Identification of denatured and normal biological tissues based on compressed sensing and refined composite multi-scale fuzzy entropy during high intensity focused ultrasound treatment

In high intensity focused ultrasound(HIFU)treatment,it is crucial to accurately identify denatured and normal biological tissues.In this paper,a novel method based on compressed sensing(CS)and refined composite multi-scale fuzzy entropy(RCMFE)is proposed.First,CS is used to denoise the HIFU echo signals.Then the multi-scale fuzzy entropy(MFE)and RCMFE of the denoised HIFU echo signals are calculated.This study analyzed 90 cases of HIFU echo signals,including 45 cases in normal status and 45 cases in denatured status,and the results show that although both MFE and RCMFE can be used to identify denatured tissues,the intra-class distance of RCMFE on each scale factor is smaller than MFE,and the inter-class distance is larger than MFE.Compared with MFE,RCMFE can calculate the complexity of the signal more accurately and improve the stability,compactness,and separability.When RCMFE is selected as the characteristic parameter,the RCMFE difference between denatured and normal biological tissues is more evident than that of MFE,which helps doctors evaluate the treatment effect more accurately.When the scale factor is selected as 16,the best distinguishing effect can be obtained.

Assessment and sequencing of air target threat based on intuitionistic fuzzy entropy and dynamic VIKOR

In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-target threat assessment problems. The target attribute weight is calculated by the intuitionistic fuzzy entropy(IFE) algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data. Finally,assessment and sequencing of the air multi-target threat model based on IFE and dynamic Vlse Kriterijumska Optimizacija I Kompromisno Resenje(VIKOR) is established with an example which indicates that the method is reasonable and effective.

Dynamic Weapon Target Assignment Based on Intuitionistic Fuzzy Entropy of Discrete Particle Swarm

Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzzy Entropy of Discrete Particle Swarm Optimization(IFDPSO) and makes it applied to Dynamic Weapon Target Assignment(WTA). First, the strategy of choosing intuitionistic fuzzy parameters of particle swarm is defined, making intuitionistic fuzzy entropy as a basic parameter for measure and velocity mutation. Second, through analyzing the defects of DPSO, an adjusting parameter for balancing two cognition, velocity mutation mechanism and position mutation strategy are designed, and then two sets of improved and derivative algorithms for IFDPSO are put forward, which ensures the IFDPSO possibly search as much as possible sub-optimal positions and its neighborhood and the algorithm ability of searching global optimal value in solving large scale 0-1 knapsack problem is intensified. Third, focusing on the problem of WTA, some parameters including dynamic parameter for shifting firepower and constraints are designed to solve the problems of weapon target assignment. In addition, WTA Optimization Model with time and resource constraints is finally set up, which also intensifies the algorithm ability of searching global and local best value in the solution of WTA problem. Finally, the superiority of IFDPSO is proved by several simulation experiments. Particularly, IFDPSO, IFDPSO1~IFDPSO3 are respectively effective in solving large scale, medium scale or strict constraint problems such as 0-1 knapsack problem and WTA problem.

FEW-NNN: A Fuzzy Entropy Weighted Natural Nearest Neighbor Method for Flow-Based Network Traffic Attack Detection

Attacks such as APT usually hide communication data in massive legitimate network traffic, and mining structurally complex and latent relationships among flow-based network traffic to detect attacks has become the focus of many initiatives. Effectively analyzing massive network security data with high dimensions for suspicious flow diagnosis is a huge challenge. In addition, the uneven distribution of network traffic does not fully reflect the differences of class sample features, resulting in the low accuracy of attack detection. To solve these problems, a novel approach called the fuzzy entropy weighted natural nearest neighbor(FEW-NNN) method is proposed to enhance the accuracy and efficiency of flowbased network traffic attack detection. First, the FEW-NNN method uses the Fisher score and deep graph feature learning algorithm to remove unimportant features and reduce the data dimension. Then, according to the proposed natural nearest neighbor searching algorithm(NNN_Searching), the density of data points, each class center and the smallest enclosing sphere radius are determined correspondingly. Finally, a fuzzy entropy weighted KNN classification method based on affinity is proposed, which mainly includes the following three steps: 1、 the feature weights of samples are calculated based on fuzzy entropy values, 2、 the fuzzy memberships of samples are determined based on affinity among samples, and 3、 K-neighbors are selected according to the class-conditional weighted Euclidean distance, the fuzzy membership value of the testing sample is calculated based on the membership of k-neighbors, and then all testing samples are classified according to the fuzzy membership value of the samples belonging to each class;that is, the attack type is determined. The method has been applied to the problem of attack detection and validated based on the famous KDD99 and CICIDS-2017 datasets. From the experimental results shown in this paper, it is observed that the FEW-NNN method improves the accuracy and efficiency of flow-based network traffic attack detection.

Adaptive image enhancement algorithm based on fuzzy entropy and human visual characteristics

To overcome the shortcomings of the Lee image enhancement algorithm and its improvement based on the logarithmic image processing(LIP) model, this paper proposes what we believe to be an effective image enhancement algorithm. This algorithm introduces fuzzy entropy, makes full use of neighborhood information, fuzzy information and human visual characteristics.To enhance an image, this paper first carries out the reasonable fuzzy-3 partition of its histogram into the dark region, intermediate region and bright region. It then extracts the statistical characteristics of the three regions and adaptively selects the parameter αaccording to the statistical characteristics of the image’s gray-scale values. It also adds a useful nonlinear transform, thus increasing the ubiquity of the algorithm. Finally, the causes for the gray-scale value overcorrection that occurs in the traditional image enhancement algorithms are analyzed and their solutions are proposed.The simulation results show that our image enhancement algorithm can effectively suppress the noise of an image, enhance its contrast and visual effect, sharpen its edge and adjust its dynamic range.

Fuzzy Entropy Based Combined Learning Algorithm for Neural Networks

Learning is one of key problems of artificial neural networks. In this paper, we present a kind of combined learning algorithm based on fuzzy entropy criterion for neural networks. The basic idea is to simulate the learning mechanism of human brain and overcome the limitations of monocrifsterion learning. The comparison is made between the given learning algorithm and the typical BP algorithm in order to show the characteristics of the new algorithm.

Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.

2-D mini mumfuzzy entropy method of image thresholding based on genetic algorithm

A new image thresholding method is introduced, which is based on 2-D histgram and minimizing the measures of fuzziness of an input image. A new definition of fuzzy membership function is proposed, it denotes the characteristic relationship between the gray level of each pixel and the average value of its neighborhood. When the threshold is not located at the obvious and deep valley of the histgram, genetic algorithm is devoted to the problem of selecting the appropriate threshold value. The experimental results indicate that the proposed method has good performance.

Relations Among Some Fuzzy Entropy Formulae

Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.

New Definition and Properties of Fuzzy Entropy

Let X = （x1 ,x2 ,…… ,xn ） and F（X） be a fuzzy set on a universal set X. A new def＇mition of fuzzy entropy about a fuzzy set A on F（X）, e^＊＇ , is defined based on the order relation ＂≤＂ on [ 0,1/2 ]^n. It is proved that e^＊ is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Optical Fibre Communication Feature Analysis and Small Sample Fault Diagnosis Based on VMD-FE and Fuzzy Clustering

To solve the problems of a few optical fibre line fault samples and the inefficiency of manual communication optical fibre fault diagnosis,this paper proposes a communication optical fibre fault diagnosis model based on variational modal decomposition(VMD),fuzzy entropy(FE)and fuzzy clustering(FC).Firstly,based on the OTDR curve data collected in the field,VMD is used to extract the different modal components(IMF)of the original signal and calculate the fuzzy entropy(FE)values of different components to characterize the subtle differences between them.The fuzzy entropy of each curve is used as the feature vector,which in turn constructs the communication optical fibre feature vector matrix,and the fuzzy clustering algorithm is used to achieve fault diagnosis of faulty optical fibre.The VMD-FE combination can extract subtle differences in features,and the fuzzy clustering algorithm does not require sample training.The experimental results show that the model in this paper has high accuracy and is relevant to the maintenance of communication optical fibre when compared with existing feature extraction models and traditional machine learning models.

A New Exponential Fuzzy Entropy of Order-(α,β)and its Application in Multiple Attribute Decision-Making Problems

Fuzzy entropy is an important concept to measure the fuzzy information.Measure of fuzziness of a fuzzy set is the measure of its fuzziness.In the present communication,we have defined an exponential fuzzy entropy of order-(α,β).Besides establishing the validity of the proposed measure,we have also discussed some of its properties.At last,we have given the application of the proposed measure in multiple attribute decision-making problems.In this section,we have considered two cases for the weights of attributes:One is the case when weights are completely unknown to us,and the other is the case when weights are partially known to us.

Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets

In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.

Fuzzy-entropy based robust optimization criteria for tuned mass dampers

Tuned mass dampers (TMD) are well known as one of the most widely adopted devices in vibration control passive strategies. In the past few decades,many methods have been developed to find the optimal parameters of a TMD installed on a structure and subjected to a random base excitation process,but most of them are usually based on an implicit assumption that all of the structural parameters are deterministic. However,in many real cases this simplification is unacceptable,so robust optimal design criteria becomes aviable alternative to better support engineers in the design process. In Robust Design Optimization (RDO) approaches,indeed the solution must be able to not only minimize the performance but also to limitits variation induced by uncertainty. Most of the currently available RDO methods are based on a probabilistic description of the model uncertainty,even if in many cases they are not able to explicitly include the influence of all the possible sources of uncertainties. Therefore,in this study,a fuzzy version of the robust TMD design optimization problem is proposed. The consistency of the fuzzy approach is studied with respect to the available non-probabilistic formulations reported in the literature and an application to an example of a robust design of a linear TMD subjected to base random vibrations in the presence of fuzzy uncertainties. The results show that the proposed fuzzy-based approach is able to give a set of optimal solutions both in terms of structural efficiency and sensitivity to mechanical and environmental uncertainties.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

FLNL:Fuzzy entropy and lion neural learner for EDoS attack mitigation in cloud computing

Cloud computing is a technology that allows the end-users to access the network through a shared area of resources.As the demand for the cloud computing increases,vulnerabilities in the service provision also increase.EDoS is one of the attacks that take over the provider,financially affecting the various organizations which use the cloud data.This paper utilizes fuzzy entropy and lion neural learner(FLNL)for the classification of cloud users to mitigate EDoS attacks in the cloud.This technique includes a training phase,which creates a log file using various parameters and then transforms the features into database considering certain key features.There are two important stages in this classification approach:feature selection and classification.Here,the fuzzy entropy function is utilized for feature selection which effectively selects useful features without information loss.The classification is performed using lion neural learner(LNL)which incorporates Lion algorithm(LA)into the neural network and uses Levenberg–Marquardt(LM)algorithm.The experimental results finalize that the proposed FLNL is effective with 89%precision,78%recall,and 83.13%of f-measure compared with the existing Na¨ıve Bayes(NB),Neural Network+Back Propagation(NN+BP),and Neural Network+Levenberg–Marquardt(NN+LM).

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

Discrete Variable Structural Optimization based on Multidirectional Fuzzy Genetic Algorithm

Round method is the common method for discrete variable optimization in optimal design of complex mechanical structures;however,it has some disadvantages such as poor precision,simple model and lacking of working conditions＇ description,etc.To solve these problems,a new model is constructed by defining parameterized fuzzy entropy,and the rationality of parameterized fuzzy entropy is verified.And a new multidirectional searching algorithm is further put forward,which takes information of actual working conditions into consideration and has a powerful local searching capability.Then this new algorithm is combined with the GA by the fuzzy clustering algorithm（FCA）.With the application of FCA,the optimal solution can be effectively filtered so as to retain the diversity and the elite of the optimal solution,and avoid the structural re-analysis phenomenon between the two algorithms.The structure design of a high pressure bypass-valve body is used as an example to make a structural optimization by the proposed HGA and finite element method（FEM）,respectively.The comparison result shows that the improved HGA fully considers the characteristic of discrete variable and information of working conditions,and is more suitable to the optimal problems with complex working conditions.Meanwhile,the research provides a new approach for discrete variable structure optimization problems.

Mining Representative Subset Based on Fuzzy Clustering

Two new concepts-fuzzy mutuality and average fuzzy entropy are presented. Then based on these concepts, a new algorithm-RSMA （representative subset mining algorithm） is proposed, which can abstract representative subset from massive data. To accelerate the speed of producing representative subset, an improved algorithm-ARSMA（accelerated representative subset mining algorithm） is advanced, which adopt combining putting forward with backward strategies. In this way, the performance of the algorithm is improved. Finally we make experiments on real datasets and evaluate the representative subset. The experiment shows that ARSMA algorithm is more excellent than RandomPick algorithm either on effectiveness or efficiency.