Articles

Exploiting nearest neighbor data and fuzzy membership function to address missing values in classification.

The accuracy of most classification methods is significantly affected by missing values. Therefore, this study aimed to propose a data imputation method to handle missing values through the application of nearest neighbor data and fuzzy membership function as well as to compare the results with standard methods. A total of five datasets related to classification problems obtained from the UCI Machine Learning Repository were used. The results showed that the proposed method had higher accuracy than standard imputation methods. Moreover, triangular method performed better than Gaussian fuzzy membership function. This showed that the combination of nearest neighbor data and fuzzy membership function was more effective in handling missing values and improving classification accuracy.

Interval Type-2 Mutual Subsethood Cauchy Fuzzy Neural Inference System (IT2MSCFuNIS)

An interval type-2 (IT2) mutual subsethood Cauchy fuzzy neural inference system has been proposed in this paper. The network architecture consists of 3-layers with all connection weights being IT2 Cauchy fuzzy membership functions (CMFs). The crisp inputs to the system are fuzzified into IT2CMFs with fixed centers and uncertain spreads. The hidden layer represents the rule-based knowledge. The firing degree of the antecedent part of each rule at the hidden layer is computed by aggregating the product of the mutual subsethood similarity measures between the inputs and the connection weights. A volume defuzzification is used to compute the numeric output. A gradient descent back-propagation algorithm is used to train the model. The novelty of the proposed model is threefold. First, is enriching the theory of the mutual subsethood fuzzy neural models by adopting the Cauchy membership function (CMF) as another powerful fuzzy basis function (FBF) rather than the classical choice of Gaussian fuzzy membership functions (GMFs). Second, is the success of computing the mutual subsethood similarity measure between the IT2CMFs and all the model parameters’ updating equations in analytic closed-form formulas, not numerically or approximately. Third, is the ability to extract the type-1 (T1) mutual subsethood Cauchy fuzzy neural inference system (T1MSCFuNIS) with all its analytic closed-form formulas directly as a special case from the general formulas of IT2MSCFuNIS model. Such a novelty makes the proposed model a concrete and effective development of the theory of mutual subsethood fuzzy neural models. Both IT2MSCFuNIS and T1MSCFuNIS models have been tested using different examples from the domains of function approximation, classification, and prediction. The results ensure the efficacy of both models compared with other models reported in the literature.

STIF: Intuitionistic fuzzy Gaussian membership function with statistical transformation weight of evidence and information value for private information preservation.

Data sharing to the multiple organizations are essential for analysis in many situations. The shared data contains the individual's private and sensitive information and results in privacy breach. To overcome the privacy challenges, privacy preserving data mining (PPDM) has progressed as a solution. This work addresses the problem of PPDM by proposing statistical transformation with intuitionistic fuzzy (STIF) algorithm for data perturbation. The STIF algorithm contains statistical methods weight of evidence, information value and intuitionistic fuzzy Gaussian membership function. The STIF algorithm is applied on three benchmark datasets adult income, bank marketing and lung cancer. The classifier models decision tree, random forest, extreme gradient boost and support vector machines are used for accuracy and performance analysis. The results show that the STIF algorithm achieves 99% of accuracy for adult income dataset and 100% accuracy for both bank marketing and lung cancer datasets. Further, the results highlights that the STIF algorithm outperforms in data perturbation capacity and privacy preserving capacity than the state-of-art algorithms without any information loss on both numerical and categorical data.

Evaluating types of soil suitable for construction using radial basis function fuzzy neural network

This paper deals with radial basis fuzzy neural network using bipolar picture fuzzy soft sets. Firstly a bipolar picture fuzzy decision matrix is constructed. A bipolar picture fuzzy Gaussian membership function is defined. Next degree values are calculated and used for finding the entropy. These entropy values help in determining the weights of bipolar picture fuzzy sets. Output is obtained by multiplication of weight values and BPFS Gaussian membership values. By using this method, the soil suitable for construction of buildings is found.

An appliance of adaptive Neuro-Fuzzy inference system for predicting the surface roughness of Al-4.5%Cu-TiC MMC in turning operation of CNC milling

In the recent decade, due to extensive application of computerized machine tools in the manufacturing industries, manufacturing processes are in need of highly reliable predictive model for the stable machining. Surface roughness(SR) essentially affects the strength of the developed parts, thus in order to attain high quality and productivity in CNC milling process prediction of surface roughness is very essential as it plays an imperative role in this sector. Hence in this present investigation, an effort has been given to predict the surface roughness of Al-4.5%Cu-TiC MMC, while turning in CNC milling by the use of Adaptive Neuro-Fuzzy Inference System (ANFIS). The experimentation is based on Taguchi’s L25 orthogonal array with the significant parameters such as cutting speed, depth of cut and feed rate. Using the experimental results, an ANFIS model is developed for prediction of surface roughness. The Gaussian fuzzy membership function is adopted in this present investigation for the analysis of ANFIS training as it gives better accuracy. Simulation results are validated through a number of trial cases and the results obtained by training of ANFIS are compared with the results obtained by regression analysis. Comparison result shows that the ANFIS results are better than the results obtained by regression model.

A fuzzy gaussian rank aggregation ensemble feature selection method for microarray data

In Microarray Data, it is complicated to achieve more classification accuracy due to the presence of high dimensions, irrelevant and noisy data. And also It had more gene expression data and fewer samples. To increase the classification accuracy and the processing speed of the model, an optimal number of features need to extract, this can be achieved by applying the feature selection method. In this paper, we propose a hybrid ensemble feature selection method. The proposed method has two phases, filter and wrapper phase in filter phase ensemble technique is used for aggregating the feature ranks of the Relief, minimum redundancy Maximum Relevance (mRMR), and Feature Correlation (FC) filter feature selection methods. This paper uses the Fuzzy Gaussian membership function ordering for aggregating the ranks. In wrapper phase, Improved Binary Particle Swarm Optimization (IBPSO) is used for selecting the optimal features, and the RBF Kernel-based Support Vector Machine (SVM) classifier is used as an evaluator. The performance of the proposed model are compared with state of art feature selection methods using five benchmark datasets. For evaluation various performance metrics such as Accuracy, Recall, Precision, and F1-Score are used. Furthermore, the experimental results show that the performance of the proposed method outperforms the other feature selection methods.

Fuzzy based Search in Motion Estimation for Real Time Video Compression

Video compression ratio, quality and efficiency are determined by the motion estimation algorithm. Motion estimation is used to perform inter frame prediction in video sequences. The individual frames are divided into blocks the motion estimation is computed by a video codec such as H.264. A video codec computes the displacement of block between the previous frame (reference frame) and the current frame, for each block in current frame the best motion vector is determined in the reference frame as a block belongs to a current frame. In this, research paper, a novel technique has been presented for motion vector calculation, using fuzzy Gaussian membership function. The motion estimation block uses fuzzy membership function to estimate the connectedness of different blocks of the current frame to that of the reference frame The fuzzy decision matching is done based on the matching criterion and the best matching block is selected. The motion vectors are thus calculated with respect to the reference frame. The fuzzification process produces optimally matched blocks, which are then utilized to calculate the motion vectors of the predicted frame. Using fuzzy based search the search area is automatically updated and adaptive search steps provides an optimized result of search. As in real time streaming no file is exchanged during the transmission user is not able to download the file the only way for smooth transmission is frame management fuzzy based search for the motion estimation provides a better compression for the predicted frames.

Fuzzy based Techniques for Handling Missing Values

Usually, time series data suffers from high percentage of missing values which is related to its nature and its collection process. This paper proposes a data imputation technique for imputing the missing values in time series data. The Fuzzy Gaussian membership function and the Fuzzy Triangular membership function are proposed in a data imputation algorithm in order to identify the best imputation for the missing values where the membership functions were used to calculate weights for the data values of the nearest neighbor’s before using them during imputation process. The evaluation results show that the proposed technique outperforms traditional data imputation techniques where the triangular fuzzy membership function has shown higher accuracy than the gaussian membership function during evaluation.

Identification of Circulating Fluidized Bed Boiler Bed Temperature Based on Hyper-Plane-Shaped Fuzzy C-Regression Model

Bed temperature in dense-phase zone is the key parameter of circulating fluidized bed (CFB) boiler for stable combustion and economic operation. It is difficult to establish an accurate bed temperature model as the complexity of circulating fluidized bed combustion system. T-S fuzzy model was widely applied in the system identification for it can approximate complex nonlinear system with high accuracy. Fuzzy c-regression model (FCRM) clustering based on hyper-plane-shaped distance has the advantages in describing T-S fuzzy model, and Gaussian function was adapted in antecedent membership function of T-S fuzzy model. However, Gaussian fuzzy membership function was more suitable for clustering algorithm using point to point distance, such as fuzzy c-means (FCM). In this paper, a hyper-plane-shaped FCRM clustering algorithm for T-S fuzzy model identification algorithm is proposed. The antecedent membership function of proposed identification algorithm is defined by a hyper-plane-shaped membership function and an improved fuzzy partition method is applied. To illustrate the efficiency of the proposed identification algorithm, the algorithm is applied in four nonlinear systems which shows higher identification accuracy and simplified identification process. At last, the algorithm is used in a circulating fluidized bed boiler bed temperature identification process, and gets better identification result.

Krishna Sudarsana—A Z-Space Interest Measure for Mining Similarity Profiled Temporal Association Patterns

Similarity profiled association mining from time stamped transaction databases is an important topic of research relatively less addressed in the field of temporal data mining. Mining temporal patterns from these time series databases requires choosing and applying similarity measure for similarity computations and subsequently pruning temporal patterns. This research proposes a novel z-space based interest measure named as Krishna Sudarsana for time-stamped transaction databases by extending interest measure Srihass proposed in previous research. Krishna Sudarsana is designed by using the product based fuzzy Gaussian membership function and performs similarity computations in z-space to determine the similarity degree between any two temporal patterns. The interest measure is designed by considering z-values between z = 0 and z = 3.09. Applying the Krishna Sudarsana requires moving the threshold value given by user to a different transformation space (z-space) which is a defined as a function of standard deviation. In addition to proposing interest measure, new expressions for standard deviation and equivalent z-space threshold are derived for similarity computations. For experimental evaluation, we considered Naive, Sequential and Spamine algorithms that applies Euclidean distance function and compared performance of these three approaches to Z-Spamine algorithm that uses Krishna Sudarsana by choosing various test cases. Experiment results proved the performance of the proposed approach is better to Sequential approach that uses snapshot database scan strategy and Spamine approach that uses lattice based database scan strategy.

Managing privacy of sensitive attributes using fuzzy-based data transformation methods in privacy preserving data mining environment

When we extract personal, sensitive and business information in data mining applications, then certain problems occurs. Privacy attack occurs due to the misuse of individual information. In centralised database environment, data transformation methods in fuzzy-based data in the field of privacy preserving clustering are proposed in this paper. In first case, a fuzzy data transformation method is proposed and different experiments are conducted by changing the fuzzy membership functions such as Z-shaped fuzzy membership function, Triangular fuzzy membership function, Gaussian fuzzy membership function to transform the original dataset. In second case, a hybrid method is proposed as a combination of fuzzy data transformation approach which is specified in first case and random rotation perturbation (RRP). The experimental outcome verified that the hybrid approach permits finest results for every member functions.

Nonlinear Behavior in Fractional-Order Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Function

Over the last three decades, chaotic dynamics in the field of mathematics, physics, chemistry, engineering, and social science have been studied by many researchers and scholars. In this paper, we reviewed period and chaotic behaviors in fractional-order love model of Romeo and Juliet with Gaussian fuzzy membership function as an external force or external environment. To do this, we fixed parameters a = − 1, b = − 5, c = d = 1 and varied α and β in the fractional-order differential equation of Romeo and Juliet love model, with α and β indicating the magnitude of love status of Romeo and Juliet, respectively. If α and β are the same, the magnitude of love status of Romeo is equal to that of Juliet. If α and β are different, then the magnitude of love status of Romeo is different from that of Juliet. We confirmed that when the difference of fractional order between Romeo and Juliet was small, their love status showed chaotic dynamics. This means that they love each other and the relationship between Romeo and Juliet is mutual and equivalent. When the difference is large, love status showed periodic motion. This means that the relationship between Romeo and Juliet is not equivalent.

On the Monotonicity Property of the TSK Fuzzy Inference System: The Necessity of the Sufficient Conditions and the Monotonicity Test

The sufficient conditions for satisfying the monotonicity property of the Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) have shown to be useful in many different applications. However, the related sufficient and necessary conditions are still unknown. As such, even when the sufficient conditions are violated, the TSK FIS model may still able to satisfy the monotonicity property. Therefore, the monotonicity test is used as an approximated method to determine the validness of the monotonicity property. To the best of our knowledge, the use of the monotonicity test in FIS is new. In this paper, we focus on single-input zero-order TSK FIS with Gaussian fuzzy membership functions. An algorithm to test the monotonicity property, either accepting or rejecting an TSK FIS model of being monotone, is devised and analyzed. The relationship between TSK FIS and its capability of satisfying the monotonicity property, along with the sufficient conditions and the outcome of the monotonicity test, is established through a Monte Carlo simulation. The Monte Carlo simulation is a useful necessity test for the sufficient conditions. We define a necessity measure of the sufficient conditions (NMSC) as the probability that a randomly generated monotone TSK FIS model (evaluated based on the monotonicity test algorithm) satisfies the sufficient conditions. We empirically show that the NMSC score reduces with increasing number of fuzzy rules. In addition, an application of the TSK FIS model to failure modes and effects analysis is demonstrated. As compared with the sufficient conditions, a better FIS-based model with a lower error measure can be obtained using the monotonicity test. The outcome indicates the effectiveness of the monotonicity test for designing low-dimensional TSK FIS models with large numbers of fuzzy rules.

An Improved Fuzzy Neural Network for Traffic Speed Prediction Considering Periodic Characteristic

This paper proposes a new method in construction fuzzy neural network to forecast travel speed for multi-step ahead based on 2-min travel speed data collected from three remote traffic microwave sensors located on a southbound segment of a fourth ring road in Beijing City. The first-order Takagi–Sugeno system is used to complete the fuzzy inference. To train the evolving fuzzy neural network (EFNN), two learning processes are proposed. First, a $K$ -means method is employed to partition input samples into different clusters and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated. Second, a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi–Sugeno type fuzzy rules. Furthermore, a trigonometric regression function is introduced to capture the periodic component in the raw speed data. Specifically, the predicted performance between the proposed model and six traditional models are compared, which are artificial neural network, support vector machine, autoregressive integrated moving average model, and vector autoregressive model. The results suggest that the prediction performances of EFNN are better than those of traditional models due to their strong learning ability. As the prediction time step increases, the EFNN model can consider the periodic pattern and demonstrate advantages over other models with smaller predicted errors and slow raising rate of errors.

가우시안 퍼지 소속 함수를 외력으로 가진 사랑 모델에서의 비선형 거동 해석

최근 카오스 동력학에 대한 연구가 많은 연구자들에 의해서 물리학, 화학, 수학, 공학, 및 사회과학 분야에서 관심을 받고 있다. 특별히 사회과학에서는 중독, 행복, 가족, 사랑 모델이 주요 연구 대상이다. 이중 사랑은 사람이 가지고 있는 4가지 감정 중 하나로서 많은 정의가 있으나 그 각각의 정의가 모두 일치하지 않는다. 최근에는 사랑을 미분방정식으로 표현하고 이 수식에서 비선형 거동 또는 카오스 거동을 찾고자 하는 노력이 중요한 연구의 하나이다. 본 논문에서는 외력을 가진 로미오와 줄리엣의 사랑모델을 기반으로 이 외력을 사람의 행동이나 인식 가까운 형태로 만들기 위해 가우시안 퍼지 소속 함수를 제시하고, 시계열과 위상공간을 통하여 이들의 특성에서 비선형 특성이 존재하는지를 확인한다. Recently, studying chaotic dynamic have been concerned by many researchers in areas of physics, chemistry, mathematics, engineering and social science. Especially, model of addiction, happiness, family and love become major research subjects in the social science. Among these models, love is one of the four emotions that human being have. There are many definitions for love, however, each definitions of love does not coincide with each other. Recently, one of the most important efforts for research is love and it is represented by derivative equation. Then they try to find nonlinear or chaotic behavior from this derivative equation. This paper propose Gaussian fuzzy membership function in order to make external force that are close to action and awareness of human based on love model of Romeo and Juliet with external force. This paper also confirms the existence of nonlinear characteristics through time series and phase portrait.

Travel Time Estimation Using Freeway Point Detector Data Based on Evolving Fuzzy Neural Inference System.

Travel time is an important measurement used to evaluate the extent of congestion within road networks. This paper presents a new method to estimate the travel time based on an evolving fuzzy neural inference system. The input variables in the system are traffic flow data (volume, occupancy, and speed) collected from loop detectors located at points both upstream and downstream of a given link, and the output variable is the link travel time. A first order Takagi-Sugeno fuzzy rule set is used to complete the inference. For training the evolving fuzzy neural network (EFNN), two learning processes are proposed: (1) a K-means method is employed to partition input samples into different clusters, and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated; (2) a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi-Sugeno type fuzzy rules. Testing datasets consisting of actual and simulated data are used to test the proposed method. Three common criteria including mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE) are utilized to evaluate the estimation performance. Estimation results demonstrate the accuracy and effectiveness of the EFNN method through comparison with existing methods including: multiple linear regression (MLR), instantaneous model (IM), linear model (LM), neural network (NN), and cumulative plots (CP).

An adaptive semi-supervised Fuzzy GrowCut algorithm to segment masses of regions of interest of mammographic images

According to the World Health Organization, breast cancer is the most common cancer in women worldwide, becoming one of the most fatal types of cancer. Mammography image analysis is still the most effective imaging technology for breast cancer diagnosis, which is based on texture and shape analysis of mammary lesions. The GrowCut algorithm is a general-purpose segmentation method based on cellular automata, able to perform relatively accurate segmentation through the adequate selection of internal and external seed points. In this work we propose an adaptive semi-supervised version of the GrowCut algorithm, based on the modification of the automaton evolution rule by adding a Gaussian fuzzy membership function in order to model non-defined borders. In our proposal, manual selection of seed points of the suspicious lesion is changed by a semiautomatic stage, where just the internal points are selected by using a differential evolution algorithm. We evaluated our proposal using 57 lesion images obtained from MiniMIAS database. Results were compared with the semi-supervised state-of-the-art approaches BEMD, BMCS, Wavelet Analysis, LBI, Topographic Approach and MCW. Results show that our method achieves better results for circumscribed, spiculated lesions and ill-defined lesions, considering the similarity between segmentation results and ground-truth images.

Image Denoising using Patch based Processing with Fuzzy Gaussian Membership Function

paper image denoising scheme based on fuzzy Gaussian membership function. For a given corrupted image at first converted to the fuzzy values using the fuzzification method. Then extract all patches with overlaps, after extracting all patches each patch is to be permuted and apply the fuzzy Gaussian membership function. Extraction means all patches with overlaps, refer to these as coordinates in high-dimensional space, and arrange them such that they are chained in the shortest possible path. The obtained ordering, applying the fuzzy defuzzification method to convert fuzzy values to the crisp values to what should be a normal signal. This enables us to get high-quality recovery of the clean image by applying relatively simple one-dimensional smoothing operations to the reordered set of pixels. The performance of this approach is experimentally verified on a diversity of images and noise levels. The results presented here demonstrate that proposed technique is on similarity or more than the existing state of the art, in terms of both peak signal-to-noise ratio and subjective visual quality. Keywords-based processing, fuzzification, defuzzification, gaussian membership function, traveling salesman, pixel permutation, denoising.

Heart Disease Prediction Using Hybrid Genetic Fuzzy Model

The objective of the work is to diagnose heart disease using computing techniques like genetic algorithm and fuzzy logic. The system would help the doctors to automate heart disease diagnosis and to enhance the medical care. In this paper a hybrid genetic-fuzzy heart disease diagnosis system is designed. The genetic algorithm is used for a stochastic search that provides the optimal solution to the feature selection problem. The relevant features selected from the dataset help the diagnosing system to develop a classification model using fuzzy inference system. The rules for the fuzzy system are generated from the sample data. Among the entire rule set the important and relevant subset of rules are selected using genetic algorithm. The proposed work uses the benefits of genetic algorithms and fuzzy inference system for effective prediction of heart disease in patients. The selected features are sex, serum cholesterol (chol), maximum heart rate achieved (thalach), Exercise induced angina (exang), ST depression induced by exercise relative to rest (oldpeak), number of major vessels coloured (ca) and thal value. Fuzzification using Fuzzy Gaussian membership function and defuzzification using centroid method improves the performance of the system. The work has been evaluated using the performance metrics like accuracy, specificity, sensitivity, confusion matrix that help in proving the efficiency of the work. The obtained classification accuracy is 86% using the stratified k fold technique with the values for specificity and sensitivity as .90 and .80 respectively. The number of attributes has been reduced from 13 to 7 from heart disease dataset available in the UCI Machine learning repository. When compared with the existing system the accuracy of the proposed work has been increased by 1.54%. The proposed model is named as GAFL model called Genetic Algorithm Fuzzy Logic model for effective heart disease prediction. It is easy to build the model thereby providing an easy option to be used in hospitals and medical centers for the aid of the physicians.

CFNN: Correlated fuzzy neural network

Abstract In this paper, a new fuzzy neural network model with correlated fuzzy rules (CFNN) based on the Levenberg–Marquardt (LM) optimization method is proposed. The proposed method is a new fuzzy network structure that is presented to approximate nonlinear functions especially the functions with high correlation between input variables with less number of fuzzy rules. A multivariable Gaussian fuzzy membership function is introduced that can consider the correlation between input variables and consequently it can model non-separable relations for interactive variables. The LM optimization method is used to learn parameters of both premise and consequent parts of the fuzzy rules. The suggested algorithm is successfully applied to seven tested examples including static function approximation, time-series prediction, non-linear dynamic system identification and a real-world complex regression problem. According to test observations; it can approximate nonlinear functions better than the other past algorithms with more compact structure and less number of fuzzy rules.