Test of consistency is critical for the analytic hierarchy process(AHP) methodology. When a pairwise comparison matrix(PCM) fails the consistency test, the decision maker(DM) needs to make revisions. The state of the ...Test of consistency is critical for the analytic hierarchy process(AHP) methodology. When a pairwise comparison matrix(PCM) fails the consistency test, the decision maker(DM) needs to make revisions. The state of the art focuses on changing a single entry or creating a new matrix based on the original inconsistent matrix so that the modified matrix can satisfy the consistency requirement. However, we have noticed that the reason that causes inconsistency is not only numerical inconsistency, but also logical inconsistency, which may play a more important role in the whole inconsistency. Therefore, to realize satisfactory consistency, first of all, we should change some entries that form a directed circuit to make the matrix logically consistent, and then adjust other entries within acceptable deviations to make the matrix numerically consistent while preserving most of the original comparison information. In this paper, we firstly present some definitions and theories, based on which two effective methods are provided to identify directed circuits. Four optimization models are proposed to adjust the original inconsistent matrix. Finally, illustrative examples and comparison studies show the effectiveness and feasibility of our method.展开更多
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
针对风力发电机组频发的火灾事故,首先从人-机-环-管角度出发,通过统计分析近20年来全球81起风力发电机组火灾事故案例,得到了21项风力发电机组火灾事故的影响因素;然后通过事故树分析(fault tree analysis,FTA)法演绎推理得到了风力发...针对风力发电机组频发的火灾事故,首先从人-机-环-管角度出发,通过统计分析近20年来全球81起风力发电机组火灾事故案例,得到了21项风力发电机组火灾事故的影响因素;然后通过事故树分析(fault tree analysis,FTA)法演绎推理得到了风力发电机组火灾事故各基本事件的逻辑关系,并根据结构重要度进行了火灾事故致因的定性分析;接着采用模糊层次分析(fuzzy analytic hierarchy process,FAHP)法,将事故树的基本事件从人、机、环、管4个方面整合,构建出风力发电机组火灾事故致因评价指标体系,并以结构重要度系数的顺序为模糊判断矩阵的赋值依据,进行了火灾事故致因的定量分析;最后,根据综合分析结果提出了风力发电机组火灾事故的对策措施。结果表明:机和环境的不安全因素是引发火灾事故的主要致因;电气设备故障和雷击是最主要因素。该研究成果可为风力发电机组的火灾防治提供理论参考。展开更多
Value analysis of grain production influencing factors is a complex decision problem. This paper introduced a modified Analytic Hierarchy Process （AHP） accumulation factor, namely Solving Weight by AHP＇s Accumulati...Value analysis of grain production influencing factors is a complex decision problem. This paper introduced a modified Analytic Hierarchy Process （AHP） accumulation factor, namely Solving Weight by AHP＇s Accumulation Factor Sequence Evaluating Data. We used the arithmetical average to replace the expert marking, so that the possible decision mistakes by the subjective judgments could be avoided. We computed the case with this method, which obtained attribute value of 17 influencing factors of the potential food production in Heilongjiang Province, and the result of which was reasonable展开更多
基金supported by the National Natural Science Foundation of China(61601501 61502521)
文摘Test of consistency is critical for the analytic hierarchy process(AHP) methodology. When a pairwise comparison matrix(PCM) fails the consistency test, the decision maker(DM) needs to make revisions. The state of the art focuses on changing a single entry or creating a new matrix based on the original inconsistent matrix so that the modified matrix can satisfy the consistency requirement. However, we have noticed that the reason that causes inconsistency is not only numerical inconsistency, but also logical inconsistency, which may play a more important role in the whole inconsistency. Therefore, to realize satisfactory consistency, first of all, we should change some entries that form a directed circuit to make the matrix logically consistent, and then adjust other entries within acceptable deviations to make the matrix numerically consistent while preserving most of the original comparison information. In this paper, we firstly present some definitions and theories, based on which two effective methods are provided to identify directed circuits. Four optimization models are proposed to adjust the original inconsistent matrix. Finally, illustrative examples and comparison studies show the effectiveness and feasibility of our method.
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.
文摘Value analysis of grain production influencing factors is a complex decision problem. This paper introduced a modified Analytic Hierarchy Process （AHP） accumulation factor, namely Solving Weight by AHP＇s Accumulation Factor Sequence Evaluating Data. We used the arithmetical average to replace the expert marking, so that the possible decision mistakes by the subjective judgments could be avoided. We computed the case with this method, which obtained attribute value of 17 influencing factors of the potential food production in Heilongjiang Province, and the result of which was reasonable
