New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Shapley-Based Estimation of Company Value—Concept,Algorithms and Parameters

The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson’s correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies.     

Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.     

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.     

混沌时间序列的模糊神经网络预测

设计一种新型混合模糊神经推理系统，该系统仅从期望输入输出数据集即可达到获取知识、确定模糊初始规则基的目的.再利用神经网络学习能力便不难修改规则库中的模糊规则以及隶属函数和网络权值等参数，这样大大减少了规则匹配过程，加快了推理速度，从而极大程度地提高了系统的自适应能力.用它对Mackey-Glass混沌时间序列进行预测试验,结果表明利用该网络模型无论离线还是在线学习均能对Mackey-Glass混沌时间序列进行准确的预测，证明了该系统的有效性. 关键词： 神经网络模型 模糊逻辑 混合推理系统 混沌时间序列     

基于模糊集理论的运动目标检测

针对复杂自然环境下运动目标检测中噪声多、目标检测不完整等问题,提出一种改进的基于模糊集理论的解决方法。使用金字塔多分辨率模型进行背景差分获取初步的前景掩膜,将当前帧的颜色、时间、空间、位置4种特征用模糊集表示,形成模糊向量集合簇,用模糊数学理论结合这4个向量的特征,得到每个像素点对前景的隶属度,从而检测运动目标。该方法不仅能有效地检测较完整运动目标,也可以克服自然环境下微小运动背景的影响。实验结果显示:该方法前景的识别率为0.717 4,错误率为0.011 8,能适应自然环境下动态背景的影响。     

Modeling shear modulus distribution in magnetic resonance elastography with piecewise constant level sets

Magnetic resonance elastography (MRE) is designed for imaging the mechanical properties of soft tissues. However, the interpretation of shear modulus distribution is often confusing and cumbersome. For reliable evaluation, a common practice is to specify the regions of interest and consider regional elasticity. Such an experience-dependent protocol is susceptible to intrapersonal and interpersonal variability. In this study we propose to remodel shear modulus distribution with piecewise constant level sets by referring to the corresponding magnitude image. Optimal segmentation and registration are achieved by a new hybrid level set model comprised of alternating global and local region competitions. Experimental results on the simulated MRE data sets show that the mean error of elasticity reconstruction is 11.33% for local frequency estimation and 18.87% for algebraic inversion of differential equation. Piecewise constant level set modeling is effective to improve the quality of shear modulus distribution, and facilitates MRE analysis and interpretation.     

A New Hybrid Possibilistic-Probabilistic Decision-Making Scheme for Classification

Uncertainty is at the heart of decision-making processes in most real-world applications. Uncertainty can be broadly categorized into two types: aleatory and epistemic. Aleatory uncertainty describes the variability in the physical system where sensors provide information (hard) of a probabilistic type. Epistemic uncertainty appears when the information is incomplete or vague such as judgments or human expert appreciations in linguistic form. Linguistic information (soft) typically introduces a possibilistic type of uncertainty. This paper is concerned with the problem of classification where the available information, concerning the observed features, may be of a probabilistic nature for some features, and of a possibilistic nature for some others. In this configuration, most encountered studies transform one of the two information types into the other form, and then apply either classical Bayesian-based or possibilistic-based decision-making criteria. In this paper, a new hybrid decision-making scheme is proposed for classification when hard and soft information sources are present. A new Possibilistic Maximum Likelihood (PML) criterion is introduced to improve classification rates compared to a classical approach using only information from hard sources. The proposed PML allows to jointly exploit both probabilistic and possibilistic sources within the same probabilistic decision-making framework, without imposing to convert the possibilistic sources into probabilistic ones, and vice versa.     

Studies on Cancer Diagnosis by Using Spectroscopy Combined with ChemometricsSCIEI北大核心CSCD

Studies on cancer diagnosis using various spectroscopic methods combined with chemometrics are briefly reviewed. Elemental contents in serum samples were determined by inductively coupled plasma atomic emission spectroscopy (ICP-AFS), bidirectional associative memory (BAM) networks were used to establish diagnosis models for the relationships between elemental contents and lung cancer, liver cancer, and stomach cancer, respectively. Near infrared spectroscopy (NIRS) is a non-destructive detection technology. Near infrared spectra of endometrial carcinoma samples were determined and spectral features were extracted by chemoometric methods, a fuzzy rule-based expert system (FuRES) was used for establishing diagnosis model, satisfactory results were obtained. We also proposed a novel variable selection method based on particle swarm optimization (PSO) for near infrared spectra of endometrial carcinoma samples. Spectra with optimized variable were then modeled by support victor machine (SVM). Terahertz technology is an emerging technology for non-destructive detection, which has some unique characteristics. Terahertz time domain spectroscopy (THz-TDS) was used for cervical carcinoma measurement. Absorption coefficients. were calculated from the measured time domain spectra and then processed with derivative, orthogonal signal correction (PC-OSC) to reduce interference components, and then fuzzy rule-based expert system (FuRES), fuzzy optimal associative memory (FOAM), support victor machine (SVM), and partial least squares discriminant analysis (PLS-DA) were used for diagnosis model establishment. The above results provide useful information for cancer occurring and development, and provide novel approaches for early stage diagnosis of various cancers.     

光谱学方法结合化学计量学用于癌诊断研究

对近年来采用多种光谱学方法对癌诊断研究工作进行了简要综述。利用电感耦合等离子体原子发射光谱分析(ICP-AES)法对人血清中微量元素含量进行了测定,将双向联想记忆神经网络(BAM)用于建立微量元素与肺癌、肝癌和胃癌之间的关系,建立了分类鉴定模型;利用近红外光谱技术非破坏无损检测的特性,采用化学计量学方法对子宫内膜癌组织的近红外光谱(NIRS)进行特征变量提取,用模糊规则专家系统建立诊断模型,取得了满意的结果;建立了一种基于粒子群优化(PSO)方法对近红外光谱变量进行选择,然后采用支持向量机(SVM)建立诊断模型;太赫兹时域光谱(THz-TDS)技术是近年来受到重视的一种非破坏无损检测方法,由于其辐射能量低,因此对于生物样品检测具有很好的发展前景。采用THz-TDS技术对子宫颈癌组织进行测试,对这些癌组织的THz光谱采用导数光谱、正交信号校正(OSC)等光谱预处理方法减少干扰成分和变量选择后,分别采用模糊规则专家系统(FuRES)、模糊优化联想记忆网络(FOAM)、支持向量机(SVM)和偏最小二乘判别分析(PLS-DA)等方法建立分类模型,均取得了较满意的结果。这些研究结果为研究癌的发生和发展提供了有用的信息,为癌的早期诊断提供了新的方法。     

TNT: An Interpretable Tree-Network-Tree Learning Framework using Knowledge Distillation

Deep Neural Networks (DNNs) usually work in an end-to-end manner. This makes the trained DNNs easy to use, but they remain an ambiguous decision process for every test case. Unfortunately, the interpretability of decisions is crucial in some scenarios, such as medical or financial data mining and decision-making. In this paper, we propose a Tree-Network-Tree (TNT) learning framework for explainable decision-making, where the knowledge is alternately transferred between the tree model and DNNs. Specifically, the proposed TNT learning framework exerts the advantages of different models at different stages: (1) a novel James–Stein Decision Tree (JSDT) is proposed to generate better knowledge representations for DNNs, especially when the input data are in low-frequency or low-quality; (2) the DNNs output high-performing prediction result from the knowledge embedding inputs and behave as a teacher model for the following tree model; and (3) a novel distillable Gradient Boosted Decision Tree (dGBDT) is proposed to learn interpretable trees from the soft labels and make a comparable prediction as DNNs do. Extensive experiments on various machine learning tasks demonstrated the effectiveness of the proposed method.     

Fuzzy logic membership implementation using optical hardware components

Intelligent control techniques consist of knowledge-based expert or fuzzy logic control. One obvious drawback in many such applications is that fuzzy logic memberships are implemented at the lowest level. In high-bandwidth processes, this form of fuzzy logic membership implementation would require high speed and accuracy in the presence of strong nonlinearities and dynamic coupling. This paper presents a novel methodology called the Opto-fuzzy method to design a fuzzy logic membership using an optical hardware component. The proposed scheme is applied to triangular-shaped and half trapezoidal-shaped membership functions.