Gray Code Research Articles

Approach for Multiattribute Decision‐Making with an Interval Grey Number Based on Bonferroni Mean

Aiming at the multiattribute decision‐making problem in the form of interval grey number, considering the interrelationship between the scheme attributes, this study defines the grey number weighted geometric Bonferroni mean (GNWGBM) operator for aggregating information. The feasibility of the proposed method is verified through a comparison of the example analysis and methods.

A Hybrid Approach for Assessing Problem Solving Skills under Fuzzy Conditions

Volumes of research have been written about problem solving, which is one of the most important components of the human cognition affecting the progress of the human society for ages. In this work a hybrid method is applied for the assessment of a student group’s problem solving skills with qualitative grades (i.e. under fuzzy conditions). Namely, soft sets are used as tools for a parametric assessment of the group’s performance, the calculation of the GPA index and the Rectangular Fuzzy Assessment Model are applied for evaluating the group’s qualitative performance, grey numbers are used as tools for assessing the group’s mean performance and neutrosophic sets are utilized when the teacher is not sure about the individual grades obtained by some (or all) students of the group

Reversible code converters in QCA nanotechnology

Quantum-dot cellular automata (QCA) is evolving as an outshining nanotechnology. It is being efficiently used for designing of digital circuits, and devices. Incorporation of logical injectivity function in QCA enhances the energy efficiency by obviating the bit erasure energy loss. This paper presents the design implementations of the proposed exclusive-OR (EXOR) gate, 2-input, 3-input, and 4-input binary to gray (B2G) code converters in QCA. The proposed designs outperform the existing designs in factors of complexity, area, latency, and power dissipation. The cells count for the proposed EXOR, 2-input, 3-input, and 4-input B2G converters are 11, 15, 27, and 39, respectively. The delay values are 0.25 for all the proposed designs, without any crossover.

Prediction of Transformer Oil Breakdown Voltage with Barriers Using Optimization Techniques

A new procedure to optimally identifying the prediction equation of oil breakdown voltage with the barrier parameters’ effect is presented. The specified equation is built based on the results of experimental works to link the response with the barrier parameters as the inputs for hemisphere-hemisphere electrode gap configuration under AC voltage. The AC HV is applied using HV Transformer Type (PGK HB-100 kV AC) to the high voltage electrode in the presence of a barrier immersed in Diala B insulating oil. The problem is formulated as a nonlinear optimization problem to minimize the error between experimental and estimated breakdown voltages (VBD). Comprehensive comparative analyses are addressed using three recent innovative marine predators, grey wolf, and equilibrium optimization algorithms to reduce the error between the experimental and estimated breakdown voltages. In addition, the experimental results are expressed in two different models via grey and real coding. Finally, simulation results are conducted with statistical indices that show the effectiveness of the proposed models for experimental verification. The total percentage errors of the tested samples between the observed and estimated VBD are 1.207, 1.222, and 1.207 for EO, GWO, MPA, respectively. The marine predator algorithm has the best performance compared with the other two competitive algorithms for grey and actual codes.

Privacy-Preserving Boolean Range Query with Temporal Access Control in Mobile Computing

With increasingly popular GPS-equipped mobile devices (e.g., smartphones, tablets, laptops), massive spatio-textual data has been outsourced to cloud servers for storage and analysis such as spatial keyword search. However, existing privacy-preserving spatial keyword query schemes only support coarse-grained non-temporal access control in single-user sharing scenarios, which does not scale well in time-related scenes such as message valid period. To solve the above issues, we propose Privacy-preserving Boolean Range Query with Temporal access control in mobile computing (PBRQ-T). Specifically, we first achieve PBRQ with linear search complexity using the adapted Gray code, Bloom filter, and Katz-Sahai-Waters encryption. Then, we provide fine-grained and temporal access control in PBRQ based on the forward/backward derivation function and attribute-based encryption, where PBRQ is executed only when the spatio-textual data is accessible. Finally, an enhanced PBRQ-T (i.e., PBRQ-T+) with faster-than-linear search complexity is proposed by constructing a Quadtree index structure. Our formal security analysis shows that data privacy and index privacy can be guaranteed during the query process. Our extensive experiments using a real-world dataset demonstrate the efficiency and feasibility of our schemes.

Mercury mediated DNA-Au/Ag nanocluster ensembles to generate a gray code encoder for biocomputing.

Boolean operations utilizing DNA as a platform for biocomputing have become a promising tool for next-generation bio-molecular computers. In the whole process of any binary data transmission, bit errors are unavoidable and commonly occur. Cascades of exclusive-OR (XOR) operations show the great potential to evaluate these errors by introducing a parity generator (pG) and a parity checker (pC). Herein, we constructed a DNA hybrid architecture platform employing a chemosensing ensemble of mercury-mediated DNA-Au/Ag nanoclusters (M-Au/Ag NCs) to operate unconventional pG/pC for "error detection". Taking advantage of pG/pC, the transmitted and received data is converted to secure information using a binary to gray code encoder. To the best of our knowledge, this is the first molecular gray code encoder for biocomputing, which discovers an exciting avenue to protect information security through sophisticated logic circuits.

Dynamic Three-Dimensional Shape Measurement Method Based on Misaligned Gray Code

Dynamic Three-Dimensional Shape Measurement Method Based on Misaligned Gray Code

ЗАСТОСУВАННЯ МЕТОДУ ЗРОСТАЮЧИХ ДЕРЕВ ДЛЯ ОПТИМІЗАЦІЇ ПЛАНІВ БАГАТОФАКТОРНИХ ЕКСПЕРИМЕНТІВ

Nowadays, the high cost of production and resources is the problem in the world, because of this, the issue of optimizing production to reduce the use of resources becomes acute. The research of the experiment at the initial stage makes it possible to reduce resource costs due to detailed analysis. For this we identify steps that we can simplify, which saves resources during production or research. Most often, experiments are multifactorial and related to the search for optimal conditions, selection of the most rational equipment and high-quality raw materials. There is a need to increase the effectiveness of experimental research. These researches allow us to study objects in detail, which provides the ability to obtain more information and offers conditions for their optimization. In the process of researching objects, it is necessary to build their mathematical models, which allow us to determine a rational ratio of parameters. Experiment planning allows for calculating the most effective order of performing experiments and studying the influence of individual factors on optimization criteria. The use of experimental planning methods helps in obtaining the maximum amount of useful information with minimal cost and time spent. This article examines the growing tree method for cost optimization of multifactor experimental plans. To confirm its functionality and effectiveness, a comparative analysis is conducted with existing optimization methods. The method is inspired by the evolution of growing trees and includes the stages of planting and growth. An algorithm and software that implement this method have been developed. The software implementation of the algorithm is made with the help of the framework Angular. In the study of technological processes, the functionality and effectiveness of the method of growing trees for cost optimization of plans of multifactor experiments has been proven. It has been compared with the bacterial optimization method and the method based on the use of the Gray code. The object of research: the process of optimization of plans of multifactor experiments according to its cost. The subject of study: growing tree method for cost optimization of multifactor experimental plans and software implementing it.

Intraoral 3-D Measurement by Means of Group Coding Combined With Consistent Enhancement for Fringe Projection Pattern

Intraoral 3D measurement can obtain digital impressions in real time. However, owing to saliva, enamel, metallic denture, etc., the quality of the captured 2D image using the intraoral equipment, which is used for feature measurement and 3D reconstruction, is usually degraded. In this paper, we propose a equipment with high performance for intraoral 3D measurement. First, group-multi-line coding algorithm instead of sinusoidal or gray code for fringe projection profilometry (FPP) was applied for stripe pattern decoding. The distance between adjacent stripes was large enough to avoid the scatter of the tooth. It can also overcome the shortcoming of sinusoidal-based phase computing, leading to accuracy degradation owing to scanner jittering. Second, a consistent stripe feature enhancement method is proposed. The stripe feature in the mirror, exposure, and low-contrast area was homogeneously enhanced. Consequently, an individual scene is reconstructed using more effective and accurate points. This not only improves the precision of point cloud registration, it also reduces the probability of mismatch and shortens the scanning time for a full-arch. Our results showed that the accuracy of intraoral 3D measurements conducted through the proposed equipment by using novel algorithms increased to 10 - 20 μm and the measurement efficiency increased to 30%.

Optimal Embedding of Hypercube into Cylinder

We study the problem of Embedding Wirelength of $n$-dimensional Hypercube $Q_n$ into Cylinder $C_{2^{n_1}}\times P_{2^{n_2}}$, where $n_1+ n_2=n$, called EWHC. We show that such wirelength corresponding to Gray code embedding is $2^{n_2}(3\cdot 2^{2n_1-3}-2^{n_1-1})+2^{n_1} (2^{2n_2-1}-2^{n_2-1})$. In addition, we prove that Gray code embedding is an optimal strategy of EWHC.

Hamiltonian surfaces in the 4-cube, 4-bit gray codes and Venn diagrams

We study Hamiltonian surfaces in the d-dimensional cube Id as intermediate objects useful for comparative analysis of Venn diagrams and Gray cycles. In particular we emphasize the importance of 0-Hamiltonian spheres and the "sphericity" of Gray odes in the context of reducible Venn diagrams. For illustration we show that precisely two, out of the nine known types of 4-bit Gray cycles, are not spherical. The unique, balanced Gray cycle is spherical, which in turn leads to a new construction of a reducible Venn diagram with 5 ellipses (originally constructed by P. Hamburger and R.E. Pippert).

Dynamic Multi-Attribute Decision Analysis on Three-Parameter Interval Grey Number of Upper (Lower) Deviation Quasi-Normal Distribution

Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval grey number, a three-parameter interval grey number dynamic multiattribute grey target decision making method with attribute value following quasi-normal distribution is proposed. Firstly, the position relationship between the “center of gravity” point and the kernel of the three-parameter interval grey number is discussed. According to the characteristic that the attribute value obeys the quasi-normal distribution, a new weight is given to the “center of gravity” point, and a new distance measure formula of the three-parameter interval grey number is defined. Secondly, according to the principle of maximum entropy, the objective programming model is constructed to determine the stage weight and attribute weight. Then, the schemes are sorted according to the size of the comprehensive bull’s-eye-distance. Finally, an example is given to illustrate the effectiveness of the decision model.

A Novel Multi-Criteria Decision-Making Framework in Electrical Utilities Based on Gray Number Approach

Given the current trend of reviving the power system, which is considered by competitive markets, the privatization of the power system is forcing them to develop the necessary decision-making policies from a technical and economic point of view to improve their asset management practices. Reliability-centered maintenance is an efficient process to consider these two important aspects, i.e. technical and economic ones, when performing maintenance optimization. This paper proposes a new technique to solve the actual stochastic Multi-Criteria Decision-Making (MCDM) problems with uncertain weight information using a combination of Stochastic Multi-Criteria Acceptability Analysis (SMAA) and Elimination Et Choice Translating Reality (ELECTREIII) methods combined with gray system theory. In maintenance planning, gray system theory is used to determine the specific types of power system components that should receive the most attention. Then, the optimal maintenance strategy of every critical component is determined by recognizing the lowest costs associated with various strategies. The suggested framework demonstrates its relevance and efficacy for actual asset management optimizations in electric power systems, as demonstrated in the IEEE 14-bus test system.

A combined Data Envelopment Analysis (DEA) and Grey Based Multiple Criteria Decision Making (G-MCDM) for solar PV power plants site selection: A case study in Vietnam

The transition from fossil fuels to more clean, affordable, and sustainable energy resources is of strategic importance for developing Asian countries like Vietnam, in which solar energy is an attractive option. The government of Vietnam is implementing various policy measures and has substantial investment plans to accelerate the national spread of solar energy. In this regard, location optimization for solar power installation is a vital strategic decision that needs to be analysed in-depth to harness solar power. This study aims to determine suitable areas for solar power installation in a case study in Vietnam. For the decision-making that influences solar plant site selection, while some criteria can be evaluated based on a numerical database, numerous qualitative criteria must be under experts’ judgements in linguistic terms and can be represented through grey numbers. To deal with the complex nature of the prioritization problem posed by the coexistence of multiple factors, this study proposes a combination of the Data Envelopment Analysis (DEA) method, Grey Analytic Hierarchy Process (G-AHP), and Grey Technique for Order Preference by Similarity to Ideal Solution (G-TOPSIS). With the utilized integrated approach, both quantitative and qualitative effective criteria are considered to evaluate locations. DEA is used in the first phase to select high-efficiency locations based on various measurable criteria. In the second phase, these locations are further assessed in terms of qualitative criteria: technical, economic, environmental, and socio-political factors. For this evaluation, G-AHP is used for criteria weighting, and G-TOPSIS ranks the locations. While the proposed approach is expected to help save costs and resources towards determining hot spots for solar power plants installation all around the country, it is recommended that governments and local authorities take into account suitability policies and support mechanisms for sustainable solar energy development.

Analysis on the related factors of China's technological innovation ability using greyness relational degree

PurposeIn order to make grey relational analysis applicable to the interval grey number, this paper discusses the model of grey relational degree of the interval grey number and uses it to analyze the related factors of China's technological innovation ability.Design/methodology/approachFirst, this paper gives the definitions of the lower bound domain, the value domain, the upper bound domain of interval grey number and the generalized measure and the generalized greyness of interval grey number. Then, based on the grey relational theory, this paper proposes the model of greyness relational degree of the interval grey number and analyzes its relationship with the classical grey relational degree. Finally, the model of greyness relational degree is applied to analyze the related factors of China's technological innovation ability.FindingsThe results show that the model of greyness relational degree has strict theoretical basis, convenient calculation and easy programming and can be applied to the grey number sequence, real number sequence and grey number and real number coexisting sequence. The relational order of the four related factors of China's technological innovation ability is research and development (R&D) expenditure, R&D personnel, university student number and public library number, and it is in line with the reality.Practical implicationsThe results show that the sequence values of greyness relational degree have large discreteness, and it is feasible and effective to analyze the related factors of China's technological innovation ability.Originality/valueThe paper succeeds in realizing both the model of greyness relational degree of interval grey number with unvalued information distribution and the order of related factors of China's technological innovation ability.

Design and simulation of QCA-based 3-bit binary to gray and vice versa code converter in reversible and non-reversible mode

The current Very Large-Scale Integration (VLSI) technology has reached its peak due to the fundamental physical limits of Complementary Metal-Oxide-Semiconductor (CMOS). Quantum-dot Cellular Automata (QCA) is considered a proper alternative to CMOS technology in digital circuit design. QCA has features like low power, small area, and high speed in nanoscale digital circuit design. A code converter is a circuit that converts a determined code to another one. Code converters such as Binary to Gray, Gray to Binary, and Binary to BCD converters have a crucial role in fast signal processing in digital systems. Also, code converters are used as a base unit for data transmission into the Arithmetic Logic Unit (ALU) to perform processes. A Binary-to-Gray converter converts the input data to a Gray number. In this paper, we propose a 3-bit Binary to Gray and vice versa code converter in QCA. Previous proposed designs could only convert Binary to Gray code or vice versa, but the proposed design convert both B2G and G2B codes into a circuit. We design our circuit in both reversible and non-reversible modes. The simulation of the proposed design is done using the QCADesigner 2.0.3 tools. The simulation results show that the proposed design is superior to the existing designs in terms of evaluation parameters such as cell count, area, latency, and quantum cost.

E-Learning Platform Assessment and Selection Using Two-Stage Multi-Criteria Decision-Making Approach with Grey Theory: A Case Study in Vietnam

Education has changed dramatically due to the severe global pandemic COVID-19, with the phenomenal growth of e-learning, whereby teaching is undertaken remotely and on digital platforms. E-learning is revolutionizing education systems, as it remains the only option during the ongoing crisis and has tremendous potential to fulfill instructional plans and safeguard students’ learning rights. The selection of e-learning platforms is a multi-criteria decision-making (MCDM) problem. Expert analyses over numerous criteria and alternatives are usually linguistic terms, which can be represented through grey numbers. This article proposes an integrated approach of grey analytic hierarchy process (G-AHP) and grey technique for order preference by similarity to ideal solution (G-TOPSIS) to evaluate the best e-learning website for network teaching. This introduced approach handles the linguistic evaluation of experts based on grey systems theory, estimates the relative importance of evaluation criteria with the G-AHP method, and acquires e-learning websites’ ranking utilizing G-TOPSIS. The applicability and superiority of the presented method are illustrated through a practical e-learning website selection case in Vietnam. From G-AHP analysis, educational level, price, right and understandable content, complete content, and up-to-date were found as the most impactful criteria. From G-TOPSIS, Edumall is the best platform. Comparisons are conducted with other MCDM methods; the priority orders of the best websites are similar, indicating the robust proposed methodology. The proposed integrated model in this study supports the stakeholders in selecting the most effective e-learning environments and could be a reference for further development of e-learning teaching-learning systems.

Risk assessment on drug production safety based on Grey-Analytic Network Process

PurposeTo strengthen the correlation analysis on risk factors of drug production safety and reduce the influence due to fuzzy judgments, a safety risk assessment method based on Grey-Analytic Network Process (G-ANP) is proposed.Design/methodology/approachFirst, an index system evaluating drug production safety risk is constructed according to the “Good Manufacture Practice of Medical Products,” next the influence weight of each risk index is derived by using the Analytic Network Process, then the grey number of each risk index is determined by further utilizing the grey statistical theory, and finally the risk level of drug production is obtained.FindingsAn empirical study is conducted and the results support the feasibility and practicability to use G-ANP method for drug production safety risk evaluation. The results of the case show that it is feasible and practical to use G-ANP method for drug production safety risk evaluation.Originality/valueThe innovation lies in the use of G-ANP method to fully consider the interdependence and interaction between the risk factors of drug production safety, which improves the objectivity in judging the risk level of drug production and provides a scientific basis for pharmaceutical manufacturers to formulate further decisions and management in the case of insufficient quantification of risk factors. Based on the findings, more targeted suggestions are made to reduce the production risk of pharmaceutical enterprises.

Geometric feature statistics histogram for both real-valued and binary feature representations of 3D local shape

3D local feature description is now at the core of many 3D vision technologies. However, most of the existing 3D feature descriptors can't strike a balance among descriptiveness, robustness, compactness, and efficiency. To overcome the challenges, we propose a real-valued 3D local feature descriptor named Geometric Feature Statistics Histogram (GFSH) and its binary extension descriptor named B-GFSH. A GFSH descriptor first constructs an improved-weighted covariance matrix to solve a stable and reliable Local Reference Frame (LRF), and then achieves a comprehensive description of the 3D local surface by performing statistics on multiple geometric distribution features, namely voxel density, voxel centroid, and projection density. A particular trait of our GFSH descriptor is its seamless extension to the binary representation to reduce storage consumption and accelerate feature matching. For each sub-feature of GFSH, B-GFSH respectively adopts the corresponding binarization strategy, i.e., improved Gray code quantization, thresholding based on coordinates, and neighbor comparison. Extensive experiments on six public datasets prove that both GFSH and B-GFSH have high descriptiveness, strong robustness, and fast real-time performance. In addition, B-GFSH further has the characteristics of fast matching speed, low memory footprint, and high compactness. Finally, we conduct 3D scene registration and 3D object recognition experiments to visually demonstrate the actual effectiveness of GFSH and B-GFSH.

A grey Bayesian inference framework for structural damage assessment

Real-life civil structures often stay in a grey situation due to lack of knowledge and measurements. In a poor information condition, classic Bayesian inference is practically difficult to perform owing to intractable likelihood functions. Under such circumstance, a structure should be defined as a grey system. Thereby, a grey Bayesian inference framework has been proposed by incorporating the grey theory with approximate Bayesian computation for damage assessment purposes. Structural parameters are represented by interval grey variables, whose grey kernels and degrees of greyness are used to define probability distributions for sampling. A grey population Monte Carlo sampler has also been developed by introducing interval grey numbers and an evolutionary particle pool into the particle filtering process. A novel particle interchange mechanism is simultaneously proposed for effective particle interflow. Meanwhile, stochastic response surfaces are used to correlate structural parameters with responses for fast response computation. Also, likelihood calculation is replaced with a distance measure between simulated and measured samples. Lastly, the proposed inference strategy has been verified against both the numerical and experimental beams having the different damage scenarios. The damage locations and severities were successfully identified by the changes in the grey intervals and kernels.