Weighted Membership Functions Research Articles

Characterization and Comprehensive Evaluation of Phenotypic and Yield Traits in Salt-Stress-Tolerant Peanut Germplasm for Conservation and Breeding

Salt stress is a limiting factor affecting the growth, development, and yield of peanuts. Breeding improvement is a possible solution to overcome salt stress. The salt tolerance of 57 peanut cultivars in Northeast China was identified using indoor simulation at the germination stage, the seedling stage, and field natural identification. At the germination stage, 75 mM NaCl was the most suitable screening concentration, and the seed vitality index of 57 cultivars was analyzed using the membership function and cluster analysis. Among these cultivars, 11 were identified as salt-tolerant and 19 were salt-sensitive during germination. In the seedling stage, six salt tolerance coefficients (STCs) showed significant correlation. A gray relational analysis was used in combination with evaluation grading, resulting in the identification of 14 salt-tolerant cultivars and 12 salt-sensitive cultivars. In the field screening, a comprehensive analysis was conducted using a principal component analysis of nine indices, including agronomic characteristics, yield characteristics, and SPAD. This analysis led to the determination of three comprehensive indices. The weighted membership function was used for comprehensive evaluation. Finally, three salt-tolerant cultivars and four salt-sensitive cultivars suitable for planting in Northeast China were screened out to provide an excellent germplasm for researching the salt-tolerant mechanism of peanuts.

Evaluation and Screening of Wild Elymus sibiricus L. Germplasm Resources under Salt Stress

Soil salinization is a significant obstacle to improving natural grasslands, also affecting farmland productivity. The main distribution area of high salinity soils is primarily located in western China, with a significant presence in the Qinghai–Tibet Plateau (QTP). Siberian wildrye (Elymus sibiricus L.) has been widely used in ecological restoration and reseeding in the QTP, due to its strong salt and alkali resistance. To comprehensively evaluate its salt tolerance and to screen salt-tolerant and salt-sensitive germplasm resources, 50 wild E. sibiricus accessions were assessed through the measurement of several physiological parameters. These included the relative water content (RWC); relative electrical conductivity (REC); malondialdehyde content (MDA); proline content (Pro); and Na+/K+ ratio after 14 days of salt stress treatment (200 mmol L−1 NaCl). Through principal component analysis (PCA) based on both material sources and physiological indexing, it was found that the salt damage score (SDS) and RWC had a strong positive correlation (p < 0.05), in opposition to other indices. The positive indicators were REC, Pro, Na+/K+, and MDA, and the negative indicators were RWC and SDS. Ultimately, by combining the results of the conventional membership function analysis and the weighted membership function analysis based on major components, three salt-tolerant accessions—including XJ013-28, NM021-13 and XJ012-17—and four salt-sensitive accessions, including XZ008-20, QH013-8, XZ009-20, and QH005-35, were screened out. These results could be effectively used to assess the effects of salt stress on Siberian wildrye and its related species. This study provides a reference for the discovery and breeding of salt-tolerant cultivars among the Elymus species.

CardioLabelNet: An uncertainty estimation using fuzzy for abnormalities detection in ECG

AbstractElectrocardiography (ECG) abnormalities are evaluated through several automatic detection methods. Primarily, real‐world ECG data are digital signals those are stored in the form of images in hospitals. Also, the existing automated detection technique eliminates the cardiac pattern that is abnormal and it is difficult to multiple abnormalities at some instances. To address those issues in this paper conventional ECG image automated techniques CardioLabelNet model is proposed. The proposed model incorporates two stages for image abnormality detection. At first fuzzy membership is performed in the image for computation of uncertainty. In second stage, classification is performed for computation of abnormal activity. The proposed CardioLabelNet collect ECG image data set for the uncertainty estimation while taking the account of various image classes which includes the global and local entropy of image pixels. For each waveform, uncertainties are calculated on the basis of global entropy. The computation of uncertainty in the images is performed with the fuzzy membership function. The spatial likelihood estimation of a fuzzy weighted membership function is used to calculate local entropy. Upon completion of fuzzification, classification is performed for the detection of normal and abnormal patterns in the ECG signal images. Through integration of stacked architecture model classification is performed for ECG images. The proffered algorithm performance is calculated in terms of accuracy for segmentation, Dice similarity coefficient, and partition entropy. Additionally, classification parameters accuracy sensitivity, specificity, and AUC are evaluated. The proposed approach outperforms the existing methodology, according to the results of a comparative analysis.

A Novel Distributed Matching Global and Local Fuzzy Clustering (DMGLFC) for 3D Brain Image Segmentation for Tumor Detection

In this paper, we proposed a novel Distribution Matching Global and Local Fuzzy Clustering (DMGLFC) for image segmentation. The proposed DMGLFC targeted 3D MRI brain images for tumor detection. The DMGLFC is involved in the estimation of uncertainties with consideration of different classes. The number of uncertainties is estimated based on the consideration of global entropy and local entropy. The identified voxel in 3D brain MRI images is measured with a fuzzy weighted membership function for the estimation of global entropy. The local entropy measurement utilizes spatial likelihood estimation of fuzzifier weighted membership function. The proposed DMGLFC is involved in the effective segmentation of MRI tumors based on fuzzy objective function entropy measurement. Depending upon the weighted parameters, the tumors present in the 3D images are classified regarding the global and local entropy. The performance of the proposed algorithm is measured in terms of Dice similarity coefficient (DSC), accuracy (Acc), sensitivity (true positive rate), specificity (true negative rate), and Bit Error Rate (BER). Comparative analysis of results expressed that the proposed DMGLFC approach exhibits significant performance rather than the existing technique.

Ranking Function to Solve a Fuzzy Multiple Objective Function

In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

Segmenting Tooth Components in Dental X-Ray Images Using Gaussian Kernel- Based Conditional Spatial Fuzzy C-Means Clustering Algorithm

Tooth component segmentation is a crucial task in computer-aided design for forensic odontology, especially to estimate chronological age. Tooth segmentation on radiographic data is a very challenging task due to noise, low contrast, and uneven illumination. The Fuzzy C-Means clustering is generally used for image segmentation that allow pixels to be classified into one or more clusters according to their membership value. However, this clustering method still has problems associated with the shifting of cluster centers and sensitivity to the overlapping intensity distributions between classes. This paper proposes a modified strategy of the conditional spatial Fuzzy C-Means (csFCM) that incorporates global and spatial information into a weighted membership function by replacing the Euclidean distance with the Gaussian kernel distance to increase insensitivity to noise and outliers. The aim of this paper is to divide the tooth into 3 components, i.e. enamel, dentine, and pulp. Therefore, this modified algorithm is preceded by dental X-ray image pre-processing and continued by combining each dental component clusters into one composite image. The tooth image is pre-processed using Contrast Limited Adequate Histogram Equalization (CLAHE) and gamma adjustment to enhance the dental X-ray images quality from the non-uniform lighting. The Gausian kernel-based conditional spatial Fuzzy C-Means (GK-csFCM) segments the dental image into four class clusters, namely enamel, dentine, pulp, and background. Through iterations, the resulting cluster centers are more convergent with real cluster centers, thus ensuring the proposed method improves the drawback of inherent FCM-based methods and further promoting image segmentation performance. The experimental results on the real dental X-ray images showed that GK-csFCM has better performance than the typical FCM and csFCM clustering algorithms in terms of both qualitative and quantitative metrics, i.e. accuracy, specificity, sensitivity, and precision.

MRI Image Segmentation Using Conditional Spatial FCM Based on Kernel-Induced Distance Measure

Fuzzy C-means (FCM) clustering is the widest spread clustering approach for medical image segmentation because of its robust characteristics for data classification. But, it does not fully utilize the spatial information and is therefore very sensitive to noise and intensity inhomogeneity in magnetic resonance imaging (MRI). In this paper, we propose a conditional spatial kernel fuzzy C-means (CSKFCM) clustering algorithm to overcome the mentioned problem. The approach consists of two successive stages. First stage is achieved through the incorporation of local spatial interaction among adjacent pixels in the fuzzy membership function imposed by an auxiliary variable associated with each pixel. The variable describes the involvement level of each pixel for construction of membership functions and different clusters. Then, we adapted a kernel-induced distance to replace the original Euclidean distance in the FCM, which is shown to be more robust than FCM. The problem of sensitivity to noise and intensity inhomogeneity in MRI data is effectively reduced by incorporating a kernel-induced distance metric and local spatial information into a weighted membership function. The experimental results show that the proposed algorithm has advantages in accuracy and robustness against noise in comparison with the FCM, SFCM and CSFCM methods on MRI brain images.

SQI Quality Evaluation Mechanism of Single-Lead ECG Signal Based on Simple Heuristic Fusion and Fuzzy Comprehensive Evaluation.

For both the acquisition of mobile electrocardiogram (ECG) devices and early warning and diagnosis of clinical work, high-quality ECG signals is particularly important. We describe an effective system which could be deployed as a stand-alone signal quality assessment algorithm for vetting the quality of ECG signals. The proposed ECG quality assessment method is based on the simple heuristic fusion and fuzzy comprehensive evaluation of the SQIs. This method includes two modules, i.e., the quantification and extraction of Signal Quality Indexes (SQIs) for different features, intelligent assessment and classification. First, simple heuristic fusion is executed to extract SQIs and determine the following SQIs: R peak detection match qSQI, QRS wave power spectrum distribution pSQI, kurtosis kSQI, and baseline relative power basSQI. Then, combined with Cauchy distribution, rectangular distribution and trapezoidal distribution, the membership function of SQIs was quantified, and the fuzzy vector was established. The bounded operator was selected for fuzzy synthesis, and the weighted membership function was used to perform the assessment and classification. The performance of the proposed method was tested on the database from Physionet ECG database, with an accuracy (Acc) of 97.67%, sensitivity (Se) of 96.33% and specificity (Sp) of 98.33% on the training set. Testing against the test datasets resulted in scores of 94.67, 90.33, and 93.00%, respectively. There's no gold standard exists for determining the quality of ECGs. However, the proposed algorithm discriminates between high- and poor-quality ECGs, which could aid in ECG acquisition for mobile ECG devices, early clinical diagnosis and early warning.

Fuzzy Naive Bayesian for constructing regulated network with weights.

In the data mining field, classification is a very crucial technology, and the Bayesian classifier has been one of the hotspots in classification research area. However, assumptions of Naive Bayesian and Tree Augmented Naive Bayesian (TAN) are unfair to attribute relations. Therefore, this paper proposes a new algorithm named Fuzzy Naive Bayesian (FNB) using neural network with weighted membership function (NEWFM) to extract regulated relations and weights. Then, we can use regulated relations and weights to construct a regulated network. Finally, we will classify the heart and Haberman datasets by the FNB network to compare with experiments of Naive Bayesian and TAN. The experiment results show that the FNB has a higher classification rate than Naive Bayesian and TAN.

Conditional spatial fuzzy C-means clustering algorithm for segmentation of MRI images

The fuzzy C-means (FCM) algorithm has got significant importance due to its unsupervised form of learning and more tolerant to variations and noise as compared to other methods in medical image segmentation. In this paper, we propose a conditional spatial fuzzy C-means (csFCM) clustering algorithm to improve the robustness of the conventional FCM algorithm. This is achieved through the incorporation of conditioning effects imposed by an auxiliary (conditional) variable corresponding to each pixel, which describes a level of involvement of the pixel in the constructed clusters, and spatial information into the membership functions. The problem of sensitivity to noise and intensity inhomogeneity in magnetic resonance imaging (MRI) data is effectively reduced by incorporating local and global spatial information into a weighted membership function. The experimental results on four volumes of simulated and one volume of real-patient MRI brain images, each one having 51 images, show that the csFCM algorithm has superior performance in terms of qualitative and quantitative studies such as, cluster validity functions, segmentation accuracy, tissue segmentation accuracy and receiver operating characteristic (ROC) curve on the image segmentation results than the k-means, FCM and some other recently proposed FCM-based algorithms.

Classification of high resolution satellite images using spatial constraints-based fuzzy clustering

A spatial constraints-based fuzzy clustering technique is introduced in the paper and the target application is classification of high resolution multispectral satellite images. This fuzzy-C-means (FCM) technique enhances the classification results with the help of a weighted membership function (Wmf). Initially, spatial fuzzy clustering (FC) is used to segment the targeted vegetation areas with the surrounding low vegetation areas, which include the information of spatial constraints (SCs). The performance of the FCM image segmentation is subject to appropriate initialization of Wmf and SC. It is able to evolve directly from the initial segmentation by spatial fuzzy clustering. The controlling parameters in fuzziness of the FCM approach, Wmf and SC, help to estimate the segmented road results, then the Stentiford thinning algorithm is used to estimate the road network from the classified results. Such improvements facilitate FCM method manipulation and lead to segmentation that is more robust. The results confirm its effectiveness for satellite image classification, which extracts useful information in suburban and urban areas. The proposed approach, spatial constraint-based fuzzy clustering with a weighted membership function (SCFCWmf), has been used to extract the information of healthy trees with vegetation and shadows showing elevated features in satellite images. The performance values of quality assessment parameters show a good degree of accuracy for segmented roads using the proposed hybrid SCFCWmf-MO (morphological operations) approach which also occluded nonroad parts.

Fuzzy Hybrid Filtering Techniques for Removal of Random Noise from Medical Images

Reducing or removing random noise from medical image is a very active research area in medical image processing. In recent years, technological development has significantly improved in analyzing medical images. This paper proposes various fuzzy hybrid filtering techniques for the removal of random noise from medical images, by topological approach. Each of these fuzzy filters, which apply a weighted membership function to an image within a 8-neighbours of a point, is simple and easy to implement. The quality of the noise reduction in images is measured by the statistical quantity measures: Root Mean Square Error (RMSE) and Peak Signal-to-Noise Ratio (PSNR). The performances of these fuzzy filters on images tainted with low, medium and high random noise are compared with various existing filtering techniques.

Methods for Determining the Statistical Significance of Enrichment or Depletion of Gene Ontology Classifications under Weighted Membership

High-throughput molecular biology studies, such as microarray assays of gene expression, two-hybrid experiments for detecting protein interactions, or ChIP-Seq experiments for transcription factor binding, often result in an “interesting” set of genes – say, genes that are co-expressed or bound by the same factor. One way of understanding the biological meaning of such a set is to consider what processes or functions, as defined in an ontology, are over-represented (enriched) or under-represented (depleted) among genes in the set. Usually, the significance of enrichment or depletion scores is based on simple statistical models and on the membership of genes in different classifications. We consider the more general problem of computing p-values for arbitrary integer additive statistics, or weighted membership functions. Such membership functions can be used to represent, for example, prior knowledge on the role of certain genes or classifications, differential importance of different classifications or genes to the experimenter, hierarchical relationships between classifications, or different degrees of interestingness or evidence for specific genes. We describe a generic dynamic programming algorithm that can compute exact p-values for arbitrary integer additive statistics. We also describe several optimizations for important special cases, which can provide orders-of-magnitude speed up in the computations. We apply our methods to datasets describing oxidative phosphorylation and parturition and compare p-values based on computations of several different statistics for measuring enrichment. We find major differences between p-values resulting from these statistics, and that some statistics recover “gold standard” annotations of the data better than others. Our work establishes a theoretical and algorithmic basis for far richer notions of enrichment or depletion of gene sets with respect to gene ontologies than has previously been available.

A weighted additive fuzzy multiobjective model for the supplier selection problem under price breaks in a supply Chain

Supplier selection is one of the most critical activities of purchasing management in a supply chain, because of the key role of supplier's performance on cost, quality, delivery and service in achieving the objectives of a supply chain. Supplier selection is a multiple-criteria decision-making (MCDM) problem that is affected by several conflicting factors. Depending on the purchasing situations, criteria have varying importance and there is a need to weight criteria. In practice, for supplier selection problems, most of the input information is not known precisely. In these cases, the theory of fuzzy sets is one of the best tools for handling uncertainty. The fuzzy multiobjective model is formulated in such a way as to simultaneously consider the imprecision of information and determine the order quantities to each supplier based on price breaks. The problem includes the three objective functions: minimizing the net cost, minimizing the net rejected items and minimizing the net late deliveries, while satisfying capacity and demand requirement constraints. In order to solve the problem, a fuzzy weighted additive and mixed integer linear programming is developed. The model aggregates weighted membership functions of objectives to construct the relevant decision functions, in which objectives have different relative importance. A numerical example is given to illustrate how the model is applied. Finally, the conclusions and recommendations are presented.

퍼지신경망과 비중복면적 분산 측정법을 이용한 최소의 특징입력 및 퍼지규칙의 추출

본 논문은 가중 퍼지소속함수 기반 신경망(Neural Network with Weighted Fuzzy Membership Functions, NEWFM)을 이용하여 위스콘신 유방암(Wisconsin breast cancer)의 진단을 수행하는 퍼지규칙을 추출하고, 비중복면적 분산 측정법을 사용하여 특징입력수를 최소로하는 방안을 제안하고 있다. NEWFM 구조의 중간 부분인 하이퍼박스(hyperbox)들은n 개의 대, 중, 소로 구성된 가중 퍼지소속함수 집합으로 구성되며, 학습 후 각 집합의 대, 중, 소로 구성된 가중 퍼지소속함수는 퍼지집합의 경계합(bounded sum)을 사용하여 다시 하나의 가중 퍼지소속함수로 합성(BSWFM) 된다. n 개의 특징입력(feature input)은 학습된 모든 하이퍼박스에 연결되어 예측 작업을 수행한다. 여기에 비중복면적 분산 측정법을 적용하여 중요도가 낮은 특징입력을 제거하면서 최소의 m 개 특징입력만을 사용한 하이퍼박스로 단순화시킨다. 이러한 방법으로 위스콘신 유방암의 9개의 특징입력 중 4개를 사용하여 NEWFM으로 추출된 2개의 퍼지규칙은 99.71%의 예측 인식율을 가지며 이는 퍼지규칙의 수와 인식율에 있어 현재 발표된 논문의 결과보다 우수함을 보여준다. This paper presents fuzzy rules to predict diagnosis of Wisconsin breast cancer with minimized number of feature in put using the neural network with weighted fuzzy membership functions (NEWFM) and the non-overlap area distribution measurement method. NEWFM is capable of self-adapting weighted membership functions from the given the Wisconsin breast cancer clinical training data. n set of small, medium, and large weighted triangular membership functions in a hyperbox are used for representing n set of featured input. The membership functions are randomly distributed and weighted initially, and then their positions and weights are adjusted during learning. After learning, prediction rules are extracted directly from n set of enhanced bounded sums of n set of small, medium, and large weighted fuzzy membership functions. Then, the non-overlap area distribution measurement method is applied to select important features by deleting less important features. Two sets of prediction rules extracted from NEWFM using the selected 4 input features out of 9 features outperform to the current published results in number of set of rules, number of input features, and accuracy with 99.71%.

Finding Fuzzy Rules for IRIS by Neural Network with Weighted Fuzzy Membership Function

Fuzzy neural networks have been successfully applied to analyze/generate predictive rules for medical or diagnostic data. However, most approaches proposed so far have not considered the weights for the membership functions much. This paper presents a neural network with weighted fuzzy membership functions. In our approach, the membership functions can capture the concentrated and essential information that affects the classification of the input patterns. To verify the performance of the proposed model, well-known Iris data set is performed. According to the results, the weighted membership functions enhance the prediction accuracy. The architecture of the proposed neural network with weighted fuzzy membership functions and the details of experimental results for the data set is discussed in this paper.

Neuro-fuzzy feature evaluation with theoretical analysis

The article provides a fuzzy set theoretic feature evaluation index and a connectionist model for its evaluation along with their theoretical analysis. A concept of weighted membership function is introduced which makes the modeling of the class structures more appropriate. A neuro-fuzzy algorithm is developed for determining the optimum weighting coefficients representing the feature importance. It is shown theoretically that the evaluation index has a fixed upper bound and a varying lower bound, and it monotonically increases with the lower bound. A relation between the evaluation index, interclass distance and weighting coefficients is established. Effectiveness of the algorithms for evaluating features both individually and in a group (considering their independence and dependency) is demonstrated along with comparisons on speech, Iris, medical and mango-leaf data. The results are also validated using scatter diagram and k-NN classifier.