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In this paper, we focus on generalized fuzzy complex numbers and propose a straightforward matrix method to solve the dual rectangular fuzzy complex matrix equations C · Z ˜ + L ˜ = R · Z ˜ + W ˜ , in which C and R are crisp complex matrices and Z ˜ , L ˜ and M ˜ are fuzzy complex number matrices. The existing methods for solving fuzzy complex matrix equations involve separately calculating the extended solution and the corresponding parameters of the real and imaginary parts, whereby we obtain the algebraic solution of the equations. By means of the interval arithmetic and embedding approach, the n × n dual rectangular fuzzy complex linear systems could be converted into 2n × 2n fuzzy linear systems, which are also equivalent to the 4n × 4n real linear systems. By directly solving the 4n × 4n real linear systems, the algebraic solutions can be obtained. The general dual rectangular fuzzy complex matrix equations and dual rectangular fuzzy complex linear systems are investigated by the generalized inverses of matrices. Finally, some examples are given to illustrate the effectiveness of method. [ABSTRACT FROM AUTHOR]

It plays an important role in the calculation of fuzzy numbers using some special fuzzy numbers to approximate general fuzzy numbers in fuzzy analysis, similar to fuzzy complex analysis. A method is proposed to seek an approximation operator that produces a special kind of fuzzy complex number which is the nearest one to a given fuzzy complex number in this paper. The concept of prismoid fuzzy complex number is introduced, and the nearest prismoid fuzzy complex number of fuzzy complex number which preserve the centroid of the core for the fuzzy complex number with respect to the weighted pseudometric are discussed. Finally, some properties of the approximation operator including scale invariance, identity and nearness are presented. [ABSTRACT FROM AUTHOR]

It plays an important role in the calculation of fuzzy numbers using some special fuzzy numbers to approximate general fuzzy numbers in fuzzy analysis, similar to fuzzy complex analysis. A method is proposed to seek an approximation operator that produces a special kind of fuzzy complex number which is the nearest one to a given fuzzy complex number in this paper. The concept of prismoid fuzzy complex number is introduced, and the nearest prismoid fuzzy complex number of fuzzy complex number which preserve the centroid of the core for the fuzzy complex number with respect to the weighted pseudometric are discussed. Finally, some properties of the approximation operator including scale invariance, identity and nearness are presented. [ABSTRACT FROM AUTHOR]

Complex fuzzy set, as an extension of classical fuzzy sets, could describe the fuzzy characters of things more detail and comprehensively and is very useful in dealing with vagueness and uncertainty of problems that include the periodic or recurring phenomena. Note that a complex fuzzy set is different from the fuzzy complex set introduced and discussed by many scholars, since the membership degree of a complex fuzzy set is a complex number with length less than or equal to 1 while a fuzzy complex set is a real number with membership degree less than or equal to 1, and the universe is the complex plane. As the mathematical theoretical basis of fuzzy mathematics, fuzzy set and its mapping, corresponding fuzzy complex set and its mapping have been investigated in depth because they integrate and cross the methods and results of classical real analysis and complex analysis. However, there is no comprehensive investigation on complex fuzzy set and its corresponding mathematical theory, even include decomposition theorems, extension principles and the basic operations of the complex fuzzy set. As is well known, the cut set of fuzzy sets is the bridge between fuzzy sets and classical sets, which plays a significant role in fuzzy sets and fuzzy systems. In this paper, the concept of (r, θ)-cut sets of complex fuzzy sets is proposed and their properties are discussed. Meanwhile, the decomposition theorems and the extension principles of complex fuzzy set based on (r, θ)-cut sets are deduced and corresponding properties are investigated. All these conclusions not only deeply enrich the fundamental theory of complex fuzzy set, but also provide a powerful tool to investigate complex fuzzy set. Finally, an example application of signal detection demonstrates the utility of the (r, θ)-cut sets of complex fuzzy sets in practice. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of amplitude interval-valued complex Pythagorean fuzzy sets (AIVCPFSs). The motivation for this extension is the utility of interval-valued complex fuzzy sets in membership and non-membership degree which can express the two dimensional ambiguous information as well as the interaction among any set of parameters when they are in the form of interval-valued. The principle of AIVCPFS is a mixture of the two separated theories such as interval-valued complex fuzzy set and complex Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real part is the sub-interval of the unit interval. We discuss some set-theoretic operations and laws of the AIVCPFSs. We study some particular examples and basic results of these operations and laws. We use AIVCPFSs in signals and systems because its behavior is similar to a Fourier transform in certain cases. Moreover, we develop a new algorithm using AIVCPFSs for applications in signals and systems by which we identify a reference signal out of the large number of signals detected by a digital receiver. We use the inverse discrete Fourier transform for the membership and non-membership functions of AIVCPFSs for incoming signals and a reference signal. Thus a method for measuring the resembling values of two signals is provided by which we can identify the reference signal. [ABSTRACT FROM AUTHOR]

In this paper, it is pointed out that in the existing methods [Sarangam Majumdar, Numerical solutions of fuzzy complex system of linear equations, German Journal of Advanced Mathematical Sciences 1 (2013), 20-26] for solving fuzzy complex system of linear equations in which all the parameters except variables are represented by triangular/trapezoidal fuzzy complex numbers as well as the fuzzy complex system of linear equations in which all the parameters except coefficients are represented by triangular/trapezoidal fuzzy complex numbers, Majumdar has assumed that on subtracting a fuzzy number from itself, the obtained value is a zero fuzzy number as well as on dividing a fuzzy number by itself, the obtained value is a unit fuzzy number. To resolve these flaws of the existing methods, two new methods (named as Mehar method and Keerat method) are proposed for solving the same systems of fuzzy complex linear equations. [ABSTRACT FROM AUTHOR]

The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modeling, which can formulate the uncertainty in the actual environment. In this paper, a new method based on linear algebra for resolution of a fuzzy complex system of linear equations is presented. Moreover, a new algorithm is designed to find all the solutions of the system based on the eigenvalue method. Thanks to our approach, we can find all the solutions of the system at a time. Also, we are able to determine when the solution sets of the system are nonempty sets. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

Recently many methods use encoder-decoder framework for video captioning, aiming to translate short videos into natural language. These methods usually use equal interval frame sampling. However, lacking a good efficiency in sampling, it has a high temporal and spatial redundancy, resulting in unnecessary computation cost. In addition, the existing approaches simply splice different visual features on the fully connection layer. Therefore, features cannot be effectively utilized. In order to solve the defects, we proposed filtration network (FN) to select key frames, which is trained by deep reinforcement learning algorithm actor-double-critic. According to behavior psychology, the core idea of actor-double-critic is that the behavior of agent is determined by both the external environment and the internal personality. It avoids the phenomenon of unclear reward and sparse feedback in training because it gives steady feedback after each action. The key frames are sent to combine codec network (CCN) to generate sentences. The operation of feature combination in CCN make fusion of visual features by complex number representation to make good semantic modeling. Experiments and comparisons with other methods on two datasets (MSVD/MSR-VTT) show that our approach achieves better performance in terms of four metrics, BLEU-4, METEOR, ROUGE-L and CIDEr. [ABSTRACT FROM AUTHOR]

Complex fuzzy set, as an extension of classical fuzzy sets, could describe the fuzzy characters of things more detail and comprehensively and is very useful in dealing with vagueness and uncertainty of problems that include the periodic or recurring phenomena. Note that a complex fuzzy set is different from the fuzzy complex set introduced and discussed by many scholars, since the membership degree of a complex fuzzy set is a complex number with length less than or equal to 1 while a fuzzy complex set is a real number with membership degree less than or equal to 1, and the universe is the complex plane. As the mathematical theoretical basis of fuzzy mathematics, fuzzy set and its mapping, corresponding fuzzy complex set and its mapping have been investigated in depth because they integrate and cross the methods and results of classical real analysis and complex analysis. However, there is no comprehensive investigation on complex fuzzy set and its corresponding mathematical theory, even include decomposition theorems, extension principles and the basic operations of the complex fuzzy set. As is well known, the cut set of fuzzy sets is the bridge between fuzzy sets and classical sets, which plays a significant role in fuzzy sets and fuzzy systems. In this paper, the concept of (r, θ)-cut sets of complex fuzzy sets is proposed and their properties are discussed. Meanwhile, the decomposition theorems and the extension principles of complex fuzzy set based on (r, θ)-cut sets are deduced and corresponding properties are investigated. All these conclusions not only deeply enrich the fundamental theory of complex fuzzy set, but also provide a powerful tool to investigate complex fuzzy set. Finally, an example application of signal detection demonstrates the utility of the (r, θ)-cut sets of complex fuzzy sets in practice. [ABSTRACT FROM AUTHOR]

Many factors with the perspective of bipolarity in the traditional Chinese food system "Yin and Yang food system" manipulate with types of food simultaneously to have a balanced body. This research studies the multiple attributes decision making (MADM) problem that measuring the "bipolarity of periodic" variation in bipolar information with an illustration example in order to find an optimal nutrition program for a person X. To convey this type of data to a mathematical formula and vice versa without losing the full meaning of human knowledge, we use bipolar fuzzy set in a complex geometry by extending the range of bipolar fuzzy set to the realm of a complex number. This extension needs to be successful to study and introduce intensely a new mathematical structure called a bipolar complex fuzzy set (BCFS) with its properties. Ranges of values are extended to [0, 1] eiα[0,1] and [-1, 0] eiα[-1,0] for both positive and negative membership functions, respectively, as a replacement for [-1, 0] × [0, 1] , as in the bipolar fuzzy set. The main benefit of BCFS that the amplitude and phase terms of BCFSs can convey bipolar fuzzy information. Moreover, the formal definition of BCF distance measure and illustration application are introduced. Some basic mathematical operations on BCFS are also proposed and study its properties with arithmetical examples. [ABSTRACT FROM AUTHOR]

Salient object detection plays a vital role in image processing applications like image retrieval, security and surveillance in authentic-time. In recent times, advances in deep neural network gained more attention in the automatic learning system for various computer vision applications. In order to decrement the detection error for efficacious object detection, we proposed a detection classifier to detect the features of the object utilizing a deep neural network called convolutional neural network (CNN) and discrete quaternion Fourier transform (DQFT). Prior to CNN, the image is pre-processed by DQFT in order to handle all the three colors holistically to evade loss of image information, which in-turn increase the effective use of object detection. The features of the image are learned by training model of CNN, where the CNN process is done in the Fourier domain to quicken the method in productive computational time, and the image is converted to spatial domain before processing the fully connected layer. The proposed model is implemented in the HDA and INRIA benchmark datasets. The outcome shows that convolution in the quaternion Fourier domain expedite the process of evaluation with amended detection rate. The comparative study is done with CNN, discrete Fourier transforms CNN, RNN and masked RNN. [ABSTRACT FROM AUTHOR]

Selecting suppliers for prefabricated components (PCs) involves a complex decision-making process, frequently relying on ambiguous information and subjective judgment. However, most existing methods use precise values to portray indicator information and overlook the uncertainty of weights and the subjective preferences of decision-makers (DMs). In order to address these limits, this paper proposes a novel approach to select suppliers of PCs. Initially, an evaluation index system for suppliers is established through literature analysis and a questionnaire survey. The system comprises six layers: product quality, price, service level, comprehensive ability, supply ability, and environmental sustainability. The group decision matrix is then constructed using the set-valued statistical method and the prospect theory. The index weights are determined by a combination weighting method. Next, the cobweb model is introduced to analyze the disparity between the alternative and ideal solutions, describing their similarities in terms of area and shape. Lastly, cobweb similarity is employed instead of comprehensive distance, combined with the minimum sum of squares criterion, to improve the closeness algorithm and contrast the alternatives. The results demonstrate that this method facilitates a comprehensive evaluation of the benefits and drawbacks of various alternatives from diverse perspectives. Furthermore, it allows flexible adjustments based on the risk preferences of DMs, ensuring accurate and reliable decision results. [ABSTRACT FROM AUTHOR]

The grid connected inverter is the core component of the photovoltaic grid connected power generation system, which mainly converts the direct current of the photovoltaic matrix into alternating current that meets the grid connected requirements, playing a key role in the efficient and stable operation of the photovoltaic grid connected power generation system.This paper uses fuzzy PI control model which to improve the performance of intelligent photovoltaic grid-connected inverter to simulate the intelligent photovoltaic inverter system, using mathematical analysis and reasoning methods for model analysis,adopts two-stage three-phase LCL grid-connected inverter, establishes mathematical models in two-phase synchronous rotating and two-phase static coordinate systems, and adopts an active damping strategy based on grid-connected current. Based on existing research and empirical analysis,aiming at the disadvantage of poor dynamic response of repetitive control, an improved repetitive control strategy is adopted, and the controller is analyzed from two aspects of stability and dynamic performance, and the simulation model of photovoltaic grid-connected power generation system is built. Use experimental analysis method to verify the effectiveness of the model in this article,The experimental results show that the simulation system of intelligent photovoltaic grid-connected inverter considering fuzzy PI control proposed in this paper has certain effects. [ABSTRACT FROM AUTHOR]

A singular system, assumed to possess both regularity and freedom from impulses, is categorized as a causal system. Noncausal systems (NSs) are a class of singular systems anticipated to exhibit regularity. This study focuses on investigating zero-sum games (ZSGs) in the context of NSs. We introduce recurrence equations grounded in Bellman's optimality principle. The saddle-point solution for multistage two-player ZSGs can be obtained by solving these recurrence equations. This methodology has demonstrated its effectiveness in addressing two-player ZSGs involving NSs. Analytical expressions that characterize saddle-point solutions for two types of two-player ZSGs featuring NSs, encompassing both linear and quadratic control scenarios, are derived in this paper. To enhance clarity, we provide an illustrative example that effectively highlights the utility of our results. Finally, we apply our methodology to analyze a ZSG in the realm of environmental management, showcasing the versatility of our findings. [ABSTRACT FROM AUTHOR]

Knowledge graphs are knowledge bases that represent entities and relations in the objective world through graph structure, and they have a boosting effect on many artificial intelligence tasks. To facilitate the development of downstream artificial intelligence tasks, knowledge graph embedding (KGE) is proposed. It aims to express semantic information for each entity and relation in the knowledge graph within a low-dimensional space. However, when it comes to semantic hierarchy, multiple relation patterns and multi-fold relational structures in knowledge graphs, most of the existing models tend to focus on only one or two aspects, often neglecting the importance of considering all three simultaneously. Therefore, we propose a new knowledge graph embedding model, Hierarchical relation and Entity Rotation-based Multi-Feature knowledge graph Embedding (HERotMFE). Concerning hierarchical relation rotation and entity rotation, it can represent semantic hierarchy, multiple relation patterns and multi-fold relations simultaneously. Self-attention mechanism is used to learn the weights of the two-part rotation to further enhance the model's performance. According to the findings of the experiments, HERotMFE outperforms existing models on most metrics and achieves state-of-the-art results. [ABSTRACT FROM AUTHOR]

Based on the quaternion system, we give a new representation of the complex vague soft set, and related logical operations. This new representation contains more information than before. Three quaternion distance measures are proposed and a decision model is established. The disease diagnosis of breast cancer is applied to the model to reflect the superiority of the model. By comparing the diagnostic errors under the different distance measures, the most suitable distance measure for this dataset is selected. [ABSTRACT FROM AUTHOR]

This paper presents the concepts of a complex intuitionistic fuzzy subfield (CIFSF) and the direct product of a complex intuitionistic fuzzy subfield which is generalized from the concept of a complex fuzzy subfield by adding the notion of intuitionistic fuzzy into a complex fuzzy subfield. The main contribution and originality of this research are adding the non-membership term to the definition of a complex fuzzy subfield that assigns for any element a complex-valued grade. We expand the complex fuzzy subfield and obtain a new structure called CIFSF. This new concept is innovative in that it may attain a wider range of values for both membership and non-membership functions where these functions are expanded to the unit disc in the complex plane. Furthermore, we discuss that the direct product of two CIFSFs is CIFSF, and some related properties are investigated. In addition, we present the definition of necessity and possibility operators on the direct product of CIFSF, and some associated theorems are given. Finally, we propose the level subsets of the direct product of two complex intuitionistic fuzzy subsets of a field and prove that the level subset of the direct product of two CIFSFs is a subfield and discuss some related results. [ABSTRACT FROM AUTHOR]

This paper proposes a method for solving fuzzy linear and nonlinear partial q-differential equations by the fuzzy q-differential transform. Further, we implemented the fuzzy fractional q-differential transform for solving some types of fuzzy fractional q-differential equations. The technique investigated is based on gH-differentiability, fuzzy q-derivative, and fuzzy q-fractional derivative. Various concrete problems have been tested by implementing the new method, and the results show great performance. The results also reveal that the method is a very effective and quite accurate mathematical tool for solving fuzzy fractional and integer q-differential equations. Finally, we have provided some examples illustrating our method. [ABSTRACT FROM AUTHOR]

In this paper, we explore the improper integral with exponential function f = xx is approached to infinite series, and also prove the convergence of these series. An improper integral converges if the limit defining it exists. We use Maple code to calculate the infinite series. The application of improper integral appear in several domain in science. As an application in this paper, three examples are given to illustrate the effectiveness of our main result. [ABSTRACT FROM AUTHOR]

Securing image data from prying hackers is crucial in safeguarding the secrecy of data. Over the years, this was done by encrypting the image using an algorithm and a key, where the visible image was converted into a meaningless object. It is a difficult problem to design an image encryption technique based on chaotic systems with predictable cryptographic features. In this paper, the Quaternion, along with the Rossler attractor, was used to generate the key combination. The ciphering was done using the Least Square Approximation Algorithm (LSA). The algorithm was tested on a grayscale image database. The algorithm was initially tested in software using MATLAB R2018b, and was implemented in the Cyclone II EP2C35F672C6 device FPGA. On average, for a cipher image, the Peak Signal to Noise ratio (PSNR) was 9.09303 dB and the entropy was 7.9990 bits. For the cipher image, the Number of Pixels Change Rate (NPCR) and Unified Average Change Intensity (UACI) were 99.6039 and 33.4980, respectively. This proved that the algorithm could effectively mitigate the statistical and differential attacks. The key space was 2 (M ×N ×7 ×8), which was sufficiently high and mitigated the brute force attacks. The obtained results confirm that the cipher images resulting from the proposed ciphering scheme possess good cryptographic properties in terms of entropy, PSNR, UACI, NPCR, and keyspace analysis. Furthermore, the strength of the key is evaluated by the NIST test suite. [ABSTRACT FROM AUTHOR]

Optimal control is a very important field of study, not only in theory but in applications, and fractional optimal control is also a significant branch of research in theory and applications. Based on the concept of fuzzy process, a fuzzy fractional optimal control problem is presented. In this article, we derived the necessary and sufficient optimality conditions for a class of fuzzy-fractional optimal control problems (FFOCPs) with gH-Atangana-Baleanu fuzzy-fractional derivative expressed in Caputo sense. The main aim is to find the best possible control that minimizes the fuzzy performance index and satisfies the related ABC fuzzy-fractional dynamical systems. We also presented some examples for more illustration of the subject. [ABSTRACT FROM AUTHOR]

Bonferroni means (BM) operator is the extended form of the arithmetic mean operator, used for simplifying non-dominant and non-feasible problems diagnosed in genuine life scenarios. A lot of aggregation operators are the specific parts of the BM operators under the consideration of different values of parameters which are the main parts of the BM operators. In the presence of the BM operator and a very well-known conception in the scenario of fuzzy set, called complex Pythagorean fuzzy (CPF) setting, the objective of this scenario is to diagnose the CPF power BM (CPFPBM) operator and utilize their beneficial results with important properties. Moreover, a multi-attribute decision-making (MADM) technique is evaluated in the presence of invented operators for CPF settings. In the last of this study, we diagnosed the superiority and efficiency of the invented works with the help of sensitive analysis and graphical illustrations to enhance the gap of the research works. [ABSTRACT FROM AUTHOR]

Knowledge graph link prediction uses known fact links to infer the missing link information in the knowledge graph, which is of great significance to the completion of the knowledge graph. Generating low-dimensional embeddings of entities and relations which are used to make inferences is a popular way for such link prediction problems. This paper proposes a knowledge graph link prediction method called Complex-InversE in the complex space, which maps entities and relations into the complex space. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. The Complex-InversE effectively captures the antisymmetric relations and introduces Dropout and Early-Stopping technologies into deal with the problem of small numbers of relationships and entities, thus effectively alleviates the model's overfitting. The results of comparison experiment on the public knowledge graph datasets show that the Complex-InversE achieves good results on multiple benchmark evaluation indicators and outperforms previous methods. Complex-InversE's code is available on GitHub at . [ABSTRACT FROM AUTHOR]

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead's general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed. [ABSTRACT FROM AUTHOR]

Decision-makers (DMs) usually face many obstacles to give the right decision, multiplicity of them highlights a problem to represent a set of potential values to assign a collective membership degree of an object to a set for several DM's opinions. However, a hesitant fuzzy set (HFS) deals with such problems. The complexity appears in DM's opinion which can be changed for the same object but with different times/phases. Each of them has a set of potential values in different times/phases of an object. In this paper, the periodicity of hesitant fuzzy information is studied and applied by extending the range of HFS from [0, 1] to the unit disk in the complex plane to provide more ability for illustrating the full meaning of information to overcome the obstacles in decision making in the mathematical model. Moreover, the advantage of complex hesitant fuzzy set (CHFS) is that the amplitude and phase terms of CHFSs can represent hesitant fuzzy information, some basic operations on CHFS are also presented and we study its properties, in addition, several aggregation operators under CHFS are introduced, also, the relation between CHFS and complex intuitionistic fuzzy sets (CIFS) are presented. Finally, an efficient algorithm with a consistent process and an application in multiple attributes decision-making (MADM) problems are presented to show the effectiveness of the presented approach by using CHFS aggregation operators. [ABSTRACT FROM AUTHOR]

Modular Multilevel Converter (MMC) plays a vital role in high voltage industries because of its high rating power conversion. Due to its usage in high voltage rating power conversion and switched capacitor usage in MMC structure, there arises a problem of unbalanced capacitor voltage, which causes circulating current and disturbance in output current regulation. To manage these problematic parameters, a FOPID (Fractional Order Proportional Integral Derivative) controller has been utilized, due to its dynamic tracking and fast response. Secondly, the gain values of FOPID are not efficient, and they are optimized for each control group at all times of MMC working conditions. To provide a dynamic gain value by considering the dynamic change of error tracking parameters, Wild Spider Foraging Optimization (WSFO) algorithm has been developed based on the foraging behaviour of wild spider searching food (gain values) in view of changing the error of tracking parameters. The proposed algorithm has been evaluated in MATLAB Simulink by modeling the MMC structure with FOPID controller. The parameters of FOPID are optimized by bio-inspired algorithms like WSFO, Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO). The outcomes of the proposed WSFO-FOPID provide minimum circulating current and effectively balance the capacitor voltage in MMC. When the effectiveness of the results has been verified with the existing ABC and PSO optimization approaches, the proposed algorithm outperforms. [ABSTRACT FROM AUTHOR]

In this work, we study the lacunary I -statistical convergence concept of complex uncertain triple sequence. Four types of lacunary I -statistically convergent complex uncertain triple sequences are presented, namely lacunary I -statistical convergence in measure, in mean, in distribution and with respect to almost surely, and some basic properties are proved. [ABSTRACT FROM AUTHOR]

Capturing the composite embedding representation of a multi-hop relation path is an extremely vital task in knowledge graph completion. Recently, rotation-based relation embedding models have been widely studied to embed composite relations into complex vector space. However, these models make some over-simplified assumptions on the composite relations, resulting the relations to be commutative. To tackle this problem, this paper proposes a novel knowledge graph embedding model, named QuatGE, which can provide sufficient modeling capabilities for complex composite relations. In particular, our method models each relation as a rotation operator in quaternion group-based space. The advantages of our model are twofold: (1) Since the quaternion group is a non-commutative group (i.e., non-Abelian group), the corresponding rotation matrices of composite relations can be non-commutative; (2) The model has a more expressive setting with stronger modeling capabilities, which is flexible to model and infer the complete relation patterns, including: symmetry/anti-symmetry, inversion and commutative/non-commutative composition. Experimental results on four benchmark datasets show that the proposed method outperforms the existing state-of-the-art models for link prediction, especially on composite relations. [ABSTRACT FROM AUTHOR]

Complex fuzzy aggregation operation (CFAO) is a formalized definition of combining several complex fuzzy sets into a single complex fuzzy set. It extends classical fuzzy aggregation operation (FAO) to the complex-valued domain retaining classical real-valued weight. CFAO was initially defined with complex weight by Ramot et al. However, there has been virtually no progress in developing CFAO with complex weight. In this paper, we study the CFAOs with complex weight. We first discuss how to define complex weights meeting the restriction that the sum of weights is equal to 1. We give a new natural type of complex weight which is different from Ramot et al.'s complex weight. Then we study various properties which include idempotency, homogeneity, rotational invariance and shift invariance for CFAOs with both types of complex weights. [ABSTRACT FROM AUTHOR]

This paper proposes a Wi-Fi-based indoor human detection system using a deep convolutional neural network. The system detects different human states in various situations, including different environments and propagation paths. The main improvements proposed by the system is that there is no cameras overhead and no sensors are mounted. This system captures useful amplitude information from the channel state information and converts this information into an image-like two-dimensional matrix. Next, the two-dimensional matrix is used as an input to a deep convolutional neural network (CNN) to distinguish human states. In this work, a deep residual network (ResNet) architecture is used to perform human state classification with hierarchical topological feature extraction. Several combinations of datasets for different environments and propagation paths are used in this study. ResNet's powerful inference simplifies feature extraction and improves the accuracy of human state classification. The experimental results show that the fine-tuned ResNet-18 model has good performance in indoor human detection, including people not present, people still, and people moving. Compared with traditional machine learning using handcrafted features, this method is simple and effective. [ABSTRACT FROM AUTHOR]

The purpose of this article is to investigate the existence of unique solution for the following mixed nonlinear Volterra Fredholm-Hammerstein integral equation considered in complex plane; (0.1) ξ (τ) = g (t) + ρ ∫ 0 τ K 1 (τ , ℘) ϝ 1 (℘ , ξ (℘)) d ℘ + ϱ ∫ 0 1 K 2 (τ , ℘) ϝ 2 (℘ , ξ (℘)) d ℘ , such that ξ = ξ 1 + ξ 2 , ξ 1 , ξ 2 ∈ (C ([ 0 , 1 ]) , R) g = g 1 + g 2 , g l : [ 0 , 1 ] → R , l = 1 , 2 , ϝ l (℘ , ξ (℘)) = ϝ l 1 * (℘ , ξ 1 *) + i ϝ l 2 * (℘ , ξ 2 *) , ϝ lj * : [ 0 , 1 ] × R → R for l , j = 1 , 2 , and ξ 1 * , ξ 2 * ∈ (C ([ 0 , 1 ]) , R) K l (t , ℘) = K l 1 * (t , ℘) + iK l 2 * (t , ℘) , for l , j = 1 , 2 and K lj * : [ 0 , 1 ] 2 → R , where ρ and ϱ are constants, g (t), the kernels Kl (τ, ℘) and the nonlinear functions ϝ1 (℘, ξ (℘)), ϝ 2 (℘, ξ (℘)) are continuous functions on the interval 0 ≤ τ ≤ 1. In this direction we apply fixed point results for self mappings with the concept of (ψ, ϕ) contractive condition in the setting of complex-valued fuzzy metric spaces. This study will be useful in the development of the theory of fuzzy fractional differential equations in a more general setting. [ABSTRACT FROM AUTHOR]

Zadeh's fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and complex fuzzy set with wide range of values by adding positive membership function and negative membership function to unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets. Thus this paper leads us towards a new direction of research, which has many applications in different directions. We develop the notions of union, intersection, complement, Cartesian product and De-Morgan's laws of complex bipolar fuzzy sets. Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an integrated model combining interval deep belief network (IDBN) and neural network with nonlinear weights, called IDBN-NN, is proposed for interval-valued data modeling. Firstly, the IDBN with variable learning rate is designed to initialize parameters of each sub-model. Based on a modified contrastive divergence algorithm the least square method is adopted to identify the coefficients of nonlinear weights in the output layer. Then, to improve the modeling accuracy, the Fuzzy C-Means (FCM) method and the Particle Swarm Optimization (PSO) algorithm are applied to tune the weights of sub-models. Though each sub-model can capture the nonlinear feature of the original system, by intersecting cut sets the synthesizing modeling scheme can further improve the performance of the proposed model. Some numerical examples show that the IDBN-NN with nonlinear output structure can achieve higher accuracy than some interval-valued data modeling methods. [ABSTRACT FROM AUTHOR]

Autism is a developmental disorder that influences social communication skills. It is currently diagnosed only by behavioral assessment. The assessment is susceptible to the experience of the examiner as well as to the descriptive scaling standard. This paper presents a computer aided approach to discrimination between neuro-typical and autistic children. A new method- based on the computing of the elliptic area of the Continuous Wavelet Transform complex plot of resting state EEG- is presented. First, the complex values of CWT, as a function of both time and frequency, are calculated for every EEG channel. Second, the CWT complex plot is obtained by plotting the real parts of the resulted CWT values versus the related imaginary components. Third, the 95% confidence value of the elliptic area of the complex plot is computed for every channel for both autistic and healthy subjects; and the obtained values are considered as the first set of features. Fourth, three additional features are computed for every channel: the average CWT, the maximum EEG amplitude, and the maximum real part of CWT. The classification of those features is realized through artificial neural network (ANN). The obtained accuracy, sensitivity and specificity values are: 95.9%, 96.7%, and 95.1% respectively. [ABSTRACT FROM AUTHOR]

The information measures (IMs) of complex fuzzy information are very useful tools in the areas of machine learning and decision making. In some multi-attribute group decision making (MAGDM) problems, the decision makers can make a decision mostly according to IMs such as similarity measures (SMs), distance measures (DIMs), entropy measures (EMs) and cross-entropy measures (C-EMs) in order to choose the best one. However, the relation between C-EMs and DIMs in the environment of complex fuzzy sets (CFSs) has not been developed and verified. In this manuscript, the notions of DIMs and C-EMs in the environment of CFSs are investigated and the relation between DIMs and EMs in the environment of CFSs is also discussed. The complex fuzzy discrimination measures (CFDMs), the complex fuzzy cross-entropy measures (CFC-EMs), and the symmetry complex fuzzy cross-entropy measures (SCFC-EMs) are proposed. We also examined that the C-EMs satisfied all the conditions of DIMs, and finally proved that C-EMs including CFC-EMs were also a DIMs. In last, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. [ABSTRACT FROM AUTHOR]

The complex-value-based generalized Dempster–Shafer evidence theory, also called complex evidence theory is a useful methodology to handle uncertainty problems of decision-making on the framework of complex plane. In this paper, we propose a new concept of belief function in complex evidence theory. Furthermore, we analyze the axioms of the proposed belief function, then define a plausibility function in complex evidence theory. The newly defined belief and plausibility functions are the generalizations of the traditional ones in Dempster–Shafer (DS) evidence theory, respectively. In particular, when the complex basic belief assignments are degenerated from complex numbers to classical basic belief assignments (BBAs), the generalized belief and plausibility functions in complex evidence theory degenerate into the traditional belief and plausibility functions in DS evidence theory, respectively. Some special types of the generalized belief function are further discussed as well as their characteristics. In addition, an interval constructed by the generalized belief and plausibility functions can be utilized for fuzzy measure, which provides a promising way to express and model the uncertainty in decision theory. [ABSTRACT FROM AUTHOR]

We present a novel modified complex phase synchronization (MCPS) focusing on two hyperchaotic complex systems, including a comparative structure of direct terms with absolutely differing or not completely in nonlinear terms. We have used the active control theory for analytical control limits to achieve MCPS. It is shown that MCPS contains two sorts of synchronizations (phase and anti-phase synchronizations) and the state variables of the master system synchronize with substitute state components of the slave system. Numerical results are portrayed out to reveal the phases and modules errors of these hyperchaotic complex attractors, where the complex systems appear in various basic fields of material science and building. Also, we found that MCPS of the hyperchaotic complex structure synchronizes with another state variable of the slave structure is an empowering sort of synchronization as it contributes fabulous security in secure communication. In this secure communication, synchronization amongst transmitter and collector is closed and message signals are recovered. The encryption and recovery of the signals are imitated numerically. [ABSTRACT FROM AUTHOR]

There are various high-dimensional engineering and scientific applications in communication, control, robotics, computer vision, biometrics, etc.; where researchers are facing predicament to fabricate an intelligent and robust neural system which can process higher dimensional information efficiently. In various literatures, the conventional neural networks based only on real valued, are tried to solve the problem associated with high-dimensional parameters, but these neural network structures possess high complexity and are very time consuming and weak to noise. These networks are also not able to learn magnitude and phase values simultaneously in space. The quaternion is the number, which possesses the magnitude in all four directions and phase information is embedded within it. This paper presents a learning machine with a quaternionic domain neural network that can finely process magnitude and phase information of high dimension data without any hassle. The learning and generalization capability of the proposed learning machine is performed through chaotic time series predictions (Lorenz system and Chua's circuit), 3D linear transformations, and 3D face recognition as benchmark problems, which demonstrate the significance of the work. [ABSTRACT FROM AUTHOR]

This paper aims to develop a new idea for the classification of power quality disturbances. The method is based on Stockwell's-Transform (ST) and Type-2 Fuzzy Kernel Support Vector Machine (T2FK-SVM). Through the introduction of ST and its properties, we propose a classification plan for nine types of power quality disturbances. Firstly, features of disturbance signals extracted through the ST. Secondly, features extracted by using the ST are applied as input to T2FK-SVM classifier for automatic classification of the power quality (PQ) disturbances. Design of Kernel is a main part of many kernel based methods such as Support Vector Machine (SVM), so by using of Type-2 Fuzzy sets as a kernel of SVM, the total accuracy of classification enhanced.This method can reduce the features of the disturbance signals significantly, and so less time and memory is required for classification by the T2FK-SVM method. Six single event and two complex event as well normal voltage selected as reference are considered for the classification. The simulation results showed accurate classification, fast learning and execution in the detection and classification of PQ events. Results are compared with other methods and the robustness of proposed method evaluated under noisy conditions. Finally, proposed method is also implemented on real time PQ disturbances to confirm the validity of this method in practical conditions. [ABSTRACT FROM AUTHOR]

In this paper, S0, S1 and S2 separation axioms are introduced in (L, M)-fuzzy convex spaces. Each (L, M)-fuzzy convex space can be regarded to be S0, S1 and S2 separated to some degree. Some properties of them are investigated. Moreover, the degrees to which a function is convex preserving, convex-to-convex or isomorphic are defined in (L, M)-fuzzy convex spaces by using implication operation. Their relationships with the degrees of S0, S1 and S2 separation axioms are discussed. [ABSTRACT FROM AUTHOR]

A complex fuzzy set, characterized by complex-valued membership functions, is a generalization of a fuzzy set. In this paper, we present complex fuzzy arithmetic aggregation (CFAA) operators, complex fuzzy weighted arithmetic aggregation (CFWAA) operators. Based on the partial ordering of complex fuzzy values, we develop complex fuzzy ordered weighted arithmetic aggregation (CFOWAA) operators. Highly pertinent to complex fuzzy operations is the concept of rotational. This concept has been developed for complex fuzzy aggregation operators. We show that CFAA, CFWAA and CFOWAA operators possess the property of rotational invariance. Moreover, based on the relationship between Pythagorean membership grades and complex numbers, these operators are studied under Pythagorean fuzzy values. [ABSTRACT FROM AUTHOR]

In this paper, S0, S1 and S2 separation axioms are introduced in M-fuzzifying convex spaces. Each M-fuzzifying convex space can be regarded to be S0, S1 and S2 separated to some degree. Some properties of them are investigated. The relations among them are discussed. [ABSTRACT FROM AUTHOR]

Covariance is a measure to characterize the joint variability of two complex uncertain variables. Since, calculating covariance is not easy based on uncertain measure, we present two formulas for covariance and pseudo covariance of complex uncertain variables. For calculating the covariance of complex uncertain variables, some theorems are proved and several formulas are provided by using the inverse uncertainty distribution. The main results are explained by using several examples. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for a high-resolution urban spatial load demand forecasting. This methodology is meant to improve the visualization, analysis and inference of load density information in the electric distribution systems in the near future. The proposed methodology converts input data into grid maps and then divides the grid map into larger regions, which will have their expected growth according to convolution matrices and weighting factors that search for characteristics in the history of this region. The definition of the characteristics of the region's growth is obtained by processing the imperialist competitive algorithm that searches the best array of convolution, which will set the expected growth of the region. Thus, it is possible to obtain a spatial growth forecast of high resolution and with great precision, which are important factors for smart-grid planning. [ABSTRACT FROM AUTHOR]

In this paper we introduce and study some difference double sequence spaces of fuzzy numbers by using Hausdorff metric associated with sequence of Orlicz functions. We make an effort to study some algebraic, topological properties and inclusion relations between these sequence spaces. We show that the new formed sequence spaces are complete with respect to the metric D M , Δ m , p , u (x , y). Finally, we establish some relation between Δr-statistically convergent and Δr-statistically (C, 1, 1) summable double sequences of fuzzy numbers under the slowly oscillating and statistically slowly oscillating conditions in certain sense, respectively. [ABSTRACT FROM AUTHOR]

This paper aims at putting forward several types of convergence concepts of complex uncertain random sequences. The relations among convergence concepts are derived by some limit theorems. In addition, for illustrating of convergence theorems, lots of examples are derived. Finally, a lot of counterexamples about relationships between convergence concepts are stated. [ABSTRACT FROM AUTHOR]

In paper a general complex fuzzy matrix equation Z ˜ C = W ˜ in which C is a n × p complex matrix and W ˜ is a m × p complex LR fuzzy numbers one, is investigated. A numerical procedure for calculating the solution is designed in detail and a sufficient condition for the existence of strong complex LR fuzzy solution is derived. Some examples are given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

The notion of cubic set was introduced in [23] as a generalization of the notion of fuzzy sets and intuitionistic fuzzy sets. In this paper, we initiate a study of cubic sets in left almost semihypergroups. By using the concept of cubic sets, we introduce the notion of cubic sub LA-semihypergroups (hyperideals and bi-hyperideals) and discuss some basic results on cubic sets in LA-semihypergroups. [ABSTRACT FROM AUTHOR]

The theory of fuzzy differential equation has been studied by many researchers. In this paper, the fuzzy differential equation is a different type of differential equations, its fuzziness is not only in the initial conditions and coefficients, but also in the driven process. This paper presents some methods to solve linear complex fuzzy differential equations, and proves some existence and uniqueness theorems of solution for complex fuzzy differential equations based on Lipschitz condition and linear growth condition. [ABSTRACT FROM AUTHOR]

We consider the initial value problem of quaternion fuzzy fractional differential equations in the generalized regular fuzzy function space. By the associate space theorem and fixed point theorem, some results on the existence and stability for the solution of the initial value problem are given. By the fixed point method, we also prove the Hyers-Ulam stability for the solution of the abstract Cauchy problem under some suitable conditions. [ABSTRACT FROM AUTHOR]