Fuzzy Membership Matrix Research Articles

A sonar image segmentation algorithm based on quantum-inspired particle swarm optimization and fuzzy clustering

The underwater sonar image has the characteristics of complex background and heavy noise pollution. By using multi-bit quantum system to encode particles, a new sonar image segmentation algorithm based on quantum-inspired particle swarm and fuzzy clustering is proposed. Based on its own optimal particles and global optimal particles, the rotation angle is determined. By calculating the variance of the particle group fitness, the multi-bit quantum revolving gate is used to update the particle position in real time. The output of improved particle swarm optimization is used to initialize the K-mean clustering center to converge to the global optimal solution. Based on the idea of fuzzy membership matrix in FCM, combined with the isolated spatial information characteristics of the noise, the sonar image segmentation and the denoising are carried out. The experimental results show that the proposed algorithm can improve the global search ability of particle swarm optimization effectively. It is better than the quantum fuzzy clustering and quantum genetic algorithm in image segmentation. The analysis results of multiple real underwater sonar images show that the new optimization algorithm has faster convergence speed, better optimizing capacity and better segmentation results for sonar images.

Fuzzy semi-supervised weighted linear loss twin support vector clustering

In this paper, we propose two variants of Weighted Linear Loss Twin Support Vector Clustering (WLL-TWSVC) algorithm for identifying cluster planes. Unlike, Twin Support Vector Clustering (TWSVC) where the solution is obtained by solving a Quadratic Programming Problem (QPP) and a system of linear equations, WLL-TWSVC needs to solve the system of linear equations only. In order to improve the clustering accuracy with the help of limited amount of labeled data, we have extended TWSVC and WLL-TWSVC in the semi-supervised framework which are termed as Laplacian TWSVC (Lap-TWSVC) and Laplacian WLL-TWSVC (Lap-WLL-TWSVC) respectively. Further, to build a robust clustering algorithm which is not sensitive to noise and outliers, we introduce a fuzzy membership matrix and thus extends Lap-WLL-TWSVC to Fuzzy Laplacian WLL-TWSVC. The experimental results on several benchmark UCI datasets indicate that our proposed formulations achieve better clustering accuracy over other state-of-the-art plane-based clustering algorithms with comparatively lesser computational time. As an application to our proposed algorithms, we also perform image segmentation over Berkeley Segmentation dataset.

Decision Making Problem for Medical Diagnosis Using Hexagonal Fuzzy Number Matrix

Fuzzy set theory plays a vital role in medical fields. There are varieties of models involving fuzzy matrices to deal with different complicated aspects of medical diagnosis. Fuzzy set theory is highly suitable and applicable for developing knowledge based system in medicine for the tasks of medical findings. The field of medicine and decision making are the most fruitful andinteresting area of applications of fuzzy set theory. In this paper, we have applied the notion of Hexagonal fuzzy membership matrix in a medical diagnostic model. The advantage of this model is, if the patient-matrices are known, then it is possible to find which patient is suffering from what kind of disease. Most probably the fuzzy decision model in which overall ranking or ordering of different fuzzy sets are determined by using comparison matrix.

Ensemble Based Gustafson Kessel Fuzzy Clustering

Fuzzy clustering is a clustering method whcih allows an object to belong to two or more cluster by combining hard-clustering and fuzzy membership matrix. Two popular algorithms used in fuzzy clustering are Fuzzy C-Means (FCM) and Gustafson Kessel (GK). The FCM use Euclideans distance for determining cluster membership, while GK use Fuzzy Covariance Matrix that considering covariance between variables. Although GK perform better, it has some drawbacks on handling linearly correlated data, and as FCM the algorithm produce unstable result due to random initialization. These drawbacks can be overcame by using improved covariance estimation and cluster ensemble, respectively. This research presents the implementation of improved covariance estimation and cluster ensemble on GK method and compare it with FCM-Ensemble.

Underwater Sonar Image Detection: A Novel Quantum‐Inspired Shuffled Frog Leaping Algorithm

Object detection plays an important role in the underwater object recognition technology of sonar equipment. We propose a Novel quantum-inspired shuffled frog leaping algorithm (NQSFLA) to obtain more accurate detection results in this paper. The proposed NQSFLA adopts a fitness function combining intra-class difference with inter-class difference to evaluate the frog position more accurately and a new quantum evolution update strategy to improve the searching ability in the searching process. In order to avoid the disadvantages of Quantuminspired shuffled frog leaping algorithm (QSFLA), a fuzzy membership matrix with spatial information model is developed, which can remove isolated regions and further improve the detection accuracy. Segmentation, distribution and noise entropy (SDNE) model is also proposed to quantitatively evaluate the detection results. The detection results of the original sonar images demonstrate the effectiveness and adaptability of the proposed method.

Different Treatment Stages in Medical Diagnosis using Fuzzy Membership Matrix

The field of medicine is the most important and developing area of applications of fuzzy set theory. The nature of medical documentation and uncertain information gathered in the use of fuzzy triangular matrix. In this paper, procedures are presented for medical diagnosis and treatment-stages, patient and drug is constructed in fuzzy membership matrix. Examples are given to verify the proposed approach.

Study on Bridge Aging Based on Analytic Hierarchy Process

Aiming at the problems and needs of bridge detection and evaluation, based on AHP, this paper designs and establishes multi-level evaluation model and index system for bridge aging assessment. The judgement matrix of each class objective in index system is constructed, and determine the weight of the indicator based on the judgment matrix. Design expert scoring system and establish fuzzy membership matrix for bridge evaluation based on fuzzy comprehensive evaluation method. Then evaluate the degree of aging and calculate the overall score of the bridge according to the weights and membership matrix, so as to determine the health level of the bridge, and provide decision-making basis for the relevant departments to take bridge maintenance measures.

Cluster validity index for adaptive clustering algorithms

Everyday a large number of records of surfing internet are generated. In various situations when the authors are analysing internet data they do not know the cluster structure of the author's database of traffic features, such as when the border of cluster members is vague, and the clusters' partitions have different shapes, how to establish an algorithm to solve the clustering problem? Adaptive clustering algorithms can meet this challenge. Moreover, how to determinate the number of clusters when not only fuzzy cluster but also hard cluster are used? To address those problems, a new cluster validity index is proposed in this study. The proposed index focuses on the information of the geometrical structure of dataset by analysing the neighbourhood of data objects, which makes the index independent of the traditional fuzzy membership matrix. The new index consists of two parts, namely the `compactness' and `separation measure'. The compactness indicates the degree of the similarity among the data objects in the same cluster. The separation measure indicates the degree of dissimilarity among the data objects in different clusters. The performance of their proposed index is excellent underpinned by the outcomes from the experiments based on both artificial datasets and real world datasets.

Fast automatic medical image segmentation based on spatial kernel fuzzy c-means on level set method

Fast two-cycle (FTC) model is an efficient and the fastest Level set image segmentation. But, its performance is highly dependent on appropriate manual initialization. This paper proposes a new algorithm by combining a spatially constrained kernel-based fuzzy c-means (SKFCM) algorithm and an FTC model to overcome the mentioned problem. The approach consists of two successive stages. First, the SKFCM makes a rough segmentation to select the initial contour automatically. Then, a fuzzy membership matrix of the region of interest, which is generated by the SKFCM, is used in the next stage to produce an initial contour. Eventually, the FTC scheme segments the image by a curve evolution based on the level set. Moreover, the fuzzy membership degree from the SKFCM is incorporated into the fidelity term of the Chan---Vese model to improve the robustness and accuracy, and it is utilized for the data-dependent speed term of the FTC. A performance evaluation of the proposed algorithm is carried out on the synthetic and real images. The experimental results show that the proposed algorithm has advantages in accuracy, computational time and robustness against noise in comparison with the KFCM, the SKFCM, the hybrid model of the KFCM and the FTC, and five different level set methods on medical image segmentation.

ABC and IFC: modules detection method for PPI network.

Many clustering algorithms are unable to solve the clustering problem of protein-protein interaction (PPI) networks effectively. A novel clustering model which combines the optimization mechanism of artificial bee colony (ABC) with the fuzzy membership matrix is proposed in this paper. The proposed ABC-IFC clustering model contains two parts: searching for the optimum cluster centers using ABC mechanism and forming clusters using intuitionistic fuzzy clustering (IFC) method. Firstly, the cluster centers are set randomly and the initial clustering results are obtained by using fuzzy membership matrix. Then the cluster centers are updated through different functions of bees in ABC algorithm; then the clustering result is obtained through IFC method based on the new optimized cluster center. To illustrate its performance, the ABC-IFC method is compared with the traditional fuzzy C-means clustering and IFC method. The experimental results on MIPS dataset show that the proposed ABC-IFC method not only gets improved in terms of several commonly used evaluation criteria such as precision, recall, and P value, but also obtains a better clustering result.

The Risk Assessment of High-Tech Project Based on Comprehensive Evaluation of Fuzzy and Gray Model

High-tech projects have high risks involving wide range of links, high expense of investment, long period of development and production cycle, complicated operation system, etc. When evaluating the project's risk, a separate gray method or fuzzy theory model is not comprehensive, it should combine the gray method with the fuzzy evaluation model. From the fuzzy evaluation and gray evaluation method the gray clustering statistic could be obtained by use of grey cluster theory. It is necessary to construct fuzzy membership matrix of risk and establish a fuzzy and gray comprehensive evaluation method, and adequately adopt expert's evaluation information of the fuzziness and grayness. Finally, using concrete empirical analysis in aviation armament project risk assessment, the feasibility and the correctness of the model are verified.

Application of fuzzy membership matrix in medical diagnosis and decision making

The eld of medicine and decision making are the most fruitful and interesting area of applications of fuzzy set theory. In real life situations, the imprecise nature of medical documentation and uncertain information gathered for decision making requires the use of \fuzzy. In this paper, procedures are presented for medical diagnosis and for fuzzy decision model. Examples are illustrated to verify the proposed approach.

A hybrid heuristic and learning automata-based algorithm for distribution substations siting, sizing and defining the associated service areas

SUMMARY This paper presents a new solution approach for optimal substation expansion planning (SEP) within electric power distribution networks. A modified fuzzy membership matrix as well as a memorable cost index vector is introduced to find the optimal substation service areas. Besides these, a Learning Automata-based algorithm is introduced for simultaneous determination of optimal service areas and capacities of the distribution substations. Electrical constraints such as voltage drops, power flow, radial flow constraints, as well as all prevalent cost indices are taken into consideration. The developed method is conducted to solve the distribution substation allocation problem for an actual distribution network with about 200 000 customers, and obtained results are compared to those of other methods. Detailed numerical results and comparisons presented in the paper show that the proposed solution approach could noticeably improve the quality of problem solutions with low computational burden and can be used as an effective tool for SEP in large distribution networks. Copyright © 2012 John Wiley & Sons, Ltd.

A nonnegative sparse representation based fuzzy similar neighbor classifier

This paper presents a new classification technique by combining the well-known Sparse Representation based algorithm with the theory of Fuzzy Set. The basic idea of this work is that samples with the same class-labels should be more similar to each other than those with different class-labels. Based on this similarity rule, we first impose the nonnegative coefficient constraints on the sparse representation based algorithm and obtain the desirable similar neighbors. Then by introducing the theory of Fuzzy Set into our work, we construct the fuzzy class membership matrix and then assign the decision membership of the query sample to each class. The class assigned with the dominant decision membership is wanted. The proposed approach is called the Nonnegative Sparse Representation based Fuzzy Similar Neighbor Classification (FSNC). FSNC has the following properties: (a) the neighbor parameter K is not needed to be set in advance, and K is adaptively set by the algorithm itself; (b) similar neighbors are also generated adaptively and contain much more similar properties of the query sample; (c) the degree of similarity of data is clearly recorded in the sparse nonnegative coefficient vector; (d) the fuzzy decision rule is effective and the proposed classifier FSNC is simple. Experimental results conducted on the Wine database from UCI, the AR face database, the CENPARMI handwritten numeral database, and the PolyU palmprint database show that the new proposed classification technique outperforms some other state-of-the-art classifiers.

A Fuzzy Approach for Multitype Relational Data Clustering

Mining interrelated data among multiple types of objects or entities is important in many real-world applications. Despite extensive study on fuzzy clustering of vector space data, very limited exploration has been made on fuzzy clustering of relational data that involve several object types. In this paper, we propose a new fuzzy clustering approach for multitype relational data (FC-MR). In FC-MR, different types of objects are clustered simultaneously. An object is assigned a large membership with respect to a cluster if its related objects in this cluster have high rankings. In each cluster, an object tends to have a high ranking if its related objects have large memberships in this cluster. The FC-MR approach is formulated to deal with multitype relational data with various structures. The objective function of FC-MR is locally optimized by an efficient iterative algorithm, which updates the fuzzy membership matrix and the ranking matrix of one type at once while keeping those of other types constant. We also discuss the simplified FC-MR for multitype relational data with two special structures, namely, star-structure and extended star-structure. Experimental studies are conducted on benchmark document datasets to illustrate how the proposed approach can be applied flexibly under different scenarios in real-world applications. The experimental results demonstrate the feasibility and effectiveness of the new approach compared with existing ones.

Detection and Identification of Abnormalities in Customer Consumptions in Power Distribution Systems

This paper proposes a computational technique for the classification of electricity consumption profiles. The methodology is comprised of two steps. In the first one, a C-means-based fuzzy clustering is performed in order to find consumers with similar consumption profiles. Afterwards, a fuzzy classification is performed using a fuzzy membership matrix and the Euclidean distance to the cluster centers. Then, the distance measures are normalized and ordered, yielding a unitary index score, where the potential fraudsters or users with irregular patterns of consumption have the highest scores. The approach was tested and validated on a real database, showing good performance in tasks of fraud and measurement defect detection.

A method of relational fuzzy clustering based on producing feature vectors using FastMap

The first stage of organizing objects is to partition them into groups or clusters. The clustering is generally done on individual object data representing the entities such as feature vectors or on object relational data incorporated in a proximity matrix. This paper describes another method for finding a fuzzy membership matrix that provides cluster membership values for all the objects based strictly on the proximity matrix. This is generally referred to as relational data clustering. The fuzzy membership matrix is found by first finding a set of vectors that approximately have the same inter-vector Euclidian distances as the proximities that are provided. These vectors can be of very low dimension such as 5 or less. Fuzzy c-means (FCM) is then applied to these vectors to obtain a fuzzy membership matrix. In addition two-dimensional vectors are also created to provide a visual representation of the proximity matrix. This allows comparison of the result of automatic clustering to visual clustering. The method proposed here is compared to other relational clustering methods including NERFCM, Rouben’s method and Windhams A-P method. Various clustering quality indices are also calculated for doing the comparison using various proximity matrices as input. Simulations show the method to be very effective and no more computationally expensive than other relational data clustering methods. The membership matrices that are produced by the proposed method are less crisp than those produced by NERFCM and more representative of the proximity matrix that is used as input to the clustering process.

Clustering feature vectors with mixed numerical and categorical attributes

This paper describes a method for finding a fuzzy membership matrix in case of numerical and categorical features. The set of feature vectors with mixed features is mapped to a set of feature vectors with only real valued components with the condition that the new set of vectors has the same proximity matrix as the original feature vectors. This new set of vectors is then clustered using fuzzy c-means. Simulations show the method to be very effective in comparison with other methods.

Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization

The first stage of knowledge acquisition and reduction of complexity concerning a group of entities is to partition or divide the entities into groups or clusters based on their attributes or characteristics. Clustering algorithms normally require both a method of measuring proximity between patterns and prototypes and a method for aggregating patterns. However sometimes feature vectors or patterns may not be available for objects and only the proximities between the objects are known. Even if feature vectors are available some of the features may not be numeric and it may not be possible to find a satisfactory method of aggregating patterns for the purpose of determining prototypes. Clustering of objects however can be performed on the basis of data describing the objects in terms of feature vectors or on the basis of relational data. The relational data is in terms of proximities between objects. Clustering of objects on the basis of relational data rather than individual object data is called relational clustering. The premise of this paper is that the proximities between the membership vectors, which are obtained as the objective of clustering, should be proportional to the proximities between the objects. The values of the components of the membership vector corresponding to an object are the membership degrees of the object in the various clusters. The membership vector is just a type of feature vector. Based on this premise, this paper describes another fuzzy relational clustering method for finding a fuzzy membership matrix. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort, a Bayesian stopping criterion is used in combination with a multi-start strategy for the PSO. Other relational clustering methods generally find local optimum of their objective function.