The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is ...The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is generally obtained from Continuously Operating Reference Stations data by using the spatial single-difference method(mixed-pair,station-pair,or satellite-pair)or the temporal single-difference method(time-step).The time-step method uses only a single receiver,but it still contains ionospheric temporal variations.We introduce a corrected time-step method using a fixed-ionospheric pierce point from the geostationary equatorial orbit satellite and test it through simulations based on the global ionospheric model.We also investigate the effect of satellite paths on the corrected time-step method in the region of the equator,which tends to be in a more north–south direction and to have less coverage for the east–west ionospheric gradient.This study also addresses the limitations of temporal variation correction coverage and recommends using only the correction from self-observations.All processes are developed under simulations because observational data are still difficult to obtain.Our findings demonstrate that the corrected time-step method yieldsσvig values consistent with other approaches.展开更多
INTRODUCTION Types of Contributions Full-length/Research Article(Page limit:20)A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide ...INTRODUCTION Types of Contributions Full-length/Research Article(Page limit:20)A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide their biographies and personal photos.Submitted manuscripts should be nominally around 12 pages in Elsevier's double-column format,but no more than 20 pages(including bios and photos).展开更多
Researchers around the world strive to communicate new knowledge,primarily via publication,with the abstract being crucial in conveying core insights.Previous research has generally analyzed the discourse features of ...Researchers around the world strive to communicate new knowledge,primarily via publication,with the abstract being crucial in conveying core insights.Previous research has generally analyzed the discourse features of abstracts from a macro perspective and often employed either outdated texts,such as those over a decade old,or papers written by authors with lower English academic writing proficiency as research material.In this study,we analyzed forty abstracts from leading journals in applied linguistics,evenly split between Chinese and international journals.It revealed that the use of nominalization in abstracts by Chinese and international scholars showed similarities due to the universal academic requirement for conciseness.However,due to cultural and educational differences,each group differed in their respective language choices and nominalization usage.By analyzing the application of nominalization in different cultural contexts,the results of our study offered practical suggestions for crafting abstracts that effectively convey information,thereby,contributing to the broader academic community.展开更多
INTRODUCTION.Types of Contributions.Full-length/Research Article(Page limit:20).A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide...INTRODUCTION.Types of Contributions.Full-length/Research Article(Page limit:20).A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide their biographies and personal photos.Submitted manuscripts should be nominally around 12 pages in Elsevier's double-column format,but no more than 20 pages(including bios and photos).展开更多
Dear Editor, This paper considers the disturbance/uncertainty estimation of first-order nonlinear system subject to fully unknown internal dynamic, external disturbance, and unknown control input gain.Compared with ex...Dear Editor, This paper considers the disturbance/uncertainty estimation of first-order nonlinear system subject to fully unknown internal dynamic, external disturbance, and unknown control input gain.Compared with existing extended state observer(ESO) where priori knowledge of model parameter such as nominal input gain should be known as a priori.展开更多
Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between att...Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between attributes has shown significant improvement in clustering and outlier detection,etc.However,typical existing work relies on learning pairwise value relations but weakens or overlooks the direct couplings between multiple attributes.This paper thus proposes two novel and flexible multi-attribute couplings-based distance(MCD)metrics,which learn the multi-attribute couplings and their strengths in nominal data based on information theories:self-information,entropy,and mutual information,for measuring both numerical and nominal distances.MCD enables the application of numerical and nominal clustering methods on nominal data and quantifies the influence of involving and filtering multi-attribute couplings on distance learning and clustering perfor-mance.Substantial experiments evidence the above conclusions on 15 data sets against seven state-of-the-art distance measures with various feature selection methods for both numerical and nominal clustering.展开更多
Interest rates are the key to the resource allocations of financial markets.The frequent appearance of negative nominal interest rates(NNIR)may lead to a failure of the transmission mechanism and arouse system risks i...Interest rates are the key to the resource allocations of financial markets.The frequent appearance of negative nominal interest rates(NNIR)may lead to a failure of the transmission mechanism and arouse system risks in the financial markets.Meanwhile,negative nominal interest rates is a new policy with no consensus reached by academia or policymakers.It is necessary to review the research results and promote consensus to reveal the nature and impact mechanisms of NNIR.Therefore,we retrieved original articles from the Web of Science(WoS)and China National Knowledge Infrastructure(CNKI)published from 1999 to 2020 on NNIR to determine the characteristics of current research results from various perspectives and compare literature in English and Chinese of highly productive institutions and researchers,hot topics,evolution contexts,research frontiers,and ecological characteristics.There are three major findings.In terms of research ecology,the ecological structure of the top research institutions,both domestic and abroad,remains steady,but the structure of the researchers is not stable.In terms of a research domain,NNIR is studied from many dimensions,and the early established research domains still have long-lasting impacts in English literature.In contrast,Chinese literature mainly focuses on discussing applicable policies with no highly focused domain and research topic with great influence yet.Finally,the focus in both English and Chinese literature has changed.Since the original research framework is insufficient in explanatory power,literature in English is beginning to pay attention to the empirical analyses of practical policies,and Chinese scholars are turning to theoretical study to enhance the in-depth understanding of this phenomenon.Researchers in China should focus on collecting high-quality research materials and pay more attention to the progress of empirical research in English literature to improve Chinese research efficiency and quality and then promote research progress in China.展开更多
INTRODUCTION Types of Contributions Full-length/Research Article(Page limit:20)A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide ...INTRODUCTION Types of Contributions Full-length/Research Article(Page limit:20)A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide their biographies and personal photos.Submitted manuscripts should be nominally around 12 pages in Elsevier's double-column format,but no more than 20 pages(including bios and photos).展开更多
There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate t...There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.展开更多
There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate t...There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.展开更多
Cognitive grammar,as a linguistic theory that attaches importance to the relationship between language and thinking,provides us with a more comprehensive way to understand the structure,semantics and cognitive process...Cognitive grammar,as a linguistic theory that attaches importance to the relationship between language and thinking,provides us with a more comprehensive way to understand the structure,semantics and cognitive processing of noun predicate sentences.Therefore,under the framework of cognitive grammar,this paper tries to analyze the semantic connection and cognitive process in noun predicate sentences from the semantic perspective and the method of example theory,and discusses the motivation of the formation of this construction,so as to provide references for in-depth analysis of the cognitive laws behind noun predicate sentences.展开更多
In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pa...In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pavement roughness is denoted as the sum of numerous sines or cosines with stochastic phases, and uses the discrete spectrum to approach the target stochastic process. It is a discrete numerical method used to simulate pavement roughness. According to a given pavement power spectral density (PSD) coefficient, under the condition that the character of displacement frequency based on the time domain model is in accordance with the given pavement surface spectrum, the pavement roughness is optimized to stochastic equivalent vibrations by computer simulation, and the curves that describe pavement roughness under each grade are obtained. The results show that the stochastic sinusoidal wave is suitable for simulation of measured pavement surface spectra based on the time domain model. The method of the stochastic sinusoidal wave is important to the research on vehicle ride comfort due to its rigorous mathematical derivation, extensive application range and intuitive simulation curve. Finally, a roughness index defined as the nominal roughness index (NRI) is introduced, and it has correlation with the PSD coefficient.展开更多
As an important feature of written language, nominalization is frequently used in formal texts. Using the approach of systemic functional grammar, the paper presents a detailed analysis of the three metafunctions of n...As an important feature of written language, nominalization is frequently used in formal texts. Using the approach of systemic functional grammar, the paper presents a detailed analysis of the three metafunctions of nominalization, which entails the positive and negative stylistic effects. The paper also discusses the relationship between form, function and stylistic features.展开更多
Ⅰ. Each of the Statements below is followed by four alternative answers. Choose the one that would best complete the statement and put the letter in the bracket.1. Jack of all trades is an idiom_.A. nominal in nature...Ⅰ. Each of the Statements below is followed by four alternative answers. Choose the one that would best complete the statement and put the letter in the bracket.1. Jack of all trades is an idiom_.A. nominal in nature B. adjectival in nature C. verbal in nature D. adverbial in nature2. Let the dog see the rabbit is an idiom_.A. nominal in nature B. adjectival in展开更多
This paper deals with the application of nominal indirect anaphora to unveil the essence of nominal indirect anaphora and disclose the magic power of cohesion and coherence inside it from the angle of cognitive lingui...This paper deals with the application of nominal indirect anaphora to unveil the essence of nominal indirect anaphora and disclose the magic power of cohesion and coherence inside it from the angle of cognitive linguistics.Thus we can apply the resolution mechanism for English teaching and learning for English learners.展开更多
Based on nominal model, a novel global sliding mode controller (GSMC) with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is th...Based on nominal model, a novel global sliding mode controller (GSMC) with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.展开更多
According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have rese...According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set (A ,≤) is the mapping of evaluation object (X, ≤) under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f(xi ) = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set (A, ≤) and evaluation object (X, ≤) is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.展开更多
基金funding from BRIN through the Research Collaboration Program with ORPA(No.2/III.1/HK/2024)Prayitno Abadi is participating in this study as part of a Memorandum of Understanding for Research Collaboration on Regional Ionospheric Observation at Telkom University(No.092/SAM3/TE-DEK/2021).
文摘The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is generally obtained from Continuously Operating Reference Stations data by using the spatial single-difference method(mixed-pair,station-pair,or satellite-pair)or the temporal single-difference method(time-step).The time-step method uses only a single receiver,but it still contains ionospheric temporal variations.We introduce a corrected time-step method using a fixed-ionospheric pierce point from the geostationary equatorial orbit satellite and test it through simulations based on the global ionospheric model.We also investigate the effect of satellite paths on the corrected time-step method in the region of the equator,which tends to be in a more north–south direction and to have less coverage for the east–west ionospheric gradient.This study also addresses the limitations of temporal variation correction coverage and recommends using only the correction from self-observations.All processes are developed under simulations because observational data are still difficult to obtain.Our findings demonstrate that the corrected time-step method yieldsσvig values consistent with other approaches.
文摘INTRODUCTION Types of Contributions Full-length/Research Article(Page limit:20)A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide their biographies and personal photos.Submitted manuscripts should be nominally around 12 pages in Elsevier's double-column format,but no more than 20 pages(including bios and photos).
文摘Researchers around the world strive to communicate new knowledge,primarily via publication,with the abstract being crucial in conveying core insights.Previous research has generally analyzed the discourse features of abstracts from a macro perspective and often employed either outdated texts,such as those over a decade old,or papers written by authors with lower English academic writing proficiency as research material.In this study,we analyzed forty abstracts from leading journals in applied linguistics,evenly split between Chinese and international journals.It revealed that the use of nominalization in abstracts by Chinese and international scholars showed similarities due to the universal academic requirement for conciseness.However,due to cultural and educational differences,each group differed in their respective language choices and nominalization usage.By analyzing the application of nominalization in different cultural contexts,the results of our study offered practical suggestions for crafting abstracts that effectively convey information,thereby,contributing to the broader academic community.
文摘INTRODUCTION.Types of Contributions.Full-length/Research Article(Page limit:20).A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide their biographies and personal photos.Submitted manuscripts should be nominally around 12 pages in Elsevier's double-column format,but no more than 20 pages(including bios and photos).
基金supported in part by the National Natural Science Foundation of China(51979020,52071044,52271304)the Top-Notch Young Talents Program of China(36261402)+3 种基金the Liaoning Revitalization Talents Program(XLYC2007188)the Basic Scientific Research in Colleges and Universities of Liaoning Provincial Education Department(LJKQZ2021007)the Industry-University-Research Innovation Funds for Chinese Universities(2021ZYA02003)the Dalian Science and Technology Innovation Fund(2022JJ12GX034)。
文摘Dear Editor, This paper considers the disturbance/uncertainty estimation of first-order nonlinear system subject to fully unknown internal dynamic, external disturbance, and unknown control input gain.Compared with existing extended state observer(ESO) where priori knowledge of model parameter such as nominal input gain should be known as a priori.
基金funded by the MOE(Ministry of Education in China)Project of Humanities and Social Sciences(Project Number:18YJC870006)from China.
文摘Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between attributes has shown significant improvement in clustering and outlier detection,etc.However,typical existing work relies on learning pairwise value relations but weakens or overlooks the direct couplings between multiple attributes.This paper thus proposes two novel and flexible multi-attribute couplings-based distance(MCD)metrics,which learn the multi-attribute couplings and their strengths in nominal data based on information theories:self-information,entropy,and mutual information,for measuring both numerical and nominal distances.MCD enables the application of numerical and nominal clustering methods on nominal data and quantifies the influence of involving and filtering multi-attribute couplings on distance learning and clustering perfor-mance.Substantial experiments evidence the above conclusions on 15 data sets against seven state-of-the-art distance measures with various feature selection methods for both numerical and nominal clustering.
基金Planning Projects on Philosophy and Social Sciences of Shanghai(2020BJB020).
文摘Interest rates are the key to the resource allocations of financial markets.The frequent appearance of negative nominal interest rates(NNIR)may lead to a failure of the transmission mechanism and arouse system risks in the financial markets.Meanwhile,negative nominal interest rates is a new policy with no consensus reached by academia or policymakers.It is necessary to review the research results and promote consensus to reveal the nature and impact mechanisms of NNIR.Therefore,we retrieved original articles from the Web of Science(WoS)and China National Knowledge Infrastructure(CNKI)published from 1999 to 2020 on NNIR to determine the characteristics of current research results from various perspectives and compare literature in English and Chinese of highly productive institutions and researchers,hot topics,evolution contexts,research frontiers,and ecological characteristics.There are three major findings.In terms of research ecology,the ecological structure of the top research institutions,both domestic and abroad,remains steady,but the structure of the researchers is not stable.In terms of a research domain,NNIR is studied from many dimensions,and the early established research domains still have long-lasting impacts in English literature.In contrast,Chinese literature mainly focuses on discussing applicable policies with no highly focused domain and research topic with great influence yet.Finally,the focus in both English and Chinese literature has changed.Since the original research framework is insufficient in explanatory power,literature in English is beginning to pay attention to the empirical analyses of practical policies,and Chinese scholars are turning to theoretical study to enhance the in-depth understanding of this phenomenon.Researchers in China should focus on collecting high-quality research materials and pay more attention to the progress of empirical research in English literature to improve Chinese research efficiency and quality and then promote research progress in China.
文摘INTRODUCTION Types of Contributions Full-length/Research Article(Page limit:20)A complete report on original research,development,or application of control and machine learning methods.All the authors need to provide their biographies and personal photos.Submitted manuscripts should be nominally around 12 pages in Elsevier's double-column format,but no more than 20 pages(including bios and photos).
文摘There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.
文摘There are several shape measures for quantitative variables, some of which can also be applied to ordinal variables. In quantitative variables, symmetry, peakedness, and kurtosis are essential properties to evaluate the deviation from assumptions, particularly normality. They aid in selecting the most appropriate method for estimating parameters and testing hypotheses. Initially, these properties serve a descriptive role in qualitative variables. Once defined, they can be considered to check for non-compliance with assumptions and to propose modifications for testing procedures. The objective of this article is to present three measures of the shape of the distribution of a qualitative variable. The concepts of qualitative asymmetry and peakedness are defined. The measurement of the first concept involves calculating the average frequency difference between qualitative categories matched by frequency homogeneity or proximity. For the second concept, the peak-to-shoulder difference and the qualitative percentile kurtosis are taken into consideration. This last measurement is a less effective option than the peak-to-shoulder difference to measure peakedness. A simulated example of the application of these three measures is given and the paper closes with some conclusions and suggestions.
文摘Cognitive grammar,as a linguistic theory that attaches importance to the relationship between language and thinking,provides us with a more comprehensive way to understand the structure,semantics and cognitive processing of noun predicate sentences.Therefore,under the framework of cognitive grammar,this paper tries to analyze the semantic connection and cognitive process in noun predicate sentences from the semantic perspective and the method of example theory,and discusses the motivation of the formation of this construction,so as to provide references for in-depth analysis of the cognitive laws behind noun predicate sentences.
文摘In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pavement roughness is denoted as the sum of numerous sines or cosines with stochastic phases, and uses the discrete spectrum to approach the target stochastic process. It is a discrete numerical method used to simulate pavement roughness. According to a given pavement power spectral density (PSD) coefficient, under the condition that the character of displacement frequency based on the time domain model is in accordance with the given pavement surface spectrum, the pavement roughness is optimized to stochastic equivalent vibrations by computer simulation, and the curves that describe pavement roughness under each grade are obtained. The results show that the stochastic sinusoidal wave is suitable for simulation of measured pavement surface spectra based on the time domain model. The method of the stochastic sinusoidal wave is important to the research on vehicle ride comfort due to its rigorous mathematical derivation, extensive application range and intuitive simulation curve. Finally, a roughness index defined as the nominal roughness index (NRI) is introduced, and it has correlation with the PSD coefficient.
文摘As an important feature of written language, nominalization is frequently used in formal texts. Using the approach of systemic functional grammar, the paper presents a detailed analysis of the three metafunctions of nominalization, which entails the positive and negative stylistic effects. The paper also discusses the relationship between form, function and stylistic features.
文摘Ⅰ. Each of the Statements below is followed by four alternative answers. Choose the one that would best complete the statement and put the letter in the bracket.1. Jack of all trades is an idiom_.A. nominal in nature B. adjectival in nature C. verbal in nature D. adverbial in nature2. Let the dog see the rabbit is an idiom_.A. nominal in nature B. adjectival in
文摘This paper deals with the application of nominal indirect anaphora to unveil the essence of nominal indirect anaphora and disclose the magic power of cohesion and coherence inside it from the angle of cognitive linguistics.Thus we can apply the resolution mechanism for English teaching and learning for English learners.
文摘Based on nominal model, a novel global sliding mode controller (GSMC) with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.
文摘According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set (A ,≤) is the mapping of evaluation object (X, ≤) under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f(xi ) = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set (A, ≤) and evaluation object (X, ≤) is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.