Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Nitrogen management improves lodging resistance and production in maize(Zea mays L.)at a high plant density

Lodging in maize leads to yield losses worldwide.In this study,we determined the effects of traditional and optimized nitrogen management strategies on culm morphological characteristics,culm mechanical strength,lignin content,root growth,lodging percentage and production in maize at a high plant density.We compared a traditional nitrogen(N)application rate of 300 kg ha–1(R)and an optimized N application rate of 225 kg ha^(–1)(O)under four N application modes:50%of N applied at sowing and 50%at the 10th-leaf stage(N1);100%of N applied at sowing(N2);40%of N applied at sowing,40%at the 10th-leaf stage and 20%at tasseling stage(N3);and 30%of N applied at sowing,30%at the 10th-leaf stage,20%at the tasseling stage,and 20%at the silking stage(N4).The optimized N rate(225 kg ha^(–1))significantly reduced internode lengths,plant height,ear height,center of gravity height and lodging percentage.The optimized N rate significantly increased internode diameters,filling degrees,culm mechanical strength,root growth and lignin content.The application of N in four split doses(N4)significantly improved culm morphological characteristics,culm mechanical strength,lignin content,and root growth,while it reduced internode lengths,plant height,ear height,center of gravity height and lodging percentage.Internode diameters,filling degrees,culm mechanical strength,lignin content,number and diameter of brace roots,root volume,root dry weight,bleeding safe and grain yield were significantly negatively correlated with plant height,ear height,center of gravity height,internode lengths and lodging percentage.In conclusion,treatment ON4 significantly reduced the lodging percentage by improving the culm morphological characteristics,culm mechanical strength,lignin content,and root growth,so it improved the production of the maize crop at a high plant density.

青藏高原及其周边白垩纪综合地层、生物群与古地理演化

白垩纪是新特提斯洋演化和青藏高原不同板块汇聚的关键时期,详细的地层框架和古地理格局是开展新特提斯洋演化和青藏高原形成研究的基础.本文对青藏高原及周边白垩纪地层、古生物、古地理和重大地质事件开展了系统分析,以建立综合地层框架,恢复不同时期的古地理格局,探讨重大地质事件的响应和耦合关系.青藏高原及其周边白垩纪地层以海相为主,发育少量海陆交互相和陆相沉积.印度-雅鲁藏布江缝合带发育以蛇绿岩套和含放射虫硅质岩为主的深海沉积,其南侧的特提斯喜马拉雅、印度河盆地等发育浅海至半深海-深海沉积,北侧的日喀则-拉达克弧前盆地发育浅海-半深海相沉积,拉萨地块、喀喇昆仑-塔里木盆地西部和西缅地块等发育浅海、海陆过渡相和陆相沉积,羌塘盆地等其余地区则以陆相沉积为主.青藏高原及其邻区白垩纪地层分布广泛,类型多样,富含有孔虫、钙质超微、放射虫、菊石、双壳类和孢粉等多门类化石;基于岩石地层、生物地层、同位素年代地层和稳定同位素地层等多重地层划分与对比,建立了不同分区地层的划分与对比关系,提出了新的东特提斯区白垩纪综合地层框架.划分了白垩纪新特提斯洋东段及周边不同地理分区的生物群落,阐明了其时空分布特征,恢复了不同时期的生物古地理面貌.青藏高原及周边白垩纪古地理演化可划分为3个阶段:(1)印度板块与澳大利亚-南极洲大陆逐步裂解、拉萨-羌塘地块早期碰撞阶段(145~125Ma);(2)印度板块向北漂移和拉萨-羌塘地块晚期碰撞阶段(125~100Ma);(3)印度板块快速向北漂移、塔里木-喀喇昆仑海湾形成和冈底斯山早期隆升阶段(100~66Ma).白垩纪中期(100Ma左右),印度-特提斯喜马拉雅生物区系经历了冈瓦纳大陆冷水型向特提斯暖水型的转变,海洋生物的多样性达到全盛;白垩纪末期,海洋生物急剧衰退.伴随着印度板块向北漂移和新特提斯洋的演化,新特提斯洋发生了大火成岩省、大洋缺氧、白垩纪大洋红层,以及生物辐射与灭绝等一系重大地质事件.

Effects of uniconazole with or without micronutrient on the lignin biosynthesis,lodging resistance,and winter wheat production in semiarid regions

Lodging stress results in grain yield and quality reduction in wheat. Uniconazole, a potential plant growth regulator significantly enhances lignin biosynthesis and thus provides mechanical strength to plants in order to cope with lodging stress. A field study was conducted during the 2015–2016 and 2016–2017 growing seasons, to investigate the effects of uniconazole sole application or with micronutrient on the lignin biosynthesis, lodging resistance, and production of winter wheat. In the first experiment, uniconazole at concentrations of 0(CK), 15(US1), 30(US2), and 45(US3) mg L^-1 was applied as sole seed soaking, while in the second experiment with manganese(Mn) at concentration of 0.06 g L^-1 Mn, 0.06 g L^-1 Mn+ 15 mg L^-1 uniconazole(UMS1), 0.06 g L^-1 Mn+30 mg L^-1 uniconazole(UMS2), and 0.06 g L^-1 Mn+45 mg L^-1 uniconazole(UMS3), respectively. Uniconazole sole application or with micronutrient significantly increased the lignin content by improving the lignin-related enzyme activities of phenylalanine ammonia-lyase, cinnamyl alcohol dehydrogenase, tyrosine ammonialyase, and peroxidase, ameliorating basal internode characteristics, and breaking strength. The spike length, spike diameter, spikes/plant, weight/spike, yield/spike, and grain yield increased and then decreased with uniconazole application at a higher concentration, where their maximum values were recorded with UMS2 and US2 treatments. The lignin accumulation was positively correlated with lignin-related enzyme activities and breaking strength while, negatively correlated with lodging rate. Uniconazole significantly improved the lignin biosynthesis, lodging resistance, and grain yield of winter wheat and the treatments which showed the greatest effects were uniconazole seed soaking with micronutrient at a concentration of 30 mg L^-1 and 0.06 g L^-1 , and uniconazole sole seed soaking at a concentration of 30 mg L^-1 .

Influence of Seed Priming on Performance and Water Productivity of Direct Seeded Rice in Alternating Wetting and Drying

Direct seeded rice is promising alternative to traditional transplanting, but requires appropriate crop and water management to maintain yield performance and achieve high water productivity. Present study evaluated the effect of seed priming and irrigation on crop establishment, tillering, agronomic traits, paddy yield, grain quality and water productivity of direct seeded rice in alternate wetting and drying(DSR-AWD) in comparison with direct seeded rice at field capacity(DSRFC). Seed priming treatments were osmo-priming with KCl(2.2%), Ca Cl2(2.2%) and moringa leaf extracts(MLE, 3.3%) including hydro-priming as control. Among the treatments, seed osmo-primed with MLE emerged earlier and had higher final emergence, followed by osmo-priming with Ca Cl2. Tillering emergence rate and number of tillers per plant were the highest for seed priming with Ca Cl2 in DSRAWD. Total productive and non-productive tillers, panicle length, biological and grain yields, harvest index were highest for seed priming with MLE or Ca Cl2 in DSR-AWD. Similarly, grain quality, estimated in terms of normal grains, abortive and chalky grains, was also the highest in DSR-AWD with MLE osmo-priming. Benefit cost ratio and water productivity was also the highest in DSR-AWD for seed priming with MLE. In conclusion, seed priming with MLE or Ca Cl2 can be successfully employed to improve the direct seeded rice performance when practiced with alternate wetting and drying irrigation.

一种引入互斥关系的功能单元分配算法

为使条件分支数据通道中功能单元的分配结果得到进一步优化,在数据流图操作相容性分析中引入操作间互斥关系,并构建基于图论的分配模型.使用团划分算法在该模型上进行功能单元分配,同时提出一种针对功能单元分配问题的团划分启发式方法.不仅提高了团划分算法求解功能单元分配问题的计算结果一致性,而且使算法的收敛速度得以提高.根据实验结果,该算法得到的数据通道中所需功能单元平均减少了41%,同时执行速度加快了50%.

Temperature-dependent far-infrared properties of Bi_(12)GeO_(20) single crystal

Far-infrared reflectivity spectra of bismuth germanium oxide (Bi12GeO20) single crystals are measured from room temperature down to 10 K. All the reflectivity spectra are fitted to a complex dielectric function ε(ω) in the factorised form. Phonon modes at low frequency are found to develop upon decreasing temperature and gain considerable spectrum weight below 150 K. The temperature-dependent static dielectric constants are obtained from the Lyddane-Sachs-Teller relation based on the obtained oscillator parameters. The dielectric constants are found to increase upon decreasing temperature, which is attributed to the charge transfer among the ions in the unit cell with the temperature varying.

A Threshold Scheme under Peer-to-Peer Network

Resource sharing among peers is one of important application in Peer-to-Peer(P2P) network. Inexistence of server makes P2P network to be a less trustable tool for property owners to distribute their resource. In order to protect intelligent property, reputation management strategy is adopted in many P2P network. As long as a P2P network reputation strategy is confirmed, application designer can employ a special detailed distribution scheme to fulfill content distribution within the net. Shmir (k,n) threshold scheme, for example, is an encryption scheme to enhance the distribution security of this kind of design. (k,n) threshold scheme is a new tool similar to Shmir scheme is proposed in this paper. The new scheme based on polynomial expansion and its security is decided by the one way function used in the secret distribution procedure. The scheme efficiency and its features as well as comparison between new and Shmir scheme are also discussed in this paper.

Multi-Seed Key Distribution Scheme Test

The key problem of securing multicast is to generate, distribute and update Session Encryption Key(SEK). Polynomial expansion with multi-seed(MPE) scheme is an approach which is based on Polynomial expansion(PE) scheme and overcomes PE’s shortage. Its operation is demonstrated by using multi-seed, the group member is partitioned to many subgroups. While updating the SEK, computation is needed only in one of subgroups, the other of them will use the computation history to update their SEK. The key problems to design a MPE scheme application includes to find a feasible one way function as well as to generate a Strict Prime Number(SPN). Those technologies with multi-seed and computation history concepts make MPE as a good choice in practical applications. A prototype test system is designed and solutions of all above mentioned problems are included in this proposed paper.

Transmutation Scheme of Coin Flipping Protocol and Utilization

Coin flipping by telephone protocol(CFP) is utilized in a system to exchange a binary sequence at random between two person apart far from each other. However, CFP cannot be used in a system with many users like in a group environment system. A transmutation of CFP named T-CFP is proposed in this paper. The precondition of T-CFP is the system’s user trusts the system center and center’s cheating is meaningless at the same time. The significant difference between CFP and T-CFP is that CFP supports only two users while T-CFP can support many users to exchange special information. The security and efficiency of T-CFP are discussed with a detailed example on T-CFP utilization is demonstrated in this paper.

A Novel Database Watermarking Technique Using Blockchain as Trusted Third Party

With widespread use of relational database in various real-life applications,maintaining integrity and providing copyright protection is gaining keen interest of the researchers.For this purpose,watermarking has been used for quite a long time.Watermarking requires the role of trusted third party and a mechanism to extract digital signatures(watermark)to prove the ownership of the data under dispute.This is often inefficient as lots of processing is required.Moreover,certain malicious attacks,like additive attacks,can give rise to a situation when more than one parties can claim the ownership of the same data by inserting and detecting their own set of watermarks from the same data.To solve this problem,we propose to use blockchain technology—as trusted third party—along with watermarking for providing a means of rights protection of relational databases.Using blockchain for writing the copyright information alongside watermarking helps to secure the watermark as changing the blockchain is very difficult.This way,we combined the resilience of our watermarking scheme and the strength of blockchain technology—for protecting the digital rights information from alteration—to design and implement a robust scheme for digital right protection of relational databases.Moreover,we also discuss how the proposed scheme can also be used for version control.The proposed technique works with nonnumeric features of relational database and does not target only selected tuple or portion(subset)from the database for watermark embedding unlike most of the existing techniques;as a result,the chances of subset selection containing no watermark decrease automatically.The proposed technique employs zerowatermarking approach and hence no intentional error(watermark)is added to the original dataset.The results of the experiments proved the effectiveness of the proposed scheme.

A Particle Swarm Optimization Based Deep Learning Model for Vehicle Classification

Image classification is a core field in the research area of image proces-sing and computer vision in which vehicle classification is a critical domain.The purpose of vehicle categorization is to formulate a compact system to assist in real-world problems and applications such as security,traffic analysis,and self-driving and autonomous vehicles.The recent revolution in the field of machine learning and artificial intelligence has provided an immense amount of support for image processing related problems and has overtaken the conventional,and handcrafted means of solving image analysis problems.In this paper,a combina-tion of pre-trained CNN GoogleNet and a nature-inspired problem optimization scheme,particle swarm optimization(PSO),was employed for autonomous vehi-cle classification.The model was trained on a vehicle image dataset obtained from Kaggle that has been suitably augmented.The trained model was classified using several classifiers;however,the Cubic SVM(CSVM)classifier was found to out-perform the others in both time consumption and accuracy(94.8%).The results obtained from empirical evaluations and statistical tests reveal that the model itself has shown to outperform the other related models not only in terms of accu-racy(94.8%)but also in terms of training time(82.7 s)and speed prediction(380 obs/sec).

Induced Production of Exoglucanase, and <i>β</i>-Glucosidase from Fungal Co-Culture of T. <i>viride</i>and G. <i>lucidum</i>

In the present study, a co-culture technique was adopted with an aim to investigate a hyper production of exoglucanase, and β-glucosidase using cheap and easily available agro-industrial residue corn stover as growth supporting substrate. Various physio-chemical and nutritional variables were optimized using classical and completely randomized designs for induced production of exoglucanase, and β-glucosidase from the co-culture of Trichoderma viride and Ganoderma lucidum in solid state fermentation (SSF). Analysis profile showed that when the conditions of the SSF medium containing 15 g corn stover substrate (50% w/w moisture) inoculated with 6 mL of inoculum were optimal, the maximum productions of exoglucanase (485 ± 6.5 U/mL) and β-glucosidase (255 ± 3.3 U/mL) were recorded after 5 days of incubation at pH 6 and 35°C.

Cretaceous integrative stratigraphy,biotas,and paleogeographical evolution of the Qinghai-Tibetan Plateau and its surrounding areas

The Cretaceous Period is a vital time interval in deciphering the evolutionary history of the Neo-Tethys Ocean and the convergence of different plates and blocks across the Qinghai-Tibetan Plateau.A detailed stratigraphic framework and paleogeographic patterns are the basis for understanding the evolution of the Neo-Tethys Ocean and the formation of the QinghaiTibetan Plateau.Here,the Cretaceous stratigraphy,biota,paleogeography,and major geological events in the Qinghai-Tibetan Plateau are analyzed to establish an integrative stratigraphic framework,reconstruct the paleogeography during the Cretaceous Period,and decode the history of the major geological events.The Cretaceous rocks of the Qinghai-Tibetan Plateau and its surrounding area are predominantly marine deposits,with a small amount of interbedded marine-terrestrial and terrestrial conponents.The Indus-Yarlung Tsangpo Suture Zone was responsible for the deposition of deep marine sediments dominated by ophiolite suites and radiolarian silicalite.To the south,the Tethys Himalayas and Indus Basin received marine sediments of varying depths and lithology;to the north,the Xigaze and Ladakh forearc basins are also filled with marine sediments.The Lhasa Block,Karakorum Block,western Tarim Basin,and West Burma block consist of shallow marine,interbedded marine-terrestrial,and terrestrial sediments.The Qiangtang Basin and other areas are dominated by terrestrial sedimentation.The Cretaceous strata of the Qinghai-Tibetan Plateau and its surrounding areas are widely distributed and diversified,with abundant foraminifera,calcareous nannofossils,radiolarians,ammonites,bivalves,and palynomorphs.On the basis of integrated lithostratigraphic,biostratigraphic,geochronologic,and chemostratigraphic analyses,we proposed herein a comprehensive stratigraphic framework for the Cretaceous Period of the eastern Neo-Tethys.By analyzing the Cretaceous biota of different biogeographic zones from eastern Neo-Tethys and its surrounding areas,we reconstructed the paleobiogeography of different periods of eastern NeoTethys.The Cretaceous paleogeographic evolution of the Qinghai-Tibetan Plateau and its surrounding areas can be divided into three phases:(1)gradual breakup of the Indian Plate from the Australia-Antarctica continent and the early collision phase of the Lhasa-Qiangtang blocks(145-125 Ma);(2)northward drift of the Indian Plate and the collision phase of the Lhasa-Qiangtang blocks(125-100 Ma);(3)rapid northward drift of the Indian Plate,formation of the Tarim-Tajik-Karakorum Bay,and early uplift of the Gangdise Mountains(100-66 Ma).The Indus-Tethys Himalayan biota underwent a transition from the cold-water type in the high latitudes of the southern hemisphere to the warm-water type near the equator from the Early Cretaceous to the MidCretaceous.The biodiversity and abundance of the eastern Neo-Tethys Ocean increased gradually in the Early Cretaceous,peaking in the Mid-Cretaceous,and decreased sharply during the late Late Cretaceous(late Maastrichtian).Along with the northward drift of the Indian Plate and subduction of the Neo-Tethys,the eastern Neo-Tethys and its surrounding areas experienced a series of major geological events,including the formation of the large igneous province,oceanic anoxia events,and mass extinction,etc.

Dynamic Response and Deformation Behavior of Kadui-2 Landslide Influenced by Reservoir Impoundment and Rainfall,Baoxing,China

This study focuses on the deformation characteristics of Kadui-2 Landslide by the influence of reservoir filling-drawdown and precipitation.A three-year monitoring project was implemented in order to observe the short/long-term deformation.The slide mass experienced consistent deformation with a maximum cumulative displacement of 331.34 cm.Based on the recorded data of reservoir water level and precipitation during this period,a two-dimensional(2-D)finite element model using Geostudio software was set up for deformation simulation under different conditions to understand the real influence of these triggering factors on landslide.The numerical simulation results are in consistent with monitoring field data.Both numerical simulation and field monitoring results exhibit that the maximum deformation occurred at the foreside of slumping mass.The slip surface shows significant creep characteristics decreasing as long-term shear strength reducing gradually.Reservoir water level fluctuation is the primary triggering factor to reactivate the landslide mass and has a negative correlation with deformation rate.Displacement rate increases with the reservoir drawdown and decreases with impoundment rise.Compared with reservoir filling-drawdown operation,rainfall has no significant effect on the slide motion of landslide due to limited penetration from the ground surface.

基于遥感和GIS的中巴经济走廊多发展情景生态风险综合评价

中巴经济走廊沿线地区生态环境复杂、人地矛盾突出,走廊建设在推动区域经济发展的同时,也可能给区域生态环境安全带来潜在风险。借助遥感、地理信息和情景模拟方法,从风险源危险性、生态环境脆弱性、受体损失度三方面构建风险评价模型,结合惯性发展、投资优先和和谐发展三种情景下2030年土地利用情况,对廊道2015~2030年生态风险的时空变化规律进行分析。结果表明:中巴经济走廊高生态风险区主要分布在巴基斯坦北部山区向印度河平原的过渡区。未来情景的差异直接影响着生态风险。投资优先情景高风险区增幅最大,相比于2015年,2030年中度、高度和极高风险区面积占比分别增加了4.75%、4.84%和2.25%。惯性发展情景中度、高度和极高风险区面积占比分别增加了2.79%、2.52%和1.04%。和谐发展情景中,中度和高度风险区呈现增加趋势,极高风险区面积略微下降,增幅分别为1.15%、2.19%和-0.16%。研究表明:能兼顾经济发展和环境保护的和谐发展情景,是未来廊道规划建设的优化选择,合理规划土地利用,提高土地用途管制力度,提升土地资源使用效益,可促进社会经济可持续发展。基于遥感和GIS技术的综合评价方法能够为经济廊道的生态风险评价提供技术支撑。

Lanthanum chloride improves maize grain yield by promoting photosynthetic characteristics, antioxidants enzymes and endogenous hormone at reproductive stages

Despite an increase in application spectrum of rare earth elements in agriculture, all studies show that the suitable accumulation of rare earth elements can improve the crop seedling growth, but there is little research about REEs on physiological mechanisms of crops at reproductive stages. Therefore, this study was conducted to examine the possible potential benefits of lanthanum chloride(LaCl3) on the senescence and grain yield responses of maize. In this study, maize seeds were pre-treated by soaking with LaCl3 at the concentrations of 0(CK), 400(LC1), 800(LC2) and 1200(LC3) μmol/L, to evaluate its effect on the green leaf area, chlorophyll contents, photosynthesis, antioxidants, endogenous hormones in the later crop growth stages. The results show that LC1 and LC2 treatments evidently increase green leaf area, above ground dry biomass, accompanied by a distinct increase in the chlorophyll contents, and photo synthetic capacity, which promote the ear characteristics and grain yield of maize. In addition, LC1 and LC2 treatments simultaneously increase the activities of antioxidants, including superoxide dismutases, catalases, peroxidases, soluble protein, and enhanced levels of auxin, gibberellin and zeatin,following a dose-response tendency. Themalondialdehyde and abscisic acid levels transiently increase with the progression in the growth stage of the crop but are markedly decreased at LC1 and LC2 treatments, while LC3 treatment has no significant effect on malondialdehyde and even accelerates the accumulation of abscisic acid in maize leaves. Our data suggest that seed priming with LaCl3 at a suitable concentration range(400-800 μmol/L) can prolong the functional periods of leaves, increase photosynthetic capacity, enhance antioxidant activity, and alter endogenous hormone levels at reproductive stages, resulting in delaying leaf senescence rate and increasing yield. However, the moderate concentration of LaCl3 for maize is LC2(800 μmol/L), and can be effectively used to improve grain yield of maize.

优化算法在所有权保留数据挖掘中的应用（英文）

从敏感数据中提取知识往往需要协同工作。统计数据库根据这些敏感数据生成,并由各利益相关方共享。在此情况下,共享数据的所有权保护变得尤为重要。水印技术正逐渐成为一种推行数字数据格式所有权的有效工具,但该技术也可能导致数据失真。因此,从具有水印的数据中提取的知识可能不准确。数据失真程度由可用性约束条件来控制,这反过来又限制了可用于添加水印的带宽。尽管大带宽能保证鲁棒性,但可能降低数据质量。该问题可以通过在可用性约束条件下优化可用带宽来解决。如今,优化技术——尤其是生物启发式技术——已成为解决该类问题的首选。本文分析了多种优化方案及其可行性,用于优化添加水印的最大可用带宽,并期望达到以下两个目标:(1)保持数据中存储的知识不变;(2)在可用性约束条件下使可用带宽最大化,以取得最佳鲁棒性。第一个目标利用一个可用性约束模型实现,该模型能确保知识不会因嵌入水印而受到损害。第二个目标通过找到满足第一个目标的可用性约束条件下最大带宽实现。采用不同指标对多种优化方案性能进行了评估。

Electromechanical Fields and Their Influence on the Internal Quantum Efficiency of GaN-Based Light-Emitting Diodes

The effect of electromechanical fields, i.e., polarization fields, on the efficiency droop of GaN-based light-emitting diodes is presented using both experimental and numerical analyses.The role of incorporating such polarization charge density in device performance is numerically investigated and further compared with the experimental results of internal quantum efficiency of three different devices in consideration.