An Efficient DWT and Intuitionistic Fuzzy Based Multimodality Medical Image Fusion

Image fusion aims to integrate complementary information from multiple modalities into a single image with none distortion and loss of data. Image fusion is important in medical imaging, specifically for the purpose of detecting the tumor and identification of diseases. In this article, completely unique discrete wavelet transform (DWT) and intuitionistic fuzzy sets (IFSs) based fusion method (DWT‐IFS) is proposed. For fusion, initially, all source images are fused using DWT with the average, maximum, and entropy fusion rules. Besides, on the fused image IFS is applied. In the IFS process images are converted into intuitionistic fuzzy images (IFIs) by selecting an optimum value for the parameter in membership, non‐membership, and hesitation degree function using entropy. Then, the resulting IFIs are decomposed into the blocks, and the corresponding blocks of the images are fused using the intersection and union operations of IFS. The efficiency of the proposed DWT‐IFS fusion method is recognized by examining it with other existing methods, such as Averaging (AVG), Principal Component Analysis (PCA), Laplacian Pyramid Approach (LPA), Contrast Pyramid Approach (CPA), Discrete Wavelet Transform (DWT), Morphological Pyramid Approach (MPA), Redundancy Discrete Wavelet Transform (RDWT), Contourlet Transform (CONTRA), and Intuitionistic Fuzzy Set (IFS) using subjective and objective performance evaluation measures. The experimental results reveal that the proposed DWT‐IFS fusion method provides higher quality of information in terms of physical properties and contrast as compared to the existing methods.     

基于直觉模糊优化的双边匹配决策

为了实现不确定信息环境下的双边满意匹配，提出基于直觉模糊优化的匹配决策方法。利用直觉模糊集理论中隶属度和非隶属度的概念，将经典匹配决策模型中双目标函数转换为反映匹配双方总体满意度的单目标函数，模型中同时纳入公平性因素。通过设计交互式算法，在满足一定的公平性条件下实现总体满意度最大化。该算法为匹配决策过程注入了灵活性和协调性，具有一定的实用性和参考价值。     

直觉模糊数的表示和结构刻划

本文给出了直觉模糊数的表示定理:包括区间表示、函数表示、嵌入定理,并将直觉模糊数空间嵌入到一类特殊的二维模糊数空间—方模糊数空间,给出了直觉模糊数的结构定理;最后,利用方模糊数与一般二维模糊数的逼近定理,给出了二维模糊数的直觉模糊数逼近。     

Brightness preserving optimized weighted bi-histogram equalization algorithm and its application to MR brain image segmentation

Medical image segmentation is crucial for neuroscience research and computer-aided diagnosis. However, intensity inhomogeneity and existence of noise in magnetic resonance images lead to incorrect segmentation. In this article, an effective method called enhanced fuzzy level set algorithm is presented to segment the white matter, gray matter, and cerebrospinal fluid automatically in contrast-enhanced brain images. In this method, first, exposure threshold is computed to divide the input histogram into two sub-histograms of different gray levels. The input histogram is clipped using a mean gray level to control the excessive enhancement rate. Then, these two sub-histograms are modified and equalized independently to get a better contrast enhanced image. Finally, an enhanced fuzzy level set algorithm is employed to facilitate image segmentation. The extensive experimental results proved the outstanding performance of the proposed algorithm compared with other existing methods. The results conform its effectiveness for MR brain image segmentation.     

A novel brain image segmentation using intuitionistic fuzzy C means algorithm

A process of splitting the image into pixel bands is the image segmentation. As medical imaging contain uncertainties, there are difficulties in classification of images into homogeneous regions. There is a need for segmentation algorithm for removing the noise from the medical image segmentation. The very popular algorithm is Fuzzy C‐Means (FCM) algorithm used for image segmentation. Fuzzy sets, rough sets, and the combination of fuzzy and rough sets play a prominent role in formalizing uncertainty, vagueness, and incompleteness in diagnosis. But it will use intensity values only which will be highly sensitive to noise. In this article, an Intuitionistic FCM (IFCM) algorithm is presented for clustering. Intuitionistic fuzzy (IF) sets are generalized sets and their elements are characterized by a membership value as well as nonmembership value. This IFCM has an uncertainty parameter which is called hesitation degree and a new objective function is integrated in the standard FCM based on IF entropy. The IFCM will provide better performance than FCM for image segmentation.     

Failure mode and effect analysis using the hesitant intuitionistic fuzzy hybrid GRP approach with ordered comprehensive weights

Failure mode and effect analysis (FMEA), a multidisciplinary reliability analysis tool based on team evaluations, has been widely used in various industries. There are three critical issues in FMEA: the conversion of linguistic evaluations, the weights of risk factors, and the ranking mechanism of failure modes. Scholars have used various fuzzy theories and multi-attribute decision-making (MADM) methods to improve traditional FMEA, but there are still deficiencies. In this paper, the hesitant intuitionistic fuzzy set (HIFS), a concept that combines the intuitionistic fuzzy set (IFS) and the hesitant fuzzy set (HFS), is introduced into FMEA to convert linguistic evaluations. Some operators based on HIFS are proposed to process the converted data. Among them, a hesitant intuitionistic fuzzy comprehensive weighted Hamming distance (HIFCWHD) operator is proposed to compute the ordered comprehensive weight, effectively weakening the effect of extreme scores on results. The gray relational projection (GRP) method is adopted to determine the risk priority order of the failure modes. Finally, we give an illustrative case to demonstrate the effectiveness of the proposed FMEA method.     

Modified transform-based gamma correction for MRI tumor image denoising and segmentation by optimized histon-based elephant herding algorithm

Medical image processing is typically performed to diagnose a patient's brain tumor prior to surgery. In this study, a technique in denoising and segmentation was developed to improve medical image processing. The proposed approach employs multiple modules. In the first module, the noisy brain tumor image is transformed into multiple low- and high-pass tetrolet coefficients. In the second module, multiple low-pass tetrolet coefficients are applied through a modified transform-based gamma correction method. Generalized cross-validation is used on multiple high-pass tetrolet coefficients to obtain the best threshold value. In the third module, all enhanced coefficients are applied to the partial differential equation method. In the final module, the denoised image is applied to Atanassov's intuitionistic fuzzy set histon-based fuzzy clustering method with centroid optimization using an elephant herding method. Accordingly, the tumor part is segmented from the nontumor part in the magnetic resonance imaging brain images. The method was assessed in terms of peak signal-to-noise ratio, mean square error, specificity, sensitivity, and accuracy. The experimental results showed that the suggested method is superior to traditional methods.     

A machine learning approach for brain image enhancement and segmentation

In brain MRI analysis, image segmentation is commonly used for measuring and visualizing the brain's anatomical structures, for surgical planning, etc. However, due to presence of noise and uncertainty between different tissues in the brain image, the segmentation of brain is a challenging task. This problem is rectified in this article using two stages. In the first stage an enhancement technique called contrast limited fuzzy adaptive histogram equalization (CLFAHE) which is a combination of CLAHE and fuzzy enhancement is used to improve the contrast of MRI Brain images. Contrast of the image is controlled using contrast intensification operator (Clip limit). The second stage deals with the segmentation of enhanced image. The enhanced brain images are segmented using new level‐set method which has the property of both local and global segmentation. Signed pressure force (SPF) function is also used here which stops the contours at weak and blurred edged efficiently.     

决策实施的直觉模糊集方法

阐述<卓越绩效评价准则>决策实施的重要意义以及应用直觉模糊集的必要性.提出方案优选中多准则直觉模糊集评价,各准则权重实质重要度,方案优选的正负理想解以及直觉模糊集距离的概念及计算方法.在此基础上提出各方案评价指数的概念,由其大小决定方案的优劣.举出上海某通信有限责任公司销售代理商优选决策的示例,得出A3优于A1优于A2优于A4的结论.     

Brightness preserving bi‐level fuzzy histogram equalization for MRI brain image contrast enhancement

In this article, brightness preserving bi‐level fuzzy histogram equalization (BPFHE) is proposed for the contrast enhancement of MRI brain images. Histogram equalization (HE) is widely used for improving the contrast in digital images. As a result, such image creates side‐effects such as washed‐out appearance and false contouring due to the significant change in brightness. In order to overcome these problems, mean brightness preserving HE based techniques have been proposed. Generally, these methods partition the histogram of the original image into sub histograms and then independently equalize each sub‐histogram. The BPFHE consists of two stages. First, fuzzy histogram is computed based on fuzzy set theory to handle the inexactness of gray level values in a better way compared to classical crisp histograms. In the second stage, the fuzzy histogram is divided into two sub‐histograms based on the mean intensities of the multi‐peaks in the original image and then equalizes them independently to preserve image brightness. The quantitative and subjective enhancement of proposed BPBFHE algorithm is evaluated using two well known parameters like entropy or average information contents (AIC) and Feature Similarity Index Matrix (FSIM) for different gray scale images. The proposed method have been tested using several images and gives better visual quality as compared to the conventional methods. The simulation results show that the proposed method has better performance than the existing methods, and preserve the original brightness quite well, so that it is possible to be utilized in medical image diagnosis.     

Ranking alternatives via maximizing set and minimizing set based fuzzy MCDM approach

Abstract

This work suggests a maximizing set and minimizing set based fuzzy multiple criteria decision‐making (MCDM) model, where criteria are classified into cost and benefit criteria. The final fuzzy evaluation value of each alternative is developed based on the concept of subtracting the summation of weighted normalized benefit ratings from that of weighted normalized cost ratings. Using interval arithmetic of fuzzy numbers can develop the membership functions for the final fuzzy evaluation values. Chen's maximizing set and minimizing set is then applied to defuzzify all the final fuzzy numbers for ranking alternatives. Formulas for the membership functions and ranking procedure of the final fuzzy numbers are clearly presented. The suggested method provides an extension to the fuzzy MCDM techniques available. A numerical example demonstrates the computational process of the proposed method.     

基于直觉模糊张量的决策方法及其应用

对具有高维数据特征的直觉模糊决策问题进行了研究,定义了直觉模糊张量的一般形式和运算法则;建立了基于直觉模糊张量的广义直觉模糊加权平均算子,探索了广义直觉模糊加权平均算子的基本性质;证明了广义直觉模糊加权平均算子是直觉模糊加权平均算子的一般形式。提出了基于广义直觉模糊加权平均算子的决策方法,通过算例验证了该方法能够有效解决具有高维数据特征的直觉模糊决策问题。     

The incorporation of the Taguchi and the VIKOR methods to optimize multi-response problems in intuitionistic fuzzy environments

The Taguchi method is a powerful method of solving quality problems in various fields of engineering. However, this method was developed to optimize single-response processes. In many multi-response optimization problems, the important response is determined subjectively, based on knowledge or experience. However, using only exact numbers to represent this importance is problematic, because there is uncertainty and vagueness. The concept of intuitionistic fuzzy sets (IFSs) is a powerful method for characterization, using a membership function and a non-membership function. This paper proposes an efficient VIKOR method that optimizes multi-response problems in intuitionistic fuzzy environments. The importance weights of various responses are evaluated in terms of IFSs. In the proposed method, the similarity measure between IFSs is used to determine the crisp weights of the responses. This scheme eliminates the need for complicated intuitionistic fuzzy arithmetic operations and increases efficiency in solving multi-response optimization problems in intuitionistic fuzzy environments. Two case studies: plasma-enhanced chemical vapor deposition and a double-sided surface mount technology electronic assembly operation are used to demonstrate the effectiveness of the proposed method.     

基于灰阶熵的模糊对比度自适应图像增强算法

一般的数字图像存在噪声大、对比度低、边缘模糊等缺陷.为了有效地增强图像的模糊对比度,以满足后续的识别与检测要求,提出了一种基于灰阶熵的模糊对比度自适应图像增强算法.在模糊域内,根据邻域窗口灰阶熵值的大小,合理选取阈值,对阈值两侧的图像像素点进行不同程度的对比度增强处理,实现局部特征的增强.实验结果表明,该方法不仅增强了图像的整体对比度,而且有效地丰富了目标图像的细节信息,并抑制了噪声的放大.     

Intuitionistic Fuzzy Petri Nets Model Based on Back Propagation Algorithm for Information Services

Intuitionistic fuzzy Petri net is an important class of Petri nets, which can be used to model the knowledge base system based on intuitionistic fuzzy production rules. In order to solve the problem of poor self-learning ability of intuitionistic fuzzy systems, a new Petri net modeling method is proposed by introducing BP (Error Back Propagation) algorithm in neural networks. By judging whether the transition is ignited by continuous function, the intuitionistic fuzziness of classical BP algorithm is extended to the parameter learning and training, which makes Petri network have stronger generalization ability and adaptive function, and the reasoning result is more accurate and credible, which is useful for information services. Finally, a typical example is given to verify the effectiveness and superiority of the parameter optimization method.     

Trapezoidal Intuitionistic Fuzzy Aggregation Operator Based on Choquet Integral and Its Application to Multi-Criteria Decision-Making Problems

The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.     

Contrast limited fuzzy adaptive histogram equalization for enhancement of brain images

Contrast limited fuzzy adaptive histogram equalization (CLFAHE) is proposed to improve the contrast of MRI Brain images. The proposed method consists of three stages. First, the gray level intensities are transformed into membership plane and membership plane is modified with Contrast intensification operator. In the second stage, the contrast limited adaptive histogram equalization is applied to the modified membership plane to prevent excessive enhancement in contrast by preserving the original brightness. Finally, membership plane is mapped back to the gray level intensities. The performance of proposed method is evaluated and compared with the existing methods in terms of qualitative measures such as entropy, PSNR, AMBE, and FSIM. The proposed method provides enhanced results by giving better contrast enhancement and preserving the local information of the original image. © 2017 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 27, 98–103, 2017     

Fuzzy entropy‐based MR brain image segmentation using modified particle swarm optimization

This article presents an image segmentation technique based on fuzzy entropy, which is applied to magnetic resonance (MR) brain images in order to detect brain tumors. The proposed method performs image segmentation based on adaptive thresholding of the input MR images. The image is classified into two membership functions (MFs) of the fuzzy region: Z‐function and S‐function. The optimal parameters of these fuzzy MFs are obtained using modified particle swarm optimization (MPSO) algorithm. The objective function for obtaining the optimal fuzzy MF parameters is considered to be the maximum fuzzy entropy. Through a number of examples, The performance is compared with existing entropy based object segmentation approaches and the superiority of the proposed method is demonstrated. The experimental results are compared with the exhaustive search method and Otsu's segmentation technique. The result shows the proposed fuzzy entropy‐based segmentation method optimized using MPSO achieves maximum entropy with proper segmentation of infected areas and with minimum computational time. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 281–288, 2013     

OLED显示屏表面缺陷自动检测方法

目的 为了解决OLED显示屏表面周期性纹理背景和缺陷边界模糊、对比度低的特征导致其表面缺陷检测困难的问题,开展OLED显示屏表面缺陷自动检测方法研究.方法 对OLED显示屏图像进行奇异值分解,选择前2个较大的奇异值重构图像纹理背景,对原图像和重构图像进行差分运算,获得残差图像.将残差图像像素随机赋予初始隶属度值,采用模糊C均值聚类法获得像素最终隶属度值.根据隶属度大小,将残差图像像素聚成2类,并从残差图像中准确地分割缺陷.结果 选取较大的2个奇异值可以有效地重构OLED显示屏的周期性纹理背景;模糊C均值聚类法分割缺陷获得的区域灰度一致性(U)平均值为0.9846.结论 基于奇异值分解的背景重构方法可以有效地检测OLED显示屏表面缺陷;与分水岭法和Otsu方法相比,模糊C均值聚类可以准确地分割模糊边界的缺陷区域.     

Multi-objective mixed integer programming and an application in a pharmaceutical supply chain

Multi-objective integer linear and/or mixed integer linear programming (MOILP/MOMILP) are very useful for many areas of application as any model that incorporates discrete phenomena requires the consideration of integer variables. However, the research on the methods for the general multi-objective integer/mixed integer model has been scant when compared to multi-objective linear programming with continuous variables. In this paper, an MOMILP is proposed, which integrates various conflicting objectives. We give importance to the imprecise nature of some of the critical factors used in the modelling that can influence the effectiveness of the model. The uncertainty and the hesitation arising from estimating such imprecise parameters are represented by intuitionistic fuzzy numbers. The MOMILP model with intuitionistic fuzzy parameters is first converted into a crisp MOMILP model, using appropriate defuzzification strategies. Thereafter, the MOMILP is transformed into a single objective problem to yield a compromise solution with an acceptable degree of satisfaction, using suitable scalarisation techniques such as the gamma-connective technique and the minimum bounded sum operator technique. The proposed solution method is applied to several test problems and a multi-objective pharmaceutical supply chain management model with self generated random data.