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
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
In operation,risk arising from power transformer faults is of much uncertainty and complicacy.To timely and objectively control the risks,a transformer risk assessment method based on fuzzy analytic hierarchy process(...In operation,risk arising from power transformer faults is of much uncertainty and complicacy.To timely and objectively control the risks,a transformer risk assessment method based on fuzzy analytic hierarchy process(FAHP) and artificial neural network(ANN) from the perspective of accuracy and quickness is proposed.An analytic hierarchy process model for the transformer risk assessment is built by analysis of the risk factors affecting the transformer risk level and the weight relation of each risk factor in transformer risk calculation is analyzed by application of fuzzy consistency judgment matrix;with utilization of adaptive ability and nonlinear mapping ability of the ANN,the risk factors with large weights are used as input of neutral network,and thus intelligent quantitative assessment of transformer risk is realized.The simulation result shows that the proposed method increases the speed and accuracy of the risk assessment and can provide feasible decision basis for the transformer risk management and maintenance decisions.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
Selection of materials,as an area of design research,has been under considerable interest over the years.Materials selection is one of the most important activities in the product development process.Inappropriate dec...Selection of materials,as an area of design research,has been under considerable interest over the years.Materials selection is one of the most important activities in the product development process.Inappropriate decision of materials can cause the product to be reproduced or remanufactured.To avoid this circumstance,one of the useful tools that can be employed in determining the most appropriate material is analytical hierarchy process(AHP).To illustrate the application of AHP,six different types of composite materials were considered.The most appropriate one for suitability of use in manufacturing automotive bumper beam was determined by considering eight main selection factors and 12 sub-factors.The AHP analysis reveals that the glass fibre epoxy is the most appropriate material because it has the highest value(25.7%,mass fraction) compared with other materials.The final material is obtained by performing six different scenarios of the sensitivity analysis.It is proved that glass fibre epoxy is the most optimum decision.展开更多
子句选择是自动定理证明器(ATP)的核心部分,通过优化子句选择方法能够提升ATP的能力和效率。当前,传统基于属性优先级的逐一筛选方法虽然能够实现子句选择,但难以对子句进行全面评估,并且缺乏灵活性。因此,提出基于AHP_TOPSIS的子句动...子句选择是自动定理证明器(ATP)的核心部分,通过优化子句选择方法能够提升ATP的能力和效率。当前,传统基于属性优先级的逐一筛选方法虽然能够实现子句选择,但难以对子句进行全面评估,并且缺乏灵活性。因此,提出基于AHP_TOPSIS的子句动态选择方法。该方法通过层次分析法(AHP)计算子句各个属性的权重,再利用权重结果结合逼近理想解排序法(TOPSIS)对子句进行评估排序,从而为子句选择提供依据。在AHP中,考虑到子句属性的动态变化,引入阶段感知与平滑过渡的方法,使得判断矩阵能够根据推导进程动态调整,将AHP拓展为动态AHP。同时,根据上述子句选择方法实现相应的算法,并将算法应用于一阶逻辑定理证明器CSE(Contradiction Separation Extension)中形成新的证明器CSE_AT。利用该证明器对2021—2024年的TPTP(Thousands of Problems for Theorem Provers)问题库中的一阶逻辑问题进行测试,实验结果表明,CSE_AT比CSE多证明了22个定理,且CSE_AT证明的大部分定理的Rating值集中在[0.6,0.9]。可见,基于AHP_TOPSIS的子句动态选择方法能够优化演绎路径,从而提升证明器的证明能力。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Project(50977003) supported by the National Natural Science Foundation of China
文摘In operation,risk arising from power transformer faults is of much uncertainty and complicacy.To timely and objectively control the risks,a transformer risk assessment method based on fuzzy analytic hierarchy process(FAHP) and artificial neural network(ANN) from the perspective of accuracy and quickness is proposed.An analytic hierarchy process model for the transformer risk assessment is built by analysis of the risk factors affecting the transformer risk level and the weight relation of each risk factor in transformer risk calculation is analyzed by application of fuzzy consistency judgment matrix;with utilization of adaptive ability and nonlinear mapping ability of the ANN,the risk factors with large weights are used as input of neutral network,and thus intelligent quantitative assessment of transformer risk is realized.The simulation result shows that the proposed method increases the speed and accuracy of the risk assessment and can provide feasible decision basis for the transformer risk management and maintenance decisions.
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
基金the financial support through Research University Grant Scheme 2007 (RUG 2007) with vote number 91045
文摘Selection of materials,as an area of design research,has been under considerable interest over the years.Materials selection is one of the most important activities in the product development process.Inappropriate decision of materials can cause the product to be reproduced or remanufactured.To avoid this circumstance,one of the useful tools that can be employed in determining the most appropriate material is analytical hierarchy process(AHP).To illustrate the application of AHP,six different types of composite materials were considered.The most appropriate one for suitability of use in manufacturing automotive bumper beam was determined by considering eight main selection factors and 12 sub-factors.The AHP analysis reveals that the glass fibre epoxy is the most appropriate material because it has the highest value(25.7%,mass fraction) compared with other materials.The final material is obtained by performing six different scenarios of the sensitivity analysis.It is proved that glass fibre epoxy is the most optimum decision.
文摘子句选择是自动定理证明器(ATP)的核心部分,通过优化子句选择方法能够提升ATP的能力和效率。当前,传统基于属性优先级的逐一筛选方法虽然能够实现子句选择,但难以对子句进行全面评估,并且缺乏灵活性。因此,提出基于AHP_TOPSIS的子句动态选择方法。该方法通过层次分析法(AHP)计算子句各个属性的权重,再利用权重结果结合逼近理想解排序法(TOPSIS)对子句进行评估排序,从而为子句选择提供依据。在AHP中,考虑到子句属性的动态变化,引入阶段感知与平滑过渡的方法,使得判断矩阵能够根据推导进程动态调整,将AHP拓展为动态AHP。同时,根据上述子句选择方法实现相应的算法,并将算法应用于一阶逻辑定理证明器CSE(Contradiction Separation Extension)中形成新的证明器CSE_AT。利用该证明器对2021—2024年的TPTP(Thousands of Problems for Theorem Provers)问题库中的一阶逻辑问题进行测试,实验结果表明,CSE_AT比CSE多证明了22个定理,且CSE_AT证明的大部分定理的Rating值集中在[0.6,0.9]。可见,基于AHP_TOPSIS的子句动态选择方法能够优化演绎路径,从而提升证明器的证明能力。
