To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(...To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(CR) as benefit, and the maximum modification compared to the original pairwise comparison matrix(PCM) as cost, then the improvement of consistency is transformed to a benefit/cost analysis problem. According to the maximal marginal effect principle, the elements of PCM are modified by a fixed increment(or decrement) step by step till the consistency ratio becomes acceptable, which can ensure minimum adjustment to the original PCM so that the decision makers’ judgment is preserved as much as possible. The correctness of the proposed method is proved mathematically by theorem. Firstly, the marginal benefit/cost ratio is calculated for each single element of the PCM when it has been modified by a fixed increment(or decrement).Then, modification to the element with the maximum marginal benefit/cost ratio is accepted. Next, the marginal benefit/cost ratio is calculated again upon the revised matrix, and followed by choosing the modification to the element with the maximum marginal benefit/cost ratio. The process of calculating marginal effect and choosing the best modified element is repeated for each revised matrix till acceptable consistency is reached, i.e., CR<0.1. Finally,illustrative examples show the proposed method is more effective and better in preserving the original comparison information than existing methods.展开更多
The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new meth...The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale展开更多
This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of deci...This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.展开更多
Grasslands are the most dominant terrestrial ecosystem in China, but few national grassland maps have been generated. The grassland resource map produced in the 1980s is widely used as background data, but it has not ...Grasslands are the most dominant terrestrial ecosystem in China, but few national grassland maps have been generated. The grassland resource map produced in the 1980s is widely used as background data, but it has not been updated for almost 40 years.Therefore, a reliable map depicting the current spatial distribution of grasslands across the country is urgently needed. In this study, we evaluated the grassland consistency and accuracy of ten land cover datasets(GLC2000, GlobCover, CCI-LC,MCD12Q1, CLUD, GlobeLand30, GLC-FCS30, CGLS-LC100, CLCD, and FROM-GLC) for 2000, 2010, and 2020 based on extensive fieldwork. We concluded that the area of these ten grassland products ranges from 107.80×10^(4)to 332.46×10^(4)km^(2), with CLCD and MCD12Q1 having the highest area consistency. The spatial and sample consistency is highest in the regions of eastcentral Inner Mongolia, the Qinghai-Tibet Plateau and northern Xinjiang, while the distribution of southern grasslands is scattered and differs considerably among the ten products. MCD12Q1 is significantly more accurate than the other nine products,with an overall accuracy(OA) reaching 77.51% and a kappa coefficient of 0.51;CLCD is slightly less accurate than MCD12Q1(OA=73.02%, kappa coefficient=0.45) and is more conducive to the fine monitoring and management of grassland because of its30-meter resolution. The highest accuracy of grassland was found in the Inner Mongolia-Ningxia region and Qinghai-Tibet Plateau, while the accuracy was worst in the southeastern region. In the future grassland mapping, cartographers should improve the accuracy of the grassland distribution in South China and regions where grassland is confused with forest, cropland and bare land. We specify the availability of valuable data in existing land cover datasets for China’s grasslands and call for researchers and the government to actively produce a new generation of grassland maps.展开更多
基金supported by the National Natural Science Foundation of China(6160150161502521)
文摘To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(CR) as benefit, and the maximum modification compared to the original pairwise comparison matrix(PCM) as cost, then the improvement of consistency is transformed to a benefit/cost analysis problem. According to the maximal marginal effect principle, the elements of PCM are modified by a fixed increment(or decrement) step by step till the consistency ratio becomes acceptable, which can ensure minimum adjustment to the original PCM so that the decision makers’ judgment is preserved as much as possible. The correctness of the proposed method is proved mathematically by theorem. Firstly, the marginal benefit/cost ratio is calculated for each single element of the PCM when it has been modified by a fixed increment(or decrement).Then, modification to the element with the maximum marginal benefit/cost ratio is accepted. Next, the marginal benefit/cost ratio is calculated again upon the revised matrix, and followed by choosing the modification to the element with the maximum marginal benefit/cost ratio. The process of calculating marginal effect and choosing the best modified element is repeated for each revised matrix till acceptable consistency is reached, i.e., CR<0.1. Finally,illustrative examples show the proposed method is more effective and better in preserving the original comparison information than existing methods.
基金This project was supported by Zhejiang Provincial Natural Science Foundation of China (No. 601076).
文摘The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale
文摘This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.
基金supported by the Major Consulting Research Project of the Chinese Academy of Engineering(2020-XZ-29,2021-HZ-5,2022-HZ-09)the Fundamental Research Funds for the Central Universities,Lanzhou University(lzujbky-2020-kb29,lzujbky-2021-kb13)+3 种基金China Agriculture Research System of MOF(Ministry of Finance)and MARA(Ministry of Agriculture and Rural Affairs)Gansu Province 2021 Outstanding Graduate Student“Innovation Star”Project(2021CXZX-040)Key Laboratory of Grassland Livestock Industry Innovation,Ministry of Agriculture and Rural Affairs,China“Top Innovative Talents”Training Program(CMSYS2020-5)the 111 Project(B12002)。
文摘Grasslands are the most dominant terrestrial ecosystem in China, but few national grassland maps have been generated. The grassland resource map produced in the 1980s is widely used as background data, but it has not been updated for almost 40 years.Therefore, a reliable map depicting the current spatial distribution of grasslands across the country is urgently needed. In this study, we evaluated the grassland consistency and accuracy of ten land cover datasets(GLC2000, GlobCover, CCI-LC,MCD12Q1, CLUD, GlobeLand30, GLC-FCS30, CGLS-LC100, CLCD, and FROM-GLC) for 2000, 2010, and 2020 based on extensive fieldwork. We concluded that the area of these ten grassland products ranges from 107.80×10^(4)to 332.46×10^(4)km^(2), with CLCD and MCD12Q1 having the highest area consistency. The spatial and sample consistency is highest in the regions of eastcentral Inner Mongolia, the Qinghai-Tibet Plateau and northern Xinjiang, while the distribution of southern grasslands is scattered and differs considerably among the ten products. MCD12Q1 is significantly more accurate than the other nine products,with an overall accuracy(OA) reaching 77.51% and a kappa coefficient of 0.51;CLCD is slightly less accurate than MCD12Q1(OA=73.02%, kappa coefficient=0.45) and is more conducive to the fine monitoring and management of grassland because of its30-meter resolution. The highest accuracy of grassland was found in the Inner Mongolia-Ningxia region and Qinghai-Tibet Plateau, while the accuracy was worst in the southeastern region. In the future grassland mapping, cartographers should improve the accuracy of the grassland distribution in South China and regions where grassland is confused with forest, cropland and bare land. We specify the availability of valuable data in existing land cover datasets for China’s grasslands and call for researchers and the government to actively produce a new generation of grassland maps.
