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This research is based on the problems that exist in math subjects, especially in multiplication, adding, and subtracting. One of the fundamental problems experienced by students is a lack of understanding of basic concepts due to the lack of understanding of students reasoning and only paying attention to what is on the blackboard and the lack of learning media used during learning. In order for their understanding and numeracy skills to increase, learning resources for the Musi Board are needed. This study aims; (1) to test the feasibility of Musi Board Media on math arithmetic operations; (2) to see students response when learning using Musi Board Media on math arithmetic operations; (3) the effectiveness of Musi Board Media on math arithmetic operations. Using the ADDIE methodology (analysis, design, development, implementation, and evaluation), this study used the Research and Development approach. The study involved 26 students from grade II of SDN dukuh 08. This media had shown the validity of the media and materials with 94% and 95%, respectively, with a very feasible category. Students’ responses also reached 96%, respectively, with a very interesting category. The results show that this Musi Board Media is feasible to use to help students learning. Therefore, the solution to overcome the problems of students to understand the basic concepts of mathematics in counting operations is to use the media during the lesson. With an N-gain value of 59.26%, the effectiveness of utilizing Musi Board medium for math arithmetic operations falls into the Moderately Effective group.

This study investigates school-age children's arithmetic operations performance while solving larger-size problems which produces interferences in memory. Complex problems can trigger competing responses in working memory, which are irrelevant to a task goal and increase the likelihood of interference from previously learned problems (De Visscher et al., 2018). Interference control in working memory is required to be able to manage and suppress irrelevant information while performing cognitive tasks such as arithmetic problem-solving (Unsworth, 2010). The present study explores potential cognitive processes while performing arithmetic tasks and emphasizes the important role of interference control for better performance in such tasks. This study applied a mixed-effect model experimental design. Forty-four primary school children were involved in the study. The results showed that children's performance in terms of correct responses was similar for both small-size and large-size problems. However, their response speed was significantly lower in larger-size problems, which created more interference in working memory. [ABSTRACT FROM AUTHOR]

This research paper develops an algorithm to solve a neutrosophic linear fractional optimization problem, where the cost of the objective functions, the technology coefficients, and the resources are neutrosophic numbers (triangular and trapezoidal numbers). Two defuzzification methods are used here to convert the neutrosophic linear fractional optimization problem into a multi-objective linear fractional optimization problem (MOLFOP). The fractional objective function is defuzzified using the component-wise optimization method, and the linear constraints are defuzzified using the aggregation ranking function strategy. Hence, the MOLFOP is then solved using the fuzzy goal programming method. In order to further explain our suggested algorithm, two numerical examples are solved at the end, and the outcomes obtained by our method are compared with the outcomes obtained using the other algorithm. [ABSTRACT FROM AUTHOR]

The forthcoming wireless networks must integrate to a high density of end-user devices while ensuring a superior quality of service. It is imperative to devise solutions that reduce the density of wireless access points and associated costs, while simultaneously ensuring security and privacy throughout propagation. Herein, a novel dual-band photodetector with high selective responsivities in distinct visible and near-infrared (NIR) band is developed as an optical signal receiver. The receiver has an unprecedented fast switch speed > 500 kHz between different operation modes. Leveraging this fast switch speed, a high-speed Multiple-Input-Single-Output (MISO) system is developed, fusing spectrum resources from visible to infrared bands. The system achieves a data rate of 600 Kbps in the visible channel and 500 Kbps in the NIR channel, with a sum rate of 1.1 Mbps. This is the highest single-channel data rate and sum rate among reported dual-band photodetectors. Additionally, two previously overlooked mechanisms, the Subtraction and Addition modes, are studied in detail. The four operation modes are developed to establish a novel physical encryption method in terms of arithmetic relation. The dual-channel coupled link can support a data rate of 200 Kbps, significantly enhancing communication security. [ABSTRACT FROM AUTHOR]

This article presents a novel concept of complex cubic picture fuzzy sets (CCPFS) and introduces one more new idea of complex interval-valued picture fuzzy sets (CIVPFS) as foundational framework of CCPFS. The proposed CCPFS combines CIVPFS and complex picture fuzzy sets (CPFS), where CPFS extends the complex intuitionistic fuzzy set by incorporating a neutral membership degree. This unique model offers an expanded range of values using degrees of membership, neutral membership, and non-membership, within the unit disk of a complex plane. Additionally, we introduce two more new ideas of internal complex cubic picture fuzzy sets (ICCPFS) and external complex cubic picture fuzzy sets (ECCPFS) to further enhance the versatility of the approach. To facilitate practical applications, complement, score, and accuracy functions are developed and defined for CCPFS. Moreover, three types of averaging aggregation operators based on complex cubic picture fuzzy sets are introduced, including complex cubic picture fuzzy weighted geometric (CCPFWG) operators, complex cubic picture fuzzy ordered weighted geometric (CCPFOWG) operator, and complex cubic picture fuzzy hybrid weighted geometric (CCPFHWG) operator. The CCPFHWG operator generalizes both CCPFWG and CCPFOWG operators, providing a comprehensive framework for aggregating complex cubic picture fuzzy data. To demonstrate the practicality of the proposed approach, a multi-criteria decision-making (MCDM) problem is presented, showcasing its effectiveness in addressing today's complex decision structures. The utilization of complex cubic picture fuzzy sets and the corresponding aggregation operators in MCDM highlights their applicability and relevance in tackling real-world complexities. [ABSTRACT FROM AUTHOR]

This article presents a content analysis of articles published in Turkey on the topic of numbers and operations in mathematics education. The findings reveal that the articles mainly focus on topics such as misconceptions, difficulties, and problem posing related to fractions and natural numbers. The study provides valuable insights for researchers and educators in the field of mathematics education. The article discusses the findings of various studies related to mathematics education, including different skills and concepts that students often struggle with. The article also includes opinions and thoughts on teaching methods and activities, as well as the presence of misconceptions and difficulties in students' learning. The article discusses various topics related to teaching mathematics, including different teaching methods, student perceptions and understanding of mathematical concepts, problem-solving strategies, and teacher competencies. The articles analyze the results of studies conducted with pre-service teachers and students on various topics. The articles emphasize the importance of increasing the number and duration of activities related to mathematical concepts and improving problem-solving skills. The text discusses the findings of experimental articles related to numbers and operations learning, categorizing them into different areas. The findings show the impact of various independent variables on dependent variables related to achievement and skill. The article discusses various research articles conducted in Turkey on the topic of numbers and operations learning, focusing on different categories. The findings reveal the positive effects of number sense-based teaching, conceptual change approaches, and different teaching methods on students' learning. The research examined various articles in the field of mathematics education, focusing on topics such as mathematical modeling, problem-solving [Extracted from the article]

Complex fuzzy set was originally proposed as a mathematical tool to deal with uncertainty by taking amplitude term and phase term memberships of an element of a universal set. In this article, we study (α,θ)-cut sets of the complex fuzzy sets and describe some related properties of them. Based on these (α,θ)-cut sets, some decomposition theorems of the complex fuzzy sets are proposed. Moreover, the concept of Zadeh’s extension principle of the fuzzy sets is extended to the complex fuzzy sets and explored various related properties. Finally, some arithmetic operations are demonstrated for the complex fuzzy set by using the extension principle of the complex fuzzy sets. Numerical illustrations for each arithmetic operation are also given.

Algebraic operations on generalized hesitant fuzzy numbers are key tools to address the problems with decision uncertainty. In this paper, by studying the arithmetic operations on generalized trapezoidal hesitant fuzzy numbers, modified arithmetic operations are introduced for this class of numbers so that, using these arithmetic operations, the multiplication and division of two generalized trapezoidal hesitant fuzzy numbers are always generalized trapezoidal hesitant fuzzy numbers. Furthermore, a generalized trapezoidal hesitant fuzzy number raised to the power of a real number is a generalized trapezoidal hesitant fuzzy number, and in the defined division, the case where the denominator becomes zero is not considered. Numerical examples are used to show the shortcomings of the previous arithmetic operations as well as the efficiencies of the arithmetic operations proposed in this research for generalized trapezoidal hesitant fuzzy numbers. Finally, the application of the proposed new arithmetic operations to generalized trapezoidal hesitant fuzzy numbers in solving the generalized trapezoidal hesitant fully fuzzy equation is discussed. [ABSTRACT FROM AUTHOR]

Copyright of Ondokuz Mayis University Journal of Education is the property of Ondokuz Mayis University Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract This article presents a novel concept of complex cubic picture fuzzy sets (CCPFS) and introduces one more new idea of complex interval-valued picture fuzzy sets (CIVPFS) as foundational framework of CCPFS. The proposed CCPFS combines CIVPFS and complex picture fuzzy sets (CPFS), where CPFS extends the complex intuitionistic fuzzy set by incorporating a neutral membership degree. This unique model offers an expanded range of values using degrees of membership, neutral membership, and non-membership, within the unit disk of a complex plane. Additionally, we introduce two more new ideas of internal complex cubic picture fuzzy sets (ICCPFS) and external complex cubic picture fuzzy sets (ECCPFS) to further enhance the versatility of the approach. To facilitate practical applications, complement, score, and accuracy functions are developed and defined for CCPFS. Moreover, three types of averaging aggregation operators based on complex cubic picture fuzzy sets are introduced, including complex cubic picture fuzzy weighted geometric (CCPFWG) operators, complex cubic picture fuzzy ordered weighted geometric (CCPFOWG) operator, and complex cubic picture fuzzy hybrid weighted geometric (CCPFHWG) operator. The CCPFHWG operator generalizes both CCPFWG and CCPFOWG operators, providing a comprehensive framework for aggregating complex cubic picture fuzzy data. To demonstrate the practicality of the proposed approach, a multi-criteria decision-making (MCDM) problem is presented, showcasing its effectiveness in addressing today's complex decision structures. The utilization of complex cubic picture fuzzy sets and the corresponding aggregation operators in MCDM highlights their applicability and relevance in tackling real-world complexities.

Dyscalculia is a specific learning difficulty that affects an individual's ability to perform mathematical tasks. The research was aimed at investigating whether gender and age have a differential influence on the number sense, arithmetic operations, and working memory dimensions of dyscalculia. The research design was an expo facto research design. The population was all 87320 junior secondary school 1 and 2 students in Obio-Akpor local government area. The sample consists of 453 students who have been diagnosed with dyscalculia. This sample was randomly drawn using a multistage sampling procedure. A standardized instrument, the Dyscalculia Test by Eteng-Uket, was used for data collection. High validity and reliability indices were obtained for the test. The data were analyzed using mean, standard deviation, one-way, and two multivariate analyses of variance. The result showed that gender and age independently and in interaction had a differential influence on dyscalculia dimensions, but this differential influence was not significant. Based on these findings, it is recommended that educators use a variety of individualized instructional strategies and materials, including visual aids, manipulatives, and adaptive technologies that are effective for different genders and age groups of dyscalculics

As a novel biological computing device, the Spiking Neural P system (SNPS) has powerful computing potential. The application of SNPS in the field of arithmetic operation has been a hot research topic in recent years. Researchers have proposed methods and systems for implementing basic arithmetic operations using SNPS. This paper studies four basic arithmetic operations, improves the parallelization of addition and multiplication methods, and designs more effective natural number addition and multiplication SNPS, as well as SNPS for subtraction and for division of natural numbers based on multiple subtractions. The effectiveness of the proposed SNPS is verified by example. Compared with the same kind of SNPS, for the addition operation the number of neurons used in our system is reduced by 50% and the time overhead is reduced by 33%, while for the multiplication operation the number of neurons is reduced by 40%. [ABSTRACT FROM AUTHOR]

Developmental dyscalculia is a specific disorder that includes various problems: difficulties with estimating quantities, understanding the meaning of numbers and with counting. It is a neurodevelopmental disorder that has a genetic basis and is associated with impaired maturation of certain areas of the brain. It manifests itself at an early age in difficulties in estimating quantities, followed by problems in learning the meaning of the numbers that denote a certain number. Difficulties in mathematics are compounded by impaired regulation and control of numerical operations, problems in focusing attention and remembering numerical knowledge. Problems with understanding numbers and with counting are related to structural and functional changes in various areas of the brain, especially the parietal cortex. Aspects of dyscalculia may also be reflected in performance on intelligence tests. As dyscalculia is a complex disorder, the development of an individual profile of the abilities and skills of pupils who have difficulties in mathematics would contribute to a better understanding of their problems. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Educational Spectrum (IJES) is the property of International Journal of Educational Spectrum (IJES) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Why is math anxiety usually related to less efficient math processing? According to attentional control theory, anxiety leads to reduced attentional control, which often entails a greater investment of resources (e.g., more time or effort) to carry out a cognitive task. The executive functions mainly affected by anxiety are inhibition and shifting. Previous studies suggest that math anxiety may impair the inhibitory function. In the present study, the relationship between math anxiety and shifting efficiency when switching between two‐digit additions and subtractions was examined. Twenty highly math‐anxious and 20 low math‐anxious individuals participated in an event‐related potential (ERP) transition‐cueing experiment. Math anxiety was expected to delay the shifting process, leading to a larger switch cost in response time and no centroparietal cue‐locked switch‐specific positivity registered in the electroencephalogram during the cue‐target interval. Highly math‐anxious individuals showed a larger switch cost than their low math‐anxious peers. Asymmetrical switch effects between operations in response time were found in both groups, which might be due to larger sequential difficulty effects after subtractions than after additions. The cue‐locked switch‐specific positivity was present only in the low math‐anxious group. The present results suggest that highly math‐anxious individuals take longer to shift task sets. Additionally, the highly math‐anxious group showed a more positive frontal P2 after the cue that announced a switch to subtraction, probably indicating stronger attentional capture by this cue, because the most threatening condition is anticipated. Taken together, these data suggest that math anxiety also impairs attentional control when switching between arithmetic tasks. [ABSTRACT FROM AUTHOR]

Copyright of Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education is the property of Balikesir University, Necatibey Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Öz The purpose of this study was to investigate what factors third-grade students took into consideration when posing problems for their peers and how these factors affected the mathematical complexities of the problems. Free and semi-structured problem-posing tasks were given to 27 third-grade students, and the problems they created for their peers were analyzed in terms of their semantic structure and arithmetic complexity. According to the findings of the study, there was a statistically significant difference between the semantic structures of the problems in both tasks created for the more mathematically proficient student, but there was no difference between their arithmetic complexities. In addition, according to the qualitative findings of the study, the magnitude of the numbers, the operation types, the number of operations used, and the interests of the students were taken into consideration in posing problems for students with low and high levels of mathematical ability.

Picture fuzzy set (PFS), is a newly developed apparatus to treaty with uncertainties in problems where the opinions are yes, no, neutral, and refusal types. Extension principle is one of the key tools for describing uncertainties. It provides a general method for existing classical mathematical concepts to address fuzzy quantities. It has numerous applications in various arena of our real life. However, there are less works on extension principle for picture fuzzy sets. In this article, new extension principles namely minimal extension principle and average extension principle are proposed for picture fuzzy sets. Various properties of the minimal extension principle and the average extension principle for PFSs are also established. We also prove some properties of Zadeh's extension principle for PFSs. Finally, arithmetic operations for PFSs based on the average extension principle are developed with numerical illustrations. [ABSTRACT FROM AUTHOR]

This paper addresses the study of the complexity of products in geometric algebra. More specifically, this paper focuses on both the number of operations required to compute a product, in a dedicated program for example, and the complexity to enumerate these operations. In practice, studies on time and memory costs of products in geometric algebra have been limited to the complexity in the worst case, where all the components of the multivector are considered. Standard usage of Geometric Algebra is far from this situation since multivectors are likely to be sparse and usually full homogeneous, i.e., having their non-zero terms over a single grade. We provide a complete computational study on the main Geometric Algebra products of two full homogeneous multivectors, that are outer, inner, and geometric products. We show tight bounds on the number of the arithmetic operations required for these products. We also show that some algorithms reach this number of arithmetic operations. [ABSTRACT FROM AUTHOR]

Since the discovery of El Primer Nueva Corónica y Buen Gobierno by Guamán Poma in 1908 and the publication of the yupana in 1912, this calculation tool has been the subject of studies about its operation, from which experiences of application have been developed in mathematics education. Within this framework, the article aims to analyze the advances in terms of research and proposals developed on the yupana in the field of mathematics education, with the purpose of making visible new application and research possibilities. The technique used is the documentary review of reports, theses and scientific articles produced in Latin America. The results show that the effects of the yupana on the learning of basic operations have been extensively studied; however, the yupana has multiple potentialities, still unknown, that must be studied, such as its effectiveness in learning decimal, fractional, radical, integer numbers, matrices, logarithms, and vectors, even more so having developed digital models. It is suggested to implement and investigate the use of the yupana with the Radicati method in order to favor the development of formal thought. [ABSTRACT FROM AUTHOR]

Arithmetic operations play a substantial role in many applications, such as image processing. In image processing applications, a multiplier is a predominantly used arithmetic operation. In recent designs of Approximate Multipliers (AMs), the design metrics of multipliers are made better at the cost of Error metrics and vice versa. So, in order to balance both the error and design metrics in a multiplier design with increasing the width of the input operands, a Rounding-based AM (RAM) using a modified Karatsuba algorithm is proposed, in which the usage of the number of multipliers is reduced. Small multipliers are used with shifting and rounding operations so as to reduce power consumption, delay, and area. Both the prior and proposed AMs are later synthesized in Verilog HDL using the Cadence RTL compiler. The simulation results divulge that the proposed RAM of sizes 8 and 16 bits are designed and their performance metrics in terms of delay, and area are decreased on an average of 61.8%, and 52.6% with an improvement in power by 53.8% for 8-bit AM and also the delay, area and power are reduced on an average of 53.2%, 59.7%, and 25% for a 16-bit AM's, in comparison with the prior AMs. The proposed RAM is demonstrated using the smoothening image application, and we observe that an improved image quality is obtained with SSIM and PSNR of the ISFA incorporated proposed RAM within the range of 1.44%—84.47% and 0.28%- 24.4%, over the ISFA incorporated existing AMs. [ABSTRACT FROM AUTHOR]

A single-valued neutrosophic set, an generalization of intuitionistic fuzzy set, is a powerful model to deal with uncertainty. In this study we present a method to solve LR-type single-valued neutrosophic linear programming problems by using unrestricted LR-type single-valued neutrosophic numbers. We propose the ranking function to transform LR-type single-valued neutrosophic problems into crisp problems. The arithmetic operations for unrestricted LR-type single-valued neutrosophic numbers are introduced. We propose a method to solve the fully single-valued neutrosophic linear programming problems with equality constraints having LR-type single-valued neutrosophic numbers as right hand sides, parameters and variables. We describe our proposed method by solving real life examples.

As a novel biological computing device, the Spiking Neural P system (SNPS) has powerful computing potential. The application of SNPS in the field of arithmetic operation has been a hot research topic in recent years. Researchers have proposed methods and systems for implementing basic arithmetic operations using SNPS. This paper studies four basic arithmetic operations, improves the parallelization of addition and multiplication methods, and designs more effective natural number addition and multiplication SNPS, as well as SNPS for subtraction and for division of natural numbers based on multiple subtractions. The effectiveness of the proposed SNPS is verified by example. Compared with the same kind of SNPS, for the addition operation the number of neurons used in our system is reduced by 50% and the time overhead is reduced by 33%, while for the multiplication operation the number of neurons is reduced by 40%.

Primary challenges are the identification, segmentation, and extraction of the afflicted area from the scanning of magnetic resonance. However, it is a time-consuming and tiresome for clinical specialists. In this paper, an automated brain tumor system is proposed. The proposed system employs hybrid image processing techniques such as contrast correction, histogram normalization, thresholding techniques, arithmetic, and morphological operations to quarantine nearby organs and other tissue from the brain for improving the localization of the affected region. At first, the skull stripping process is proposed to segregate the non-designated regions to extract the designated brain regions. Those resultant brain region images are further subjected to discover the brain tumor. The planned scheme is studied on the magnetic resonance (MR) images with the use of T1, T2, T1c, and fluid-attenuated inversion recovery (FLAIR). The proposed hybrid method employed. The results reveal that the proposed method is quite efficient to extract the tumor region. The accuracy rate for segmentation and separation of area of interest in brain tumor reached to 95%. Finally, the significance of the proposed procedure is confirmed using the real image clinical dataset got from ten patients were diagnosed as begin, malignant, and metastatic brain tumors in Al-Yarmouk and Baghdad teaching hospital in Baghdad, Iraq. [ABSTRACT FROM AUTHOR]

Achieving fluency in arithmetic operations is vital if students are to develop mathematical creativity and critical thinking abilities. Nevertheless, a substantial body of literature has demonstrated that students are struggling to develop such skills, due to the absence of appropriate instructional support or motivation. A proposed solution to tackle this problem is the rapid evolution and widespread integration of educational technology into the modern school system. To be precise, the Learning Management System (LMS) has been found to be particularly useful in the instructional process, especially where matters related to personalised and self-regulated learning are concerned. In the present work, we explored the aforementioned topics in the context of a longitudinal study in which 720 primary education students (4th–6th grade), from United Arab Emirates (UAE), utilised an LMS, at least once per week, for one school year (nine months). The findings revealed that the vast majority (97% of the 6th graders, 83% of the 4th graders, and 76% of the 5th graders) demonstrated a positive improvement in their arithmetic fluency development. Moreover, the Multiple Linear Regression analysis revealed that students need to practice deliberately for approximately 68 days (a minimum of 3 min a day) before seeing any substantial improvement in their performance. The study also made an additional contribution by demonstrating how design practice compliance with gamification and Learning Analytics in LMS may lead children to be fluent in simple arithmetic operations. For educators interested in LMS-based intervention, research implications and directions are presented. [ABSTRACT FROM AUTHOR]

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively different profiles regarding students' understanding is scarce. The current study investigated the different ways students reasoned in arithmetic operation items with fractions and decimals. A cross-sectional study with 1,262 participants from 5th to 10th grade was performed. A TwoStep Cluster Analysis revealed eight different student reasoning profiles. We found that the natural number bias is first overcome in addition and subtraction, and later in multiplication and division. Moreover, differences regarding representation were only found in addition and subtraction items, indicating that natural numbers interfered more strongly in fractions than in decimal numbers. Finally, results showed that some students' difficulties with rational number multiplications and divisions had other explanations than the natural number bias. [ABSTRACT FROM AUTHOR]

The development of memristor‐based stateful logic circuits can minimize data movement during the computing process to achieve in‐memory computing, mitigating the von Neumann bottleneck in the current computing architecture. Herein, a method to combine resistance–resistance (R–R) and voltage–resistance (V–R) logic gates to implement exclusive logic gates composed of APMR‐two‐2(XOR, IMP, RIMP) and APMR‐three‐4XOR, where APMR means antiparallel memristors with a series resistor, is suggested. The proposed gates can accelerate XOR logic operation in a single cycle and expand for the n‐bit input. The performance of the proposed logic gate is then demonstrated with a 1‐bit full adder–subtractor along with the comparison of an n‐bit ripple carry adder. It shows that the implementation for the n‐bit adder takes 4n+1 memristors within 2n+1 steps, which significantly improves the optimization in terms of space‐ and time‐related costs compared with other memristive logic gates. Subsequently, the improved adder circuit can be further utilized to implement an n‐bit multiplier. In addition, the evaluation of the device stress on the various logic gates confirms that the proposed logic gates are reliable. [ABSTRACT FROM AUTHOR]

Math fluency is the ability to solve arithmetic facts quickly and accurately (i.e., addition and subtraction problems up to 20, and multiplication and division problems from the multiplication table). Curricula in primary school devote a significant period of time for learning and retrieval of arithmetic facts. Recently, a new computerized tool to assess math fluency—the BGU-MF (Ben-Gurion University Math Fluency) test—was developed and found to be a reliable and valid tool for adults. In the current study, we examine the performance of first to sixth-grade children in math fluency using the BGU-MF. The results present the performance of MF during childhood and emphasize that it continues to develop during primary school. Importantly, proficiency of MF differed by operations, and the automaticity of math facts was acquired in different grades. Moreover, we found that the BGU-MF is a reliable and valid tool not only for adults but also for children during primary school. Our study has educational implications for the teaching, practice, and retrieval of arithmetic facts. [ABSTRACT FROM AUTHOR]

This paper deals with fundamental arithmetic operations on fuzzy numbers and use of these operations for carrying out various fuzzy processes. When modelling specific problems in the field of sciences as well as engineering, it's common to notice that the problem's characteristics aren't known precisely and instead fall into a range. Interval arithmetic, which permits mathematical evaluations (operations) to be conducted on intervals in order to produce significant estimations of required values in terms of intervals, has already been used to deal with similar problems. Fuzzy arithmetic can be thought of as an extension of arithmetic interval, in which numerous levels in [0,1] are considered instead of only one (constant) level. [ABSTRACT FROM AUTHOR]

The development of memristor‐based stateful logic circuits can minimize data movement during the computing process to achieve in‐memory computing, mitigating the von Neumann bottleneck in the current computing architecture. Herein, a method to combine resistance–resistance (R–R) and voltage–resistance (V–R) logic gates to implement exclusive logic gates composed of APMR‐two‐2(XOR, IMP, RIMP) and APMR‐three‐4XOR, where APMR means antiparallel memristors with a series resistor, is suggested. The proposed gates can accelerate XOR logic operation in a single cycle and expand for the n‐bit input. The performance of the proposed logic gate is then demonstrated with a 1‐bit full adder–subtractor along with the comparison of an n‐bit ripple carry adder. It shows that the implementation for the n‐bit adder takes 4n+1 memristors within 2n+1 steps, which significantly improves the optimization in terms of space‐ and time‐related costs compared with other memristive logic gates. Subsequently, the improved adder circuit can be further utilized to implement an n‐bit multiplier. In addition, the evaluation of the device stress on the various logic gates confirms that the proposed logic gates are reliable.

In this study, we first show that the existing arithmetic operations of trapezoidal fuzzy numbers do not satisfy the basic properties. Then, for trapezoidal fuzzy numbers, we define new arithmetic operations. Furthermore, we demonstrate that the existing Simplex method for addressing fully fuzzy linear programming problems has some drawbacks. Finally, we provide a new strategy for solving fully fuzzy linear programming problems and compare our results with the existing methods. [ABSTRACT FROM AUTHOR]

Arithmetic logic unit (ALU), a core component of a processor, is one of the thrust areas of the current research. Presently, ALU is designed by transistor-based CMOS technique and its individual components are placed in different layers. The current design is affected by the limitations of Moore's law and design complexity. At present, 'Quantum cellular automata electro-spin (QCA-ES)' technology is widely accepted technology as an alternative of 'CMOS' to minimize the above discussed problems. In this research paper, the design of a novel multilayer portable, dynamic, fault-tolerant, power-efficient, thermally stable reversible ALU is proposed which is explored through QCA-ES. All the arithmetic and logical components of ALU are separately placed in different layers. Area density, delay, fault tolerance and thermal stability are investigated. A specific type of gate, known as reversible gate (modified 3:3 'TSG' gate), is used in this proposed design with QCA technology to get the optimized design ALU with low occupied area, complexity, delay and power dissipation. Investigation of a fault-free design and saturated amplitude level (of output) change with respect to temperature increment in the proposed device are also discussed in this paper. Not only the thermal stability (up to 6 k temperature) but also an investigation on cell complexity of the 100% fault-free (against multiple cell-omission, cell-displacement, cell-orientation change and extra cell deposition), multilayer nano-device is represented in this work. 'QCA-Designer' software is used in this research work to design and develop layout of the proposed components in quantum-field and find out the occupied area, delay and complexity of proposed design. 'QCA-Pro' software is used for getting the value of dissipated power. [ABSTRACT FROM AUTHOR]

A single-valued neutrosophic set, an generalization of intuitionistic fuzzy set, is a powerful model to deal with uncertainty. In this study we present a method to solve LR-type single-valued neutrosophic linear programming problems by using unrestricted LR-type single-valued neutrosophic numbers. We propose the ranking function to transform LR-type single-valued neutrosophic problems into crisp problems. The arithmetic operations for unrestricted LR-type single-valued neutrosophic numbers are introduced. We propose a method to solve the fully single-valued neutrosophic linear programming problems with equality constraints having LR-type single-valued neutrosophic numbers as right hand sides, parameters and variables. We describe our proposed method by solving real life examples. [ABSTRACT FROM AUTHOR]

As a key theoretical basis of fuzzy complex analysis, a new representation of fuzzy complex numbers is proposed in this paper which unifies the exponential form, trigonometric form and algebraic form of fuzzy complex numbers, and some arithmetic operations are investigated. The concepts of strong sum and strong difference are defined in order to simplify the addition and subtraction operations of complex fuzzy numbers and establish the calculus theory of fuzzy complex valued functions. The metric between two fuzzy complex numbers, the derivative, differentiability and analyticity of fuzzy complex-valued functions are defined and characterized. The necessary and sufficient conditions of the analyticity of fuzzy complex-valued functions are investigated. Furthermore, the integral of fuzzy complex-valued functions and Cauchy integral theorem are given and discussed. [ABSTRACT FROM AUTHOR]