Trigonometric Operations Research Articles

Resource allocation strategy selection for 5G network by using multi-attribute decision-making approach based on tangent trigonometric bipolar fuzzy aggregation operators

Resource allocation strategy selection for 5G network by using multi-attribute decision-making approach based on tangent trigonometric bipolar fuzzy aggregation operators

Utilizing sine trigonometric q-spherical fuzzy rough aggregation operators for group decision-making and their role in digital transformation

q-spherical fuzzy rough set (q-SFRS) is also one of the fundamental concepts for addressing more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi-parameters. Taking this feature and the significance of the q-SFRSs into consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the q-spherical fuzzy rough numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with applications for selecting a Cloud Service Provider and a Digital Transformation Vendor for digital transformation. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

Optimal Single-Valued Neutrosophic Sine Trigonometric Aggregation Operators for Accurate Financial Fraud Detection Model

Financial fraud may be regarded as any fraud targeting financial organisations including crypto exchanges, banks, fintech, and lending organizations, or any criminal activity associated with the payment process. Financial fraud detection cites protocol set prepared to circumvent the destruction produced by fraudulent activities happening in financial service suppliers. Ecological financial fraud detection (FD) includes the usage of ethical and sustainable performs within fraud actions recognition from the financial area. In recent times, DL and ML techniques have been used in CCF recognition owing to their ability to construct a robust mechanism to discover fraud businesses. Therefore, this study develops an Optimal Single Valued Neutrosophic Sine Trigonometric Aggregation Operator (O-SVNSTAO) for Accurate Financial Fraud Detection Model. The genetic-inspired particle swarm optimization (GIPSO) feature selection model efficiently discerns the relevant attribute from sophisticated financial databases, improving the model's discriminative power while alleviating dimensionality problems. Consequently, the SVNSTAO classifier leverages the features selected to discern complicated features inherent in fraudulent actions, which facilitates accurate diagnosis. Moreover, the COA parameter tuning mechanism enhances the SVNSTAO model's parameter, which ensures adaptability and optimum performance to varied fraud settings. Empirical analysis of real-time financial datasets demonstrates the superiority of O-SVNSTAO technique over classical methods, underlining its effectiveness in discovering financial fraud with exceptional efficiency and reliability

Review on FPGA Implementation of CORDIC Algorithm

The Coordinate Rotation Digital Computer (CORDIC) algorithm has emerged as a pivotal method for executing trigonometric and various mathematical operations within digital systems. Field-Programmable Gate Arrays (FPGAs) have witnessed a remarkable surge in adoption for implementing the CORDIC algorithm owing to their inherent flexibility and exceptional performance capabilities. This paper endeavours to provide a comprehensive overview of FPGA implementations of the CORDIC algorithm, elucidating both the advantages and challenges associated with this methodology. It thoroughly examines various FPGA architectures customized for CORDIC implementation, meticulously analyzing their respective trade-offs regarding resource utilization, performance metrics, and accuracy levels. Moreover, the paper explores numerous applications where the FPGA-based CORDIC algorithm shines, illustrating its adaptability across diverse domains like digital signal processing and control systems. These applications underscore the algorithm's efficacy in addressing real-world challenges and its potential to significantly augment system performance and efficiency.By furnishing profound insights into FPGA-based CORDIC implementations, this paper serves as an invaluable resource for engineers and researchers keen on harnessing the capabilities of FPGAs for high-performance mathematical computations in digital systems.

Multiple attribute decision making technique using single-valued neutrosophic trigonometric Dombi aggregation operators

Multiple attribute decision making technique using single-valued neutrosophic trigonometric Dombi aggregation operators

VISUALISASI OPERASI TRIGONOMETRI (SINUS DAN COSINUS)

This article discusses a scheme for creating a visual representation of trigonometry and its operations on sine and cosine. This visual representation is then called trigonometric visualisation. The formulas in the visualisation of trigonometric operations apply to all trigonometric identities constructed from sines and cosines with degrees no more than 2. Research was carried out by analyzing trigonometric representations of right triangles from various sources. The results of the research are procedures or techniques for creating trigonometry visualizations of sine and cosine and their operations. Operations in trigonometry visualization are: multiplication, addition, and subtraction of sine and cosine.

Remote Control Of A Serial Manipulator Using Depth Camera

In this study, a serial robot arm was manipulated in real time using a depth sensor. Xbox-Kinect sensor is used as depth sensor. Kinect data was transferred to an industrial computer and processed. A three-axis serial robot arm was developed, and experiments were carried out on this developed prototype in real time. The drive of the three-axis robot is provided with RC servo motors and these motors are controlled by Arduino Uno R3 board. To find the joint angles, the image obtained from the Kinect camera has evolved into a skeleton form through the image processing program developed in the ARDUINO-Processing environment. Vector elements are defined on the human limbs of which posture is to be calculated. The angles between the limbs were obtained by applying trigonometric operations to these vectors. The reference angles were sent to the Arduino Uno R3 board, and the servo motors that provide the movement of the robot were controlled according to these angle values and the movement of the system was ensured. As a result of the experiments, it has been observed that the robot arm can imitate the movements made instantly.

Assessing alternatives of including social robots in urban transport using fuzzy trigonometric operators based decision-making model

Current trends point to a not-too-distant future with qualitatively advanced interactions between humans and social robots. It is critical to consider the possibility of forming meaningful social relationships with robots when defining the future of human-robot interactions, as well as studying how these interactions will evolve to the point where humans are unable to distinguish between humans and robots in urban transportation. In this study, the advantages of using social robots in urban transportation are prioritized by using a multi-criteria decision-making tool, which consists of two consecutive stages, namely: i) a novel fuzzy sine trigonometry based on the logarithmic method of additive weights (fuzzy ST-LMAW) that is proposed to calculate the criteria weights; ii) a nonlinear fuzzy Aczel-Alsina function based the weighted aggregate sum product assessment (fuzzy ALWAS-WASPAS) that is developed to select and rank the alternatives. The proposed model enables flexible nonlinear processing of complex and uncertain information encountered in real applications. A case study is developed to rank three alternatives with twelve sub-criteria grouped into four aspects using the proposed method. The results show that the most advantageous alternative is to replace people with social robots as safety drivers in level four autonomous vehicles due to their possible impact on transportation.

Multi-attribute decision-making based on sine trigonometric aggregation operators for T-spherical fuzzy information

Multi-attribute decision-making based on sine trigonometric aggregation operators for T-spherical fuzzy information

Multiple Attribute Trigonometric Decision-Making and Its Application to the Selection of Engineers

A novel method is presented for solving MADM under a sine trigonometric Pythagorean neutrosophic normal interval-valued set (ST-PyNSNIVS). An identifying feature of ST-PyNSNIVS is that it is a combination of PyNSIVS, PyNSS, and IVNSS. This article proposes a novel concept of ST-PyNSNIVWA, ST-PyNSNIVWG, ST-GPyNSNIVWA, and ST-GPyNSNIVWG. In addition, we acquired a flowchart and an algorithm that interact with MADM and are called ST-PyNSNIVWA, ST-PyNSNIVWG, ST-GPyNSNIVWA, and ST-GPyNSNIVWG, respectively. In addition to Euclidean and Hamming distances, we addressed new types of two distances in the suggested models, which are future expansions of real-life instances. The sine trigonometric aggregation operations were examined using the PyNSNIV set technique. They are more straightforward and practical, and you can arrive at the best option quickly. Consequently, the conclusions of the defined models are more accurate and closely correlated with Σ . Our analysis shows that the investigated models are valid and useful by comparing them to some of the current models. As a final result of the study, some intriguing and enthralling findings are presented.

Multi-criteria decision-making model using trigonometric aggregation operators of single-valued neutrosophic credibility numbers

An important idea is to enhance the credibility measures of single-valued neutrosophic sets/numbers (SvNSs/SvNNs) and operational requirements of multiple time-phases/periods for ensuring the credibility and rationality of multiple periodic decision-making problems. Motivated by this idea, this study aims to propose a multi-criteria decision-making (MCDM) model based on the trigonometric weighted average and geometric operators of single-valued neutrosophic credibility numbers (SvNCNs). First, a single-valued neutrosophic credibility set is presented to enhance the credibility levels of SvNSs. Then, the score and accuracy functions of SvNCNs are defined to rank SvNCNs. Next, in view of multiple time-phase/period characteristics of trigonometric functions (sine and arcsine functions and cosine and arccosine functions), we propose the trigonometric t-norm and t-conorm operational laws of SvNCNs and the SvNCN trigonometric weighted average (SvNCNTWA) and SvNCN trigonometric weighted geometric (SvNCNTWG) operators to aggregate SvNCNs. Furthermore, a MCDM model is established in terms of the proposed two aggregation operators and the score and accuracy functions to solve MCDM problems in a SvNCN circumstance. Lastly, the proposed MCDM model is applied to an actual example of the choice issue of slope design schemes for an open-pit mine to indicate the validation and rationality of the proposed model.

Retracted: A Novel Approach Based on Sine Trigonometric Picture Fuzzy Aggregation Operators and Their Application in Decision Support System

Retracted: A Novel Approach Based on Sine Trigonometric Picture Fuzzy Aggregation Operators and Their Application in Decision Support System

A decision-making strategy to combat CO$ _2 $ emissions using sine trigonometric aggregation operators with cubic bipolar fuzzy input

<abstract><p>A cubic bipolar fuzzy set (CBFS) is by far the most efficient model for handling bipolar fuzziness because it carries both single-valued (SV) and interval-valued (Ⅳ) bipolar fuzzy numbers at the same time. The sine trigonometric function possesses two consequential qualities, namely, periodicity and symmetry, both of which are helpful tools for matching decision makers' conjectures. This article aims to integrate the sine function and cubic bipolar fuzzy data. As a result, sine trigonometric operational laws (STOLs) for cubic bipolar fuzzy numbers (CBFNs) are defined in this article. Premised on these laws, a substantial range of aggregation operators (AOs) are introduced. Certain features of these operators, including monotonicity, idempotency, and boundedness, are explored as well. Using the proffered AOs, a novel multi-criteria group decision-making (MCGDM) strategy is developed. An extensive case study of carbon capture and storage (CCS) technology has been provided to show the viability of the suggested method. A numerical example is provided to manifest the feasibility of the developed approach. Finally, a comparison study is executed to discuss the efficacy of the novel MCGDM framework.</p></abstract>

Об операторных функциях операторного переменного

A family of operator functions for which the domain and the range of values are included in the real Banach algebra of bounded linear operators acting in a real Banach space is considered. Such functions find application in the study of linear differential equations in a Banach space. Known operator functions are studied: exponential, sine, cosine, hyperbolic sine, hyperbolic cosine determined by the sums of the corresponding operator power series. For the functions of sine, cosine, hyperbolic sine, hyperbolic cosine, addition formulas are indicated, from which there follow the formulas for transforming the product of operator trigonometric functions and operator hyperbolic functions into a sum as well as those for transforming the sum and difference of operator trigonometric functions of the same name and operator hyperbolic functions of the same name into a product. The basic operator hyperbolic identity is proved. The concepts of the following operator functions are introduced: tangent, cotangent, secant, cosecant, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant, hyperbolic cosecant. The periodicity of operator trigonometric functions of sine, cosine, tangent, cotangent, and the reduction formulas for them are proved. Relationships between operator functions of tangent and cotangent, hyperbolic tangent and hyperbolic cotangent are found. One useful application of the obtained operator trigonometric formulas is pointed out: it is proved that the operator functions Y_1 (t)="sin " Bt, Y_2 (t)="cos " Bt are infinitely differentiable on R; formulas for the derivatives of any order of these functions are found.

Modulating Wave-Based Timing Calculation for a Multilevel 24-Sided Polygonal Voltage Space Vector Structure With Similar Triangles

This article proposes a multilevel 24-sided polygonal voltage space vector structure (VSVS), eliminating lower order harmonics up to 19th order and suppressing higher order harmonics in motor phase voltage throughout the modulation range. Unlike switched average vectors in literature, the proposed scheme generates real active vectors that have the advantage of less switching frequency operation. The proposed VSVS consists of two concentric polygons divided into similar triangles resulting in a simple modulation algorithm. Instantaneous error in phase voltage reduces due to the multilevel property of the proposed VSVS. The proposed scheme extends the dc bus utilization and linear range of operation. The proposed scheme is implemented on an open-end winding induction motor fed with primary and secondary inverters from either end. This article also presents a modulating wave-based method to compute nearest vector timings using sampled reference waves only. Unlike conventional methods, the proposed timing calculation method does not require trigonometric operations, sorting algorithms, and iterative search algorithms. Experimental verification of the proposed scheme is performed to validate the concept. Switching loss and Fourier analysis comparison with some existing schemes is also presented.

Boosting Archimedes optimization algorithm using trigonometric operators based on feature selection for facial analysis.

Due to technical advancements and the proliferation of mobile applications, facial analysis (FA) of humans has recently become an important area for computer vision research. FA investigates a variety of difficulties, including gender recognition, facial expression recognition, age and race recognition, with the goal of automatically comprehending social interactions. Due to the dimensional challenge posed by pre-trained CNN networks, the scientific community has developed numerous techniques inspired by biology, swarm intelligence theory, physics, and mathematical rules. This article presents a gender recognition system based on scAOA, that is a modified version of the Archimedes optimization algorithm (AOA). The latest variant (scAOA) enhances the exploitation stage by using trigonometric operators inspired by the sine cosine algorithm (SCA) in order to prevent local optima and to accelerate the convergence. The main purpose of this paper is to apply scAOA to select the relevant deep features provided by two pretrained models of CNN (AlexNet & ResNet) to recognize the gender of a human person categorized into two classes (men and women). Two datasets are used to evaluate the proposed approach (scAOA): the Brazilian FEI dataset and the Georgia Tech Face dataset (GT). In terms of accuracy, Fscore and statistical test, the comparison analysis demonstrates that scAOA outperforms other modern and competitive optimizers such as AOA, SCA, Ant lion optimizer (ALO), Salp swarm algorithm (SSA), Grey wolf optimizer (GWO), Simple genetic algorithm (SGA), Grasshopper optimization algorithm (GOA) and Particle swarm optimizer (PSO).

Fabric Selection Based on Sine Trigonometric Aggregation Operators Under Pythagorean Fuzzy Uncertainty

ABSTRACT In the textile industry, selecting the optimal fabric is crucial in the design and production process. The multiple-criteria decision-making (MCDM) technique has been applied to address fabric selection problems. Because the sine trigonometry function maintains the periodicity and symmetry of the origin in nature, it satisfies the preferences of experts over multiple parameters. Considering the advantages of the sine trigonometry function, we introduce sine trigonometry Pythagorean fuzzy sets (ST-PFSs) and weighted averaging (ST-PFWA) and geometric (ST-PFWG) aggregation operators (AOs). Additionally, we propose a novel method based on ST-PFWA and ST-PFWG AOs to solve two different types of fabric selection MCDM problems. The first problem is provided by Pythagorean fuzzy numbers (PFNs), and we apply the proposed method to address the issue and conduct a comparative analysis with other PFS AOs. The second problem is offered with crisp values, and we apply a PFS linguistic term transform system to convert the values into PFNs. Then, we apply ST-PFWA and ST-PFWG AOs to settle the problem and perform a comparative analysis among different PFS linguistic terms. The complete ranking results illustrate that our proposed methodology is more efficient and reliable than previous approaches and can be used in other textile fields.

Deep learning-enabled compact optical trigonometric operator with metasurface

In this paper, a novel strategy based on a metasurface composed of simple and compact unit cells to achieve ultra-high-speed trigonometric operations under specific input values is theoretically and experimentally demonstrated. An electromagnetic wave (EM)-based optical diffractive neural network with only one hidden layer is physically built to perform four trigonometric operations (sine, cosine, tangent, and cotangent functions). Under the unique composite input mode strategy, the designed optical trigonometric operator responds to incident light source modes that represent different trigonometric operations and input values (within one period), and generates correct and clear calculated results in the output layer. Such a wave-based operation is implemented with specific input values, and the proposed concept work may offer breakthrough inspiration to achieve integrable optical computing devices and photonic signal processors with ultra-fast running speeds.

Innovative Bipolar Fuzzy Sine Trigonometric Aggregation Operators and SIR Method for Medical Tourism Supply Chain

Bipolar fuzzy sets (BFSs) are effective tool for dealing with bipolarity and fuzziness. The sine trigonometric functions having two significant features, namely, periodicity and symmetry about the origin, are helping in decision analysis and information analysis. Taking the advantage of sine trigonometric functions and significance of BFSs, innovative sine trigonometric operational laws (STOLs) are proposed. New aggregation operators (AOs) are developed based on proposed operational laws to aggregate bipolar fuzzy information. Certain characteristics of these operators are also discussed, such as boundedness, monotonicity, and idempotency. Moreover, a modified superiority and inferiority ranking (SIR) method is proposed to cope with multicriteria group decision-making (MCGDM) with bipolar fuzzy (BF) information. To exhibit the relevance and feasibility of this methodology, a robust application of best medical tourism supply chain is presented. Finally, a comprehensive comparative and sensitivity analysis is evaluated to validate the efficiency of suggested methodology.

Multiple attributes group decision-making based on trigonometric operators, particle swarm optimization and complex intuitionistic fuzzy values

Multiple attributes group decision-making based on trigonometric operators, particle swarm optimization and complex intuitionistic fuzzy values