Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.     

A Decision Support Model for Hotel Recommendation Based on the Online Consumer Reviews Using Logarithmic Spherical Hesitant Fuzzy Information

Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.     

Accurate segmentation of leukocyte in blood cell images using Atanassov's intuitionistic fuzzy and interval Type II fuzzy set theory

In this paper automatic leukocyte segmentation in pathological blood cell images is proposed using intuitionistic fuzzy and interval Type II fuzzy set theory. This is done to count different types of leukocytes for disease detection. Also, the segmentation should be accurate so that the shape of the leukocytes is preserved. So, intuitionistic fuzzy set and interval Type II fuzzy set that consider either more number of uncertainties or a different type of uncertainty as compared to fuzzy set theory are used in this work. As the images are considered fuzzy due to imprecise gray levels, advanced fuzzy set theories may be expected to give better result. A modified Cauchy distribution is used to find the membership function. In intuitionistic fuzzy method, non-membership values are obtained using Yager's intuitionistic fuzzy generator. Optimal threshold is obtained by minimizing intuitionistic fuzzy divergence. In interval type II fuzzy set, a new membership function is generated that takes into account the two levels in Type II fuzzy set using probabilistic T co norm. Optimal threshold is selected by minimizing a proposed Type II fuzzy divergence. Though fuzzy techniques were applied earlier but these methods failed to threshold multiple leukocytes in images. Experimental results show that both interval Type II fuzzy and intuitionistic fuzzy methods perform better than the existing non-fuzzy/fuzzy methods but interval Type II fuzzy thresholding method performs little bit better than intuitionistic fuzzy method. Segmented leukocytes in the proposed interval Type II fuzzy method are observed to be distinct and clear.     

A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights

In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and some desirable special cases of the new operators. Second, a new entropy measure for q-RDHFSs is developed, which defines a method to calculate the weight information of aggregated q-rung dual hesitant fuzzy elements. Third, a novel MADM method is introduced to deal with decision-making problems under q-RDHFSs environment, wherein weight information is completely unknown. Finally, we present numerical example to show the effectiveness and performance of the new method. Additionally, comparative analysis is conducted to prove the superiorities of our new MADM method. This study mainly contributes to a novel method, which can help decision makes select optimal alternatives when dealing with practical MADM problems.     

On the Neutrosophic,Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.     

Uncertainty of Interval Type-2 Fuzzy Sets Based on Fuzzy Belief Entropy

Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA [Bel,Pl]. Then, Bel and Pl are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, which makes the result more reasonable. Compared with other methods, fuzzy belief entropy is more reasonable because it can measure the uncertainty caused by multielement fuzzy subsets. Furthermore, when the membership function belongs to type-1 fuzzy sets, fuzzy belief entropy degenerates to Shannon entropy. Compared with other methods, several numerical examples are demonstrated that the proposed entropy is feasible and persuasive.     

A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information

As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an illustrative application is provided for its better demonstration, which is subjected to the selection of a suitable company of virtual reality devices. Finally, a comparison of the initiated method is explored with some existing models, including intuitionistic fuzzy soft expert sets.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.     

基于最大模糊熵和遗传算法的图像分割

为了分割照度不均匀的网格图像,提出了一种基于最大模糊熵和遗传算法的阈值分割方法。基于模糊集合理论,根据像素灰度值把原始图像中的像素分为黑和亮两个模糊集,利用最大模糊熵准则确定模糊区间的范围,寻找模糊参数的最优组合,实现图像分割。由于穷举法搜索模糊参数的最优组合存在计算复杂度高、占用存储空间大等缺点,因此采用了遗传算法确定最优阈值。为了验证该方法的有效性,对其进行了图像分割实验,并与最大类间方差法、迭代法和一维最大熵法进行了比较。实验结果表明,该方法能够自动、有效地选取阈值,分割效果优于其它三种算法,并能保留原始图像的主要特征。     

二维广义模糊熵图像阈值分割法

针对一维广义模糊熵不能有效处理含噪图像的分割问题,在二维灰度直方图上定义了图像的二维隶属度函数,提出了二维广义模糊熵阈值分割法.该方法不仅考虑了图像的点灰度值,同时考虑了图像像素的邻域平均灰度值,能更好地利用图像中的信息.为了提高二维广义模糊熵阈值法的运行速度、解决参量选取问题,结合粒子群优化搜索方法,设计了嵌套式的优化过程.实验表明,二维广义模糊熵阈值分割法对噪音图像有更好的适应性.     

An Extended FMEA Model Based on Cumulative Prospect Theory and Type-2 Intuitionistic Fuzzy VIKOR for the Railway Train Risk Prioritization

This paper aims toward the improvement of the limitations of traditional failure mode and effect analysis (FMEA) and examines the crucial failure modes and components for railway train operation. In order to overcome the drawbacks of current FMEA, this paper proposes a novel risk prioritization method based on cumulative prospect theory and type-2 intuitionistic fuzzy VIKOR approach. Type-2 intuitionistic VIKOR handles the combination of the risk factors with their entropy weight. Triangular fuzzy number intuitionistic fuzzy numbers (TFNIFNs) applied as type-2 intuitionistic fuzzy numbers (Type-2 IFNs) are adopted to depict the uncertainty in the risk analysis. Then, cumulative prospect theory is employed to deal with the FMEA team member’s risk sensitiveness and decision-making psychological behavior. Finally, a numerical example of the railway train bogie system is selected to illustrate the application and feasibility of the proposed extended FMEA model in this paper, and a comparison study is also performed to validate the practicability and effectiveness of the novel FMEA model. On this basis, this study can provide guidance for the risk prioritization of railway trains and indicate a direction for further research of risk management of rail traffic.     

等概率符号化样本熵应用于脑电分析

样本熵(或近似熵)以信息增长率刻画时间序列的复杂性,能应用于短时序列,因而在生理信号分析中被广泛采用.然而,一方面由于传统样本熵采用与标准差线性相关的容限,使得熵值易受非平稳突变干扰的影响,另一方面传统样本熵还受序列概率分布的影响,从而导致其并非单纯反映序列的信息增长率.针对上述两个问题,将符号动力学与样本熵结合,提出等概率符号化样本熵方法,并对其物理意义、数学推导及参数选取都做了详细阐述.通过对噪声数据的仿真计算,验证了该方法的正确性及其区分不同强度时间相关的有效性.此方法应用于脑电信号分析的结果表明,在不对信号做人工伪迹去除的前提下,只需要1.25 s的脑电信号即可有效地区分出注意力集中和注意力发散两种状态.这进一步证明了该方法可很好地抵御非平稳突变干扰,能快速获得短时序列的潜在动力学特性,对脑电生物反馈技术具有很大的应用价值.     

Numerical analysis of the 2D acoustic field with fuzzy-random parameters

Regard for the fuzziness and the randomness in some acoustic fields,a method for the numerical analysis of the 2D acoustic field with Fuzzy-Random parameters was proposed based on the equivalent conversion of information entropy.In the proposed method,a fuzzyrandom acoustic field was treated as a pure fuzzy acoustic field or a pure random acoustic field by transforming all the variables into fuzzy variables or random variables.Perturbation finite element methods for analyzing the two-dimensional acoustic fuzzy and random field are deduced.The sound pressure response of a 2D acoustic tube and the 2D acoustic cavity of a car with fuzzy-random parameters were analyzed by the proposed method and the Monte Carlo method,the results show that the proposed method can be well applied to the numerical analysis of the 2D acoustic field with fuzzy-random parameters,and has good prospect of engineering application.     

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations

Recently, there has been enormous development due to advancements in technology. Industries and enterprises are moving towards a digital system, and the oil and gas industries are no exception. There are several threats and risks in digital systems, which are controlled through cyber-security. For the first time in the theory of fuzzy sets, this research analyzes the relationships between cyber-security and cyber-crimes in the oil and gas sectors. The novel concepts of complex intuitionistic fuzzy relations (CIFRs) are introduced. Moreover, the types of CIFRs are defined and their properties are discussed. In addition, an application is presented that uses the Hasse diagram to make a decision regarding the most suitable cyber-security techniques to implement in an industry. Furthermore, the omnipotence of the proposed methods is explained by a comparative study.     

Development of hedge operator based fuzzy divergence measure and its application in segmentation of chronic myelogenous leukocytes from microscopic image of peripheral blood smear

This paper introduces a hedge operator based fuzzy divergence measure and its application in segmentation of leukocytes in case of chronic myelogenous leukemia using light microscopic images of peripheral blood smears. The concept of modified discrimination measure is applied to develop the measure of divergence based on Shannon exponential entropy and Yager's measure of entropy. These two measures of divergence are compared with the existing literatures and validated by ground truth images. Finally, it is found that hedge operator based divergence measure using Yager's entropy achieves better segmentation accuracy i.e., 98.29% for normal and 98.15% for chronic myelogenous leukocytes. Furthermore, Jaccard index has been performed to compare the segmented image with ground truth ones where it is found that that the proposed scheme leads to higher Jaccard index (0.39 for normal, 0.24 for chronic myelogenous leukemia).     

Performance Evaluation of Construction Companies Using Integrated Entropy–Fuzzy VIKOR Model

The construction sector plays an important role in a country’s economic development. The financial performance of a company is a good indicator of its financial health and status. In Malaysia, the government encourages the construction industry to develop an advanced infrastructure related to health, transport, education and housing. In view of the COVID-19 pandemic, the operations and financial performance of construction sector companies have been affected recently. Additionally, uncertainty plays a vital role in the multi-criteria decision-making (MCDM) process. Based on previous studies, there has been no comprehensive study conducted on the evaluation of the financial performance of construction companies by integrating entropy and fuzzy VIKOR models. Therefore, this paper aims to propose an MCDM model to evaluate and compare the financial performance of construction companies with an integrated entropy–fuzzy VIKOR model. A case study is carried out by evaluating the listed construction companies in Malaysia with the proposed model. The findings of this paper indicate that the company ECONBHD achieves the best financial performance over the study period. The significance of this paper is to determine the priority of the financial ratios and ranking of the construction companies with the proposed entropy–fuzzy VIKOR model.     

基于空间信息的直觉模糊C-均值图像分割算法

针对模糊C-均值聚类算法的单一隶属度不能充分描述图像不确定性,且聚类过程中忽略像素空间关系的问题,提出一种基于空间信息的直觉模糊C-均值算法;该算法选取3×3的模板计算邻域像素灰度均值;并引入权重项,来控制灰度信息和空间信息各自所占的比重,同时用犹豫度更新直觉模糊集的隶属度函数;对常用标准图像的仿真结果表明,该算法能更好地保留图像细节信息,得到更加理想的图像分割效果。     

基于PSO和模糊划分熵的水下图像分割

在水下环境中,由于存在着水体对光线的吸收以及照明不均等原因,水下图像具有信噪比低、边缘模糊等特点。如果直接使用传统的分割方法,对水下图像进行处理后的效果较差。传统的基于最大熵原理的阈值法尽管能实现某些特定的分割任务,但是其时效性较差。而粒子群算法(PSO)是一类随机全局优化技术,该算法简单易实现,可调参数少。因此将群体智能中的粒子群优化算法应用到图像分割中。新方法在重新定义模糊熵的基础上,根据最大熵原理,利用粒子群算法来搜索分割阈值。相对于传统的利用穷举法来搜索分割阈值的算法,新方法大大减少了计算时间,提高了效率。通过对水下图像处理实验证明,该算法对简单背景的图像分割是有效的,和传统分割方法相比,具有更强的自适应性和抗噪性能。     

Automatic leukocyte nucleus segmentation by intuitionistic fuzzy divergence based thresholding

The paper proposes a robust approach to automatic segmentation of leukocyte's nucleus from microscopic blood smear images under normal as well as noisy environment by employing a new exponential intuitionistic fuzzy divergence based thresholding technique. The algorithm minimizes the divergence between the actual image and the ideally thresholded image to search for the final threshold. A new divergence formula based on exponential intuitionistic fuzzy entropy has been proposed. Further, to increase its noise handling capacity, a neighborhood-based membership function for the image pixels has been designed. The proposed scheme has been applied on 110 normal and 54 leukemia (chronic myelogenous leukemia) affected blood samples. The nucleus segmentation results have been validated by three expert hematologists. The algorithm achieves an average segmentation accuracy of 98.52% in noise-free environment. It beats the competitor algorithms in terms of several other metrics. The proposed scheme with neighborhood based membership function outperforms the competitor algorithms in terms of segmentation accuracy under noisy environment. It achieves 93.90% and 94.93% accuracies for Speckle and Gaussian noises, respectively. The average area under the ROC curves comes out to be 0.9514 in noisy conditions, which proves the robustness of the proposed algorithm.