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Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

The plastic modifications in synaptic connectivity is primarily from changes triggered by neuromodulated dopamine signals. These activities are controlled by neuromodulation, which is itself under the control of the brain. The subjective brain’s self-modifying abilities play an essential role in learning and adaptation. The artificial neural networks with neuromodulated plasticity are used to implement transfer learning in the image classification domain. In particular, this has application in image detection, image segmentation, and transfer of learning parameters with significant results. This paper proposes a novel approach to enhance transfer learning accuracy in a heterogeneous source and target, using the neuromodulation of the Hebbian learning principle, called NDHTL (Neuromodulated Dopamine Hebbian Transfer Learning). Neuromodulation of plasticity offers a powerful new technique with applications in training neural networks implementing asymmetric backpropagation using Hebbian principles in transfer learning motivated CNNs (Convolutional neural networks). Biologically motivated concomitant learning, where connected brain cells activate positively, enhances the synaptic connection strength between the network neurons. Using the NDHTL algorithm, the percentage of change of the plasticity between the neurons of the CNN layer is directly managed by the dopamine signal’s value. The discriminative nature of transfer learning fits well with the technique. The learned model’s connection weights must adapt to unseen target datasets with the least cost and effort in transfer learning. Using distinctive learning principles such as dopamine Hebbian learning in transfer learning for asymmetric gradient weights update is a novel approach. The paper emphasizes the NDHTL algorithmic technique as synaptic plasticity controlled by dopamine signals in transfer learning to classify images using source-target datasets. The standard transfer learning using gradient backpropagation is a symmetric framework. Experimental results using CIFAR-10 and CIFAR-100 datasets show that the proposed NDHTL algorithm can enhance transfer learning efficiency compared to existing methods.

Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric model where CCA provides an insight into their nonlinear dependence structure. The paper also investigates some of its probabilistic and inferential properties, including marginal and conditional distributions, nonlinear transformations, maximum likelihood estimation and independence testing. Perturbed independence distributions are closely related to skew-symmetric ones.

This Special Issue covers symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multi-criteria decision-making problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the Special Issue.

The dataset distribution of actual logging is asymmetric, as most logging data are unlabeled. With the traditional classification model, it is hard to predict the oil and gas reservoir accurately. Therefore, a novel approach to the oil layer recognition model using the improved whale swarm algorithm (WOA) and semi-supervised support vector machine (S3VM) is proposed in this paper. At first, in order to overcome the shortcomings of the Whale Optimization Algorithm applied in the parameter-optimization of the S3VM model, such as falling into a local optimization and low convergence precision, an improved WOA was proposed according to the adaptive cloud strategy and the catfish effect. Then, the improved WOA was used to optimize the kernel parameters of S3VM for oil layer recognition. In this paper, the improved WOA is used to test 15 benchmark functions of CEC2005 compared with five other algorithms. The IWOA–S3VM model is used to classify the five kinds of UCI datasets compared with the other two algorithms. Finally, the IWOA–S3VM model is used for oil layer recognition. The result shows that (1) the improved WOA has better convergence speed and optimization ability than the other five algorithms, and (2) the IWOA–S3VM model has better recognition precision when the dataset contains a labeled and unlabeled dataset in oil layer recognition.

Cloud based healthcare computing have changed the face of healthcare in many ways. The main advantages of cloud computing in healthcare are scalability of the required service and the provision to upscale or downsize the data storge, collaborating Artificial Intelligence (AI) and machine learning. The current paper examined various research studies to explore the utilization of intelligent techniques in health systems and mainly focused into the security and privacy issues in the current technologies. Despite the various benefits related to cloud-computing applications for healthcare, there are different types of management, technology handling, security measures, and legal issues to be considered and addressed. The key focus of this paper is to address the increased demand for cloud computing and its definition, technologies widely used in healthcare, their problems and possibilities, and the way protection mechanisms are organized and prepared when the company chooses to implement the latest evolving service model. In this paper, we focused on a thorough review of current and existing literature on different approaches and mechanisms used in e-Health to deal with security and privacy issues. Some of these approaches have strengths and weaknesses. After selecting original articles, the literature review was carried out, and we identified several models adopted in their solutions. We arrived at the reviewed articles after comparing the models used.

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.

The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.

The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Gr&uuml, nwald&ndash, Letnikov discrete-time state&ndash, space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and &sigma, inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology.

Geometrically, the affine connection is the main ingredient that underlies the covariant derivative, the parallel transport, the auto-parallel curves, the torsion tensor field, and the curvature tensor field on a finite-dimensional differentiable manifold. In this paper, we come up with a new idea of controllability and observability of states by using auto-parallel curves, and the minimum time problem controlled by the affine connection. The main contributions refer to the following: (i) auto-parallel curves controlled by a connection, (ii) reachability and controllability on the tangent bundle of a manifold, (iii) examples of equiaffine connections, (iv) minimum time problem controlled by a connection, (v) connectivity by stochastic perturbations of auto-parallel curves, and (vi) computing the optimal time and the optimal striking time. The connections with bounded pull-backs result in bang–bang optimal controls. Some significative examples on bi-dimensional manifolds clarify the intention of our paper and suggest possible applications. At the end, an example of minimum striking time with simulation results is presented.

Blockchain networks are based on cryptographic notions that include asymmetric-key encryption, hash functions and consensus protocols. Despite their popularity, mainstream protocols, such as Proof of Work or Proof of Stake still have drawbacks. Efforts to enhance these protocols led to the birth of alternative consensus protocols, catering to specific areas, such as medicine or transportation. These protocols remain relatively unknown despite having unique merits worth investigating. Although past reviews have been published on popular blockchain consensus protocols, they do not include most of these lesser-known protocols. Highlighting these alternative consensus protocols contributes toward the advancement of the state of the art, as they have design features that may be useful to academics, blockchain practitioners and researchers. In this paper, we bridge this gap by providing an overview of alternative consensus protocols proposed within the past 3 years. We evaluate their overall performance based on metrics such as throughput, scalability, security, energy consumption, and finality. In our review, we examine the trade-offs that these consensus protocols have made in their attempts to optimize scalability and performance. To the best of our knowledge, this is the first paper that focuses on these alternative protocols, highlighting their unique features that can be used to develop future consensus protocols.

Deepfake is one of the applications that is deemed harmful. Deepfakes are a sort of image or video manipulation in which a person’s image is changed or swapped with that of another person’s face using artificial neural networks. Deepfake manipulations may be done with a variety of techniques and applications. A quintessential countermeasure against deepfake or face manipulation is deepfake detection method. Most of the existing detection methods perform well under symmetric data distributions, but are still not robust to asymmetric datasets variations and novel deepfake/manipulation types. In this paper, for the identification of fake faces in videos, a new multistream deep learning algorithm is developed, where three streams are merged at the feature level using the fusion layer. After the fusion layer, the fully connected, Softmax, and classification layers are used to classify the data. The pre-trained VGG16 model is adopted for transferred CNN1stream. In transfer learning, the weights of the pre-trained CNN model are further used for training the new classification problem. In the second stream (transferred CNN2), the pre-trained VGG19 model is used. Whereas, in the third stream, the pre-trained ResNet18 model is considered. In this paper, a new large-scale dataset (i.e., World Politicians Deepfake Dataset (WPDD)) is introduced to improve deepfake detection systems. The dataset was created by downloading videos of 20 different politicians from YouTube. Over 320,000 frames were retrieved after dividing the downloaded movie into little sections and extracting the frames. Finally, various manipulations were performed to these frames, resulting in seven separate manipulation classes for men and women. In the experiments, three fake face detection scenarios are investigated. First, fake and real face discrimination is studied. Second, seven face manipulations are performed, including age, beard, face swap, glasses, hair color, hairstyle, smiling, and genuine face discrimination. Third, performance of deepfake detection system under novel type of face manipulation is analyzed. The proposed strategy outperforms the prior existing methods. The calculated performance metrics are over 99%.

This paper deals with the flow shop scheduling problem. To find the optimal solution is an NP-hard problem. The paper reviews some algorithms from the literature and applies a benchmark dataset to evaluate their efficiency. In this research work, the discrete bacterial memetic evolutionary algorithm (DBMEA) as a global searcher was investigated. The proposed algorithm improves the local search by applying the simulated annealing algorithm (SA). This paper presents the experimental results of solving the no-idle flow shop scheduling problem. To compare the proposed algorithm with other researchers’ work, a benchmark problem set was used. The calculated makespan times were compared against the best-known solutions in the literature. The proposed hybrid algorithm has provided better results than methods using genetic algorithm variants, thus it is a major improvement for the memetic algorithm family solving production scheduling problems.

Text, voice, images and videos can express some intentions and facts in daily life. By understanding these contents, people can identify and analyze some behaviors. This paper focuses on the commodity trade declaration process and identifies the commodity categories based on text information on customs declarations. Although the technology of text recognition is mature in many application fields, there are few studies on the classification and recognition of customs declaration goods. In this paper, we proposed a classification framework based on machine learning (ML) models for commodity trade declaration that reaches a high rate of accuracy. This paper also proposed a symmetrical decision fusion method for this task based on convolutional neural network (CNN) and transformer. The experimental results show that the fusion model can make up for the shortcomings of the two original models and some improvements have been made. In the two datasets used in this paper, the accuracy can reach 88% and 99%, respectively. To promote the development of study of customs declaration business and Chinese text recognition, we also exposed the proprietary datasets used in this study.

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using a, b, c ∈ ℝ, c ≠ 0, −1, −2, ... The study done in this paper extends the results on the univalence of the considered function taking a, b, c ∈ ℂ, with c ≠ 0, −1, −2, ... two criteria being stated in the corollaries of the proved theorems. An interpretation of the univalence results from the sets inclusion view is also given, underlining the geometrical properties of the outcomes. Examples showing how the univalence results can be applied are also included.

Cross-efficiency evaluation effectively distinguishes a set of decision-making units (DMUs) via self- and peer-evaluations. In constant returns to scale, this evaluation technique is usually applied for data envelopment analysis (DEA) models because negative efficiencies will not occur in this case. For situations of variable returns to scale, the negative cross-efficiencies may occur in this evaluation method. In the real world, the observations could be uncertain and difficult to measure precisely. The existing fuzzy cross-evaluation methods are restricted to production technologies with constant returns to scale. Generally, symmetry is a fundamental characteristic of binary relations used when modeling optimization problems. Additionally, the notion of symmetry appeared in many studies about uncertain theories employed in DEA problems, and this approach can be considered an engineering tool for supporting decision-making. This paper proposes a fuzzy cross-efficiency evaluation model with fuzzy observations under variable returns to scale. Since all possible weights of all DMUs are considered, a choice of weights is not required. Most importantly, negative cross-efficiencies are not produced. An example shows that this paper’s fuzzy cross-efficiency evaluation method has discriminative power in ranking the DMUs when observations are fuzzy numbers.

Automatic segmentation of the lungs in Chest X-ray images (CXRs) is a key step in the screening and diagnosis of related diseases. There are many opacities in the lungs in the CXRs of patients, which makes the lungs difficult to segment. In order to solve this problem, this paper proposes a segmentation algorithm based on U-Net. This article introduces variational auto-encoder (VAE) in each layer of the decoder-encoder. VAE can extract high-level semantic information, such as the symmetrical relationship between the left and right thoraxes in most cases. The fusion of the features of VAE and the features of convolution can improve the ability of the network to extract features. This paper proposes a three-terminal attention mechanism. The attention mechanism uses the channel and spatial attention module to automatically highlight the target area and improve the performance of lung segmentation. At the same time, the three-terminal attention mechanism uses the advanced semantics of high-scale features to improve the positioning and recognition capabilities of the attention mechanism, suppress background noise, and highlight target features. Experimental results on two different datasets show that the accuracy (ACC), recall (R), F1-Score and Jaccard values of the algorithm proposed in this paper are the highest on the two datasets, indicating that the algorithm in this paper is better than other state-of-the-art algorithms.

Recently, two classes of univalent functions S e * and K e were introduced and studied. A function f is in S e * if it is analytic in the unit disk, f ( 0 ) = f &prime, ( 0 ) - 1 = 0 and z f &prime, ( z ) f ( z ) ≺ e z . On the other hand, g &isin, K e if and only if z g &prime, &isin, S e * . Both classes are symmetric, or invariant, under rotations. In this paper, we solve a few problems connected with the coefficients of functions in these classes. We find, among other things, the estimates of Hankel determinants: H 2 , 1 , H 2 , 2 , H 3 , 1 . All these estimates improve the known results. Moreover, almost all new bounds are sharp. The main idea used in the paper is based on expressing the discussed functionals depending on the fixed second coefficient of a function in a given class.

The lurch index has recently been introduced in applied kinematics as an integral descriptor of the fluency of the motion of a rigid body in space. It may be defined in different versions, according to the component of motion under investigation. In the present paper, we analyze a rotational lurch index, which describes the fluency of the spin component of motion and whose value depends, through involved relations, on the dynamics of three canonical descriptors of the orientation of a rigid body in space. The aim of the present paper is to offer a closed-form expression of the instantaneous component of the rotational lurch, which leads to the namesake index upon integration and normalization. The closed form of the index is, then, used to evaluate its practical calculation, based on numerical approximations on a number of data sets.

In this paper the model of infection diseases by Marchuk is considered. Mathematical questions which are important in its study are discussed. Among them there are stability of stationary points, construction of the Cauchy matrices of linearized models, estimates of solutions. The novelty we propose is in a distributed feedback control which affects the antibody concentration. We use this control in the form of an integral term and come to the analysis of nonlinear integro-differential systems. New methods for the study of stability of linearized integro&ndash, differential systems describing the model of infection diseases are proposed. Explicit conditions of the exponential stability of the stationary points characterizing the state of the healthy body are obtained. The method of the paper is based on the symmetry properties of the Cauchy matrices which allow us their construction.

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

In this paper, an intra prediction method is proposed for coding of depth pictures using plane modelling. Each pixel in the depth picture is related to the distance from a camera to an object surface, and pixels corresponding to a flat surface of an object form a relationship with the 2D plane surface. The plane surface can be represented by a simple equation in the 3D camera coordinate system in such a way that the coordinate system of depth pixels can be transformed to the camera coordinate system. This paper finds the parameters which define the plane surface closest to given depth pixels. The plane model is then used to predict the depth pixels on the plane surface. A depth prediction method is also devised for efficient intra prediction of depth pictures, using variable-size blocks. For prediction with variable-size blocks, the plane surface that occupies a large part of the picture can be predicted using a large block size. The simulation results of the proposed method show that the mean squared error is reduced by up to 96.6% for a block size of 4 × 4 pixels and reduced by up to 98% for a block size of 16 × 16, compared with the intra prediction modes of H.264/AVC and H.265/HEVC.

In the algebra of single-valued structures, cyclicity is one of the fundamental properties of groups. Therefore, it is natural to study it also in the algebra of multivalued structures (algebraic hyperstructure theory). However, when one considers the nature of generalizing this property, at least two (or rather three) approaches seem natural. Historically, all of these had been introduced and studied by 1990. However, since most of the results had originally been published in journals without proper international impact and later—without the possibility to include proper background and context-synthetized in books, the current way of treating the concept of cyclicity in the algebraic hyperstructure theory is often rather confusing. Therefore, we start our paper with a rather long introduction giving an overview and motivation of existing approaches to the cyclicity in algebraic hyperstructures. In the second part of our paper, we relate these to EL-hyperstructures, a broad class of algebraic hyperstructures constructed from (pre)ordered (semi)groups, which were defined and started to be studied much later than sources discussed in the introduction were published. V algebře jednoznačných struktur je cyklicita jednou z význačných vlastností grup. Proto je zajímavé studovat ji také v algebře mnohoznačných struktur, tj. algebraické teorii hyperstruktur. Nicméně, pokud uvážíme možnosti zobecnění cyklicity, je zřejmé, že přirozené jsou dva (nebo spíše tři) přístupy. Historicky byly všechny studovány již před rokem 1990. Většina těchto výsledků však byla publikována v časopisech bez patřičného ohlasu a jejich shrnutí poté bylo bez patřičného kontextu zařazeno do některých monografií, odkud je nyní přebíráno často ve zkreslené podobě. Proto svůj článek začínáme poněkud delším úvodem, který si klade za cíl zasadit studovanou problematiku do patřičného kontextu a uvést motivaci jednotlivých přístupů. Ve druhé části článku se poté věnujeme cyklicitě v EL-hypergrupách, tj. široké třídě hyperstruktur, která byla definována mnoho let poté, co byly publikovány články zmiňované v úvodu.

The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

In this paper, a wind speed prediction method was proposed based on the maximum Lyapunov exponent (Le) and the fractional Levy stable motion (fLsm) iterative prediction model. First, the calculation of the maximum prediction steps was introduced based on the maximum Le. The maximum prediction steps could provide the prediction steps for subsequent prediction models. Secondly, the fLsm iterative prediction model was established by stochastic differential. Meanwhile, the parameters of the fLsm iterative prediction model were obtained by rescaled range analysis and novel characteristic function methods, thereby obtaining a wind speed prediction model. Finally, in order to reduce the error in the parameter estimation of the prediction model, we adopted the method of weighted wind speed data. The wind speed prediction model in this paper was compared with GA-BP neural network and the results of wind speed prediction proved the effectiveness of the method that is proposed in this paper. In particular, fLsm has long-range dependence (LRD) characteristics and identified LRD by estimating self-similarity index H and characteristic index &alpha, Compared with fractional Brownian motion, fLsm can describe the LRD process more flexibly. However, the two parameters are not independent because the LRD condition relates them by &alpha, H &gt, 1.

The purpose of the paper is to study new algebraic operations and fundamental properties of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. First, the in-coordination relationships among the original inclusion relations of totally dependent-neutrosophic sets (called type-1 and typ-2 inclusion relations in this paper) and union (intersection) operations are analyzed, and then type-3 inclusion relation of totally dependent-neutrosophic sets and corresponding type-3 union, type-3 intersection, and complement operations are introduced. Second, the following theorem is proved: all totally dependent-neutrosophic sets (based on a certain universe) determined a generalized De Morgan algebra with respect to type-3 union, type-3 intersection, and complement operations. Third, the relationships among the type-3 order relation, score function, and accuracy function of totally dependent-neutrosophic sets are discussed. Finally, some new operations and properties of totally dependent-neutrosophic soft sets are investigated, and another generalized De Morgan algebra induced by totally dependent-neutrosophic soft sets is obtained.

Zadeh’s fuzzy set theory for imprecise or vague data has been followed by other successful models, inclusive of Molodtsov’s soft set theory and hybrid models like fuzzy soft sets. Their success has been backed up by applications to many branches like engineering, medicine, or finance. In continuation of this effort, the purpose of this paper is to put forward a versatile methodology for the valuation of goods, particularly the assessment of real state properties. In order to reach this target, we develop the concept of (partial) valuation fuzzy soft set and introduce the novel problem of data filling in partial valuation fuzzy soft sets. The use of fuzzy soft sets allows us to quantify the qualitative attributes involved in an assessment context. As a result, we illustrate the effectiveness and validity of our valuation methodology with a real case study that uses data from the Spanish real estate market. The main contribution of this paper is the implementation of a novel methodology, which allows us to assess a large variety of assets where data are heterogeneous. Our technique permits to avoid the appraiser’s subjectivity (exhibited by practitioners in housing valuation) and the well-known disadvantages of some alternative methods (such as linear multiple regression).

Integral inequalities play critical roles in measure theory and probability theory. Given recent profound discoveries in the field of fuzzy set theory, fuzzy inequality has become a hot research topic in recent years. For classical Sandor type inequality, this paper intends to extend the Sugeno integral. Based on the (s,m)-convex function in the second sense, a new Sandor type inequality is proposed for the Sugeno integral. Examples are given to verify the conclusion of this paper.

This paper presents GM (1, N) models with linear cross effect and nonlinear cross effect, and discusses the difference of driving factors between these two types of models to solve the cross effects of GM (1, N) model. The model with a linear cross effect in this paper preserves the solution of whitenization in the GM (1, 1) model. While the model with nonlinear cross effect integrates the sequences of systemic features, driving factors, and the cross effect of these driving factors. While applying support vector machine (SVM) regression, it transfers the nonlinear relationship among these sequences to a linear relationship. To test the GM (1, N) model that is based on support vector machine (SVM) with nonlinear effect, the study applies it to forecast the total output of the pharmaceutical industry. The range of the data is selected from 2005&ndash, 2017, which the data from 2005&ndash, 2013 are used to fit into the model. The GM (1, N) model based on SVM with nonlinear cross effect achieves 0.6566 and 0.2956 in its fitted total of relative error and the forecast total of relative error, respectively. The new model presents a more accurate analysis on fitting and forecast precision than the classic GM (1, N) model and GM (1, N) with the linear cross effect model.

In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler&rsquo, s fixed point theorem was generalized by many authors in different ways. Using a method given by Angrisani, Clavelli in 1996 and Mureşan in 2002, we prove in this paper that, for a class of convex multivalued left A-contractions in the sense of Nadler and the right A-contractions with a convex metric, the fixed points set is non-empty and compact. In this paper we present the fixed point theorems for convex multivalued left A-contractions in the sense of Nadler and right A-contractions on the geodesic metric space. Our results are particular cases of some general theorems, to the multivalued left A-contractions in the sense of Nadler and right A-contractions, and particular cases of the results given by Rus (1979, 2008), Nadler (1969), Mureşan (2002, 2004), Bucur, Guran and Petruşel (2009), Petre and Bota (2013), etc., and are applicable in many fields, such as economy, management, society, biology, ecology, etc.

Sparse-signal recovery in noisy conditions is a problem that can be solved with current compressive-sensing (CS) technology. Although current algorithms based on L 1 regularization can solve this problem, the L 1 regularization mechanism cannot promote signal sparsity under noisy conditions, resulting in low recovery accuracy. Based on this, we propose a regularized reweighted composite trigonometric smoothed L 0 -norm minimization (RRCTSL0) algorithm in this paper. The main contributions of this paper are as follows: (1) a new smoothed symmetric composite trigonometric (CT) function is proposed to fit the L 0 -norm, (2) a new reweighted function is proposed, and (3) a new L 0 regularization objective function framework is constructed based on the idea of T i k h o n o v regularization. In the new objective function framework, Contributions (1) and (2) are combined as sparsity regularization terms, and errors as deviation terms. Furthermore, the conjugate-gradient (CG) method is used to optimize the objective function, so as to achieve accurate recovery of sparse signal and image under noisy conditions. The numerical experiments on both the simulated and real data verify that the proposed algorithm is superior to other state-of-the-art algorithms, and achieves advanced performance under noisy conditions.

For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. The aim of this paper is focus on the structure of a special class of pseudo-BCI algebras in which every element is quasi-maximal (call it QM-pseudo-BCI algebras in this paper). First, the new notions of quasi-maximal element and quasi-left unit element in pseudo-BCK algebras and pseudo-BCI algebras are proposed and some properties are discussed. Second, the following structure theorem of QM-pseudo-BCI algebra is proved: every QM-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an anti-group pseudo-BCI algebra. Third, the new notion of weak associative pseudo-BCI algebra (WA-pseudo-BCI algebra) is introduced and the following result is proved: every WA-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an Abel group.

The aim of this paper is to use the elementary method and the properties of the second kind Stirling numbers to study the congruence properties of a new sequence, which is closely related to Fubini polynomials and Euler numbers, and give some interesting congruences for it. This solves a problem proposed by the first author at an unpublished paper.

As a new generalization of the notion of the standard group, the notion of the neutrosophic triplet group (NTG) is derived from the basic idea of the neutrosophic set and can be regarded as a mathematical structure describing generalized symmetry. In this paper, the properties and structural features of NTG are studied in depth by using theoretical analysis and software calculations (in fact, some important examples in the paper are calculated and verified by mathematics software, but the related programs are omitted). The main results are obtained as follows: (1) by constructing counterexamples, some mistakes in the some literatures are pointed out, (2) some new properties of NTGs are obtained, and it is proved that every element has unique neutral element in any neutrosophic triplet group, (3) the notions of NT-subgroups, strong NT-subgroups, and weak commutative neutrosophic triplet groups (WCNTGs) are introduced, the quotient structures are constructed by strong NT-subgroups, and a homomorphism theorem is proved in weak commutative neutrosophic triplet groups.

In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala’s derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations.

A new denoising algorithm and feature extraction algorithm that combine a new kind of permutation entropy (NPE) and variational mode decomposition (VMD) are put forward in this paper. VMD is a new self-adaptive signal processing algorithm, which is more robust to sampling and noise, and also can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD). Permutation entropy (PE), as a nonlinear dynamics parameter, is a powerful tool that can describe the complexity of a time series. NPE, a new version of PE, is interpreted as distance to white noise, which shows a reverse trend to PE and has better stability than PE. In this paper, three kinds of ship-radiated noise (SN) signal are decomposed by VMD algorithm, and a series of intrinsic mode functions (IMF) are obtained. The NPEs of all the IMFs are calculated, the noise IMFs are screened out according to the value of NPE, and the process of denoising can be realized by reconstructing the rest of IMFs. Then the reconstructed SN signal is decomposed by VMD algorithm again, and one IMF containing the most dominant information is chosen to represent the original SN signal. Finally, NPE of the chosen IMF is calculated as a new complexity feature, which constitutes the input of the support vector machine (SVM) for pattern recognition of SN. Compared with the existing denoising algorithms and feature extraction algorithms, the effectiveness of proposed algorithms is validated using the numerical simulation signal and the different kinds of SN signal.

In this paper, a decision model based on a fuzzy soft set and ideal solution approaches is proposed. This new decision-making method uses the divide-and-conquer algorithm, and it is different from the existing algorithm (the choice value based approach and the comparison score based approach). The ideal solution is generated according to each attribute (pros or cons of the attributes, with or without constraints) of the fuzzy soft sets. Finally, the weighted Hamming distance is used to compute all possible alternatives and get the final result. The core of the decision process is the design phase, the existing decision models based on soft sets mostly neglect the analysis of attributes and decision objectives. This algorithm emphasizes the correct expression of the purpose of the decision maker and the analysis of attributes, as well as the explicit decision function. Additionally, this paper shows the fact that the rank reversal phenomenon occurs in the comparison score algorithm, and an example is provided to illustrate the rank reversal phenomenon. Experiments indicate that the decision model proposed in this paper is efficient and will be useful for practical problems. In addition, as a general model, it can be extended to a wider range of fields, such as classifications, optimization problems, etc.

Aiming at combining the good characteristics of a differential scale in representing human cognition and the favorable properties of interval judgments in expressing decision-makers’ uncertainty, this paper proposes the interval cognitive network process (I-CNP) to extend the primitive cognition network process (P-CNP) to handle interval judgments. The key points of I-CNP include a consistency definition for an interval pairwise opposite matrix (IPOM) and a method to derive interval utilities from an IPOM. This paper defines a feasible region-based consistency definition and a transitivity based consistency definition for an IPOM. Both of the two definitions are equivalent to the consistency definition for a crisp pairwise opposite matrix (POM) when an IPOM is reduced to a POM. Two methods that are able to derive interval utilities from both consistent and inconsistent IPOMs are developed based on the two definitions. Four numerical examples are used to illustrate the proposed methods and to compare I-CNP to interval analytic hierarchy process (IAHP). The results show that I-CNP reflects the decision-makers’ cognition better, and that the suggestions provided by I-CNP are more convincing. I-CNP provides new useful alternative tools for multi-attribute decision-making problems.

Failure mode and effects analysis (FMEA) is a popular and useful approach applied to examine potential failures in different products, designs, processes, and services. As a vital index, the risk priority number (RPN) can determine the risk priorities of failure modes by some risk factors such as occurrence (O), severity (S), and detection (D). However, in FMEA, the traditional risk priority number approach has some shortcomings, especially in setting the weight of risk factors. This paper presents an improved risk priority number approach based on a fuzzy measure and fuzzy integral. A fuzzy measure is used to reflect the importance of the individual indicators and the indicator set and a fuzzy integral is a nonlinear function defined on the basis of fuzzy measure. The weights of risk factors given by domain experts are seen as fuzzy densities to generate a λ -fuzzy measure which can reflect the weights’ difference and relevance about risk factors. Then, the Choquet integral is used to fuse every value of risk factors about failure modes so as to obtain the comprehensive evaluation result. The result can reflect the comprehensive risk level, so it has a definite physical significance. Finally, an illustrative example and a comparison with another approach are given to show the effectiveness of the proposed approach in the paper.

The goal of image steganographic methods considers three main key issues: high embedding capacity, good visual symmetry/quality, and security. In this paper, a hybrid data hiding method combining the right-most digit replacement (RMDR) with an adaptive least significant bit (ALSB) is proposed to provide not only high embedding capacity but also maintain a good visual symmetry. The cover-image is divided into lower texture (symmetry patterns) and higher texture (asymmetry patterns) areas and these textures determine the selection of RMDR and ALSB methods, respectively, according to pixel symmetry. This paper has three major contributions. First, the proposed hybrid method enhanced the embedding capacity due to efficient ALSB utilization in the higher texture areas of cover images. Second, the proposed hybrid method maintains the high visual quality because RMDR has the closest selection process to generate the symmetry between stego and cover pixels. Finally, the proposed hybrid method is secure against statistical regular or singular (RS) steganalysis and pixel difference histogram steganalysis because RMDR is capable of evading the risk of RS detection attacks due to pixel digits replacement instead of bits. Extensive experimental tests (over 1500+ cover images) are conducted with recent least significant bit (LSB)-based hybrid methods and it is demonstrated that the proposed hybrid method has a high embedding capacity (800,019 bits) while maintaining good visual symmetry (39.00% peak signal-to-noise ratio (PSNR)).

Uncertain differential equations are important mathematical models in uncertain environments. This paper investigates uncertain multi-dimensional and multiple-factor differential equations. First, the solvability of the equations is analyzed. The α-path distributions and expected values of solutions are given. Then, structure preserving uncertain differential equations, uncertain Hamiltonian systems driven by Liu processes, which possess a kind of uncertain symplectic structures, are presented. A symplectic scheme with six-order accuracy and a Yao-Chen algorithm are applied to design an algorithm to solve uncertain Hamiltonian systems. At last, numerical experiments are given to investigate four uncertain Hamiltonian systems, which highlight the efficiency of our algorithm.

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.

Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity κ(G)≤κ′(G)≤δ(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3–5.

In the last decade, the devices and appliances utilizing the Internet of Things (IoT) have expanded tremendously, which has led to revolutionary developments in the network industry. Smart homes and cities, wearable devices, traffic monitoring, health systems, and energy savings are typical IoT applications. The diversity in IoT standards, protocols, and computational resources makes them vulnerable to security attackers. Botnets are challenging security threats in IoT devices that cause severe Distributed Denial of Service (DDoS) attacks. Intrusion detection systems (IDS) are necessary for safeguarding Internet-connected frameworks and enhancing insufficient traditional security countermeasures, including authentication and encryption techniques. This paper proposes a wrapper feature selection model (SSA–ALO) by hybridizing the salp swarm algorithm (SSA) and ant lion optimization (ALO). The new model can be integrated with IDS components to handle the high-dimensional space problem and detect IoT attacks with superior efficiency. The experiments were performed using the N-BaIoT benchmark dataset, which was downloaded from the UCI repository. This dataset consists of nine datasets that represent real IoT traffic. The experimental results reveal the outperformance of SSA–ALO compared to existing related approaches using the following evaluation measures: TPR (true positive rate), FPR (false positive rate), G-mean, processing time, and convergence curves. Therefore, the proposed SSA–ALO model can serve IoT applications by detecting intrusions with high true positive rates that reach 99.9% and with a minimal delay even in imbalanced intrusion families.

In a regular (d,k)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the (d,k)-SAT problem for short. The regular exact 2-(d,k)-SAT problem is that for a (d,k)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of 2n/k such that F is 2-exactly satisfiable. This paper introduces the (d,k)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point d* of the 2-(d,k)-SAT instance with only positive literals. When d&lt, d*, the 2-(d,k)-SAT instance can be satisfied with high probability. When d&gt, d*, the 2-(d,k)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results.

With the increasing complexity of the human social environment, it is impossible to describe each object in detail with accurate numbers when solving multiple attribute decision-making (MADM) problems. Compared with the fuzzy set (FS), the intuitionistic fuzzy set (IFS) not only has obvious advantages in allocating ambiguous values to the object to be considered, but also takes into account the degree of membership and non-membership, so it is more suitable for decision makers (DMs) to deal with complex realistic problems. Therefore, it is of great significance to propose a MADM method under an intuitionistic fuzzy environment. Moreover, compared with the traditional 2WD, by putting forward the option of delay, the decision-making risk can be effectively reduced using three-way decision (3WD). In addition, the binary relations between objects in the decision-making process have been continuously generalized, such as equivalence relation which have symmetrical relationship, dominance relation and outranking relation, which are worthy of study. In this paper, we propose 3WD-MADM method based on IF environment and the objective IFS is calculated by using the information table. Then, the hybrid information table is used to solve the supplier selection problem to demonstrate the effectiveness of the proposed method.

The quantity of network attacks and the harm from them is constantly increasing, so the detection of these attacks is an urgent task in the information security field. In this paper, we investigate an approach to building intrusion detection systems using a classifier based on fuzzy rules. The process of creating a fuzzy classifier based on a given set of input and output data can be presented as a solution to the problems of clustering, informative features selection, and the parameters of the rule antecedents optimization. To solve these problems, the whale optimization algorithm is used. The performance of algorithms for constructing a fuzzy classifier based on this metaheuristic is estimated using the KDD Cup 1999 intrusion detection dataset. On average, the resulting classifiers have a type I error of 0.92% and a type II error of 1.07%. The obtained results are also compared with the results of other classifiers. The comparison shows the competitiveness of the proposed method.