Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations by ANGPan Y, UIXiao-lin G, AOJing Y, INJian-cai L, IANFeng T, HANGXue-jun Z

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A hybrid singular value thresholding algorithm with diagonal-modify for low-rank matrix recovery by Ruiping Wen, Liang Zhang, Yalei Pei

“…In this paper, a new hybrid singular value thresholding with diagonal-modify algorithm based on the augmented Lagrange multiplier (ALM) method was proposed for low-rank matrix recovery, in which only part singular values were treated by a hybrid threshold operator with diagonal-update, and which allowed the algorithm to make use of simple arithmetic operation and keep the computational cost of each iteration low. …”
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Improved SMC cardinality-balanced multi-Bernoulli forwardbackward smoothing track-before-detect algorithm by Jiazheng PEI, Yong HUANG, Yunlong DONG, Xiaolong CHEN

“…For the tracking problem of multiple maneuvering targets in radar observation,the sequential Monte-Carlo cardinality-balanced multi-Bernoulli track-before-detect (SMC-CBMeMBer-TBD) algorithm is inaccurate in the estimation of the number of targets and the precision of state estimation.An improved algorithm based on SMC-CBMeMBer forward backward smoothing track-before-detect algorithm was proposed.In the algorithm,the multi target particle swarm optimization (MOPSO) was added between the process of prediction and update,and the fitness function was set up based on the observation value to make the particle set move to the position of the larger posterior probability density distribution,and solve the particle poverty in the heavy sampling process.In the update step,the algorithm was used.Then the smoothing recursive method was added,and the arithmetic operation time was prolonged,but the number and the state estimation precision were improved.The simulation results show that compared with the CBMeMBer-TBD method,the proposed algorithm improves the accuracy of the estimation of the number of maneuvering targets and the accuracy of the target state estimation.…”
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Multifeature Contrast Enhancement Algorithm for Digital Media Images Based on the Diffusion Equation by Jijun Wang, Yi Yuan, Guoxiang Li

“…To meet the real-time applications in the field of video surveillance, this paper focuses on the optimization of the algorithm program, including software pipeline optimization, operation unit balancing, single instruction multiple data optimization, arithmetic operation optimization, and onchip storage optimization. …”
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Private-preserving scientific computation of the rational numbers by Xuhong LIU, Chen SUN

“…As a fundamental part of cryptography, secure multiparty computation (SMC) is a building block of various cryptographic protocols, and it is also a hot topic in the international cryptographic community.In recent years, many SMC problems, such as secret information comparison, secret set problems and secure multiparty computational geometry, have been widely studied.As many practical problems need to be described by rational numbers, it is both theoretically and practically important to study the SMC problems in the rational number field.However, most of the existing researches focus on integers and the studied data are mainly one-dimensional data.There are few researches on secure multiparty computation of multi-dimensional data in the rational number field, but they can’t be generalized.Based on the fractional representation of rational numbers, the new encoding schemes about rational numbers and rational number vectors were proposed, which could encode multi-dimensional data in the rational number field and provided new solutions for other SMC problems in the rational number field.Based on the encoding scheme and one-way hash function, some protocols were designed for equality problems and set problems in the rational number field.These protocols used basic arithmetic operation and hash operation to guarantee efficiency than existing related protocols.And these protocols didn’t limit the range of research data and they were more widely applicable.It proves that these protocols are secure in the semi-honest model using simulation paradigm, and demonstrates the efficiency and the applicability of these protocols by theoretical analysis and experiment.A practical example was also given to illustrate that approaches are more versatile, and they could also be directly used to solve some secure multiparty computational geometry problems in the rational number field.…”
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Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation by Sankar Prasad Mondal, Adrijit Goswami, Sujit Kumar De

“…In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number (NIFN). …”
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Enhanced NSGA-II algorithm based on novel hybrid crossover operator to optimise water supply and ecology of Fenhe reservoir operation by Qinglai Xiong, Ling Dong, Hu Chen, Xueping Zhu, Xuehua Zhao, Xuerui Gao

“…Subsequently, two strategies for the SBAX operator are discussed: SBX operator + new arithmetic operator and new arithmetic operator + SBX operator. …”
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Choice between helping vs not helping: level of mastery in the task by Claudio Carpio, Linda Pacheco-León, Maricela Chaparro, Jamillet Carranza, Raúl Narayanam-Rodríguez, Virginia Pacheco

“…Based on this, the objective of this work consisted of evaluating the effects of different levels of domain in an arithmetic task (high and low) on the choice of helping / not helping a partner to perform arithmetic operations. The task was to perform different types of arithmetic operations (addition, subtraction, multiplication and division) to obtain points. …”
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Evaluating the network security by the Read_Write transition model by LU Zhi-yong1, 2, FENG Chao1, YU Hui2

“…The Read_Write transition model and correlative concepts were presented for the root directory with Read_Write privilege setting; then the model transition function was formalized by the state transition arithmetic operator . Based on the transition model,the network security state transition machine and the network security evaluation model were designed. …”
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The Approximation of a Modified Baskakov Operator by Ma Yingdian, Wang Weimeng

“…Because of their simple form and high quality, linear arithmetical operators, particularly linear positive operators, are very popular. …”
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Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations by Xiaobin Guo, Dequan Shang

“…The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. …”
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Solution of Linear and Quadratic Equations Based on Triangular Linear Diophantine Fuzzy Numbers by Naveed Khan, Naveed Yaqoob, Mudassir Shams, Yaé Ulrich Gaba, Muhammad Riaz

“…We first introduce the concept of TLDFNs and then study the arithmetic operations on these numbers. We find a method for the ranking of these TLDFNs. …”
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Arithmetically Fast Position Transformation for View Synthesis and Depth Estimation by Krzysztof Wegner, Tomasz Grajek, Krzysztof Klimaszewski

“…As a result, the number of necessary arithmetic operations is reduced and some of the calculations can be reused for consecutive pixel position transformations. …”
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Approximate Solution of LR Fuzzy Sylvester Matrix Equations by Xiaobin Guo, Dequan Shang

“…Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. …”
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Design of a Mathematical Unit in FPGA for the Implementation of the Control of a Magnetic Levitation System by Juan José Raygoza-Panduro, Susana Ortega-Cisneros, Jorge Rivera, Alberto de la Mora

“…The core is designed to calculate trigonometric and arithmetic operations in such a way that each function is performed in a clock cycle. …”
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Design of an Efficient Real-Time Algorithm Using Reduced Feature Dimension for Recognition of Speed Limit Signs by Hanmin Cho, Seungwha Han, Sun-Young Hwang

“…Experimental results show that arithmetic operations are reduced by about 60%, while hit rates reach about 100% compared to previous works.…”
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Optimal capacity planning with economic emission considerations in isolated solar-wind-diesel microgrid using combined arithmetic-golden jackal optimization by Sujoy Barua, Adel Merabet, Ahmed Al-Durra, Tarek El Fouly, Ehab F. El-Saadany

“…This combination enhances the optimization by considering the balance in exploration and exploitation offered by the arithmetic operators of the arithmetic optimization algorithm and the dynamic adjustment by the adaptive search of the golden jackal optimization. …”
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Designing an Intuitionistic Fuzzy Network Data Envelopment Analysis Model for Efficiency Evaluation of Decision-Making Units with Two-Stage Structures by Nafiseh Javaherian, Ali Hamzehee, Hossein Sayyadi Tooranloo

“…The paper first introduces two-stage DEA models, then explains how these models can be modified with intuitionistic fuzzy coefficients, and finally describes how arithmetic operators for intuitionistic fuzzy numbers can be used for a conversion into crisp two-stage structures. …”
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Fuzzy Triangular Aggregation Operators by Ulrich Florian Simo, Henri Gwét

“…We also use the concept of triangular norms (t-norms and t-conorms) as pseudo-arithmetic operations. As a result, we get notably the fuzzy triangular weighted arithmetic (FTWA), the fuzzy triangular ordered weighted arithmetic (FTOWA), the fuzzy generalized triangular weighted arithmetic (FGTWA), the fuzzy generalized triangular ordered weighted arithmetic (FGTOWA), the fuzzy triangular weighted quasi-arithmetic (Quasi-FTWA), and the fuzzy triangular ordered weighted quasi-arithmetic (Quasi-FTOWA) operators. …”
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Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints by A. Srinivasan, G. Geetharamani

“…In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. …”
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