In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of ...In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of uncertainty comparison matrix and uncertainty weights are proposed in this paper. It also gives the uncertain variable method to calculate uncertainty weights from uncertainty comparison matrices, which can be either consistent or inconsistent. The proposed uncertain variable method (UVM) is also applicable to interval comparison matrices and fuzzy comparison ma-trices when they are transformed into uncertainty comparison matrices using linear uncertainty distribution or zigzag uncertainty distribution. The proposed approach is computationally efficient as it consists of solving only inverse uncertainty distribution. At the end of this paper, five numerical examples are given to illustrate the method.展开更多
Uncertainty theory is a new branch of axiomatic mathematics for studying the subjective uncertainty. In uncertain theory, uncertain variable is a fundamental concept, which is used to represent imprecise quantities (u...Uncertainty theory is a new branch of axiomatic mathematics for studying the subjective uncertainty. In uncertain theory, uncertain variable is a fundamental concept, which is used to represent imprecise quantities (unknown constants and unsharp concepts). Entropy of uncertain variable is an important concept in calculating uncertainty associated with imprecise quantities. This paper introduces the single parameter entropy of uncertain variable, and proves its several important theorems. In the framework of the single parameter entropy of uncertain variable, we can obtain the supremum of uncertainty of uncertain variable by choosing a proper q. The single parameter entropy of uncertain variable makes the computing of uncertainty of uncertain variable more general and flexible.展开更多
针对电力系统中故障特征和运行信息的不确定性,提出了基于随机集理论的不确定信息的表示与建模方法。该方法考虑元件故障发生的不确定性和负荷波动的随机性,将描述电网元件参数和节点负荷信息的变量转换为其随机集形式。基于随机集扩展...针对电力系统中故障特征和运行信息的不确定性,提出了基于随机集理论的不确定信息的表示与建模方法。该方法考虑元件故障发生的不确定性和负荷波动的随机性,将描述电网元件参数和节点负荷信息的变量转换为其随机集形式。基于随机集扩展准则,通过区间潮流计算将参数的不确定性映射到风险指标的不确定性,并利用随机集的信任测度和似真测度构造风险指标的上下累积概率分布函数。基于证据理论的随机集描述,利用Dempster-Shafer证据组合规则对所有系统状态下获得的基本概率分配(basic probability assignment,BPA)进行融合,获得系统风险水平的一致性描述。IEEE 39算例系统的计算结果证明了该方法的合理性。展开更多
文摘In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of uncertainty comparison matrix and uncertainty weights are proposed in this paper. It also gives the uncertain variable method to calculate uncertainty weights from uncertainty comparison matrices, which can be either consistent or inconsistent. The proposed uncertain variable method (UVM) is also applicable to interval comparison matrices and fuzzy comparison ma-trices when they are transformed into uncertainty comparison matrices using linear uncertainty distribution or zigzag uncertainty distribution. The proposed approach is computationally efficient as it consists of solving only inverse uncertainty distribution. At the end of this paper, five numerical examples are given to illustrate the method.
文摘Uncertainty theory is a new branch of axiomatic mathematics for studying the subjective uncertainty. In uncertain theory, uncertain variable is a fundamental concept, which is used to represent imprecise quantities (unknown constants and unsharp concepts). Entropy of uncertain variable is an important concept in calculating uncertainty associated with imprecise quantities. This paper introduces the single parameter entropy of uncertain variable, and proves its several important theorems. In the framework of the single parameter entropy of uncertain variable, we can obtain the supremum of uncertainty of uncertain variable by choosing a proper q. The single parameter entropy of uncertain variable makes the computing of uncertainty of uncertain variable more general and flexible.
文摘针对电力系统中故障特征和运行信息的不确定性,提出了基于随机集理论的不确定信息的表示与建模方法。该方法考虑元件故障发生的不确定性和负荷波动的随机性,将描述电网元件参数和节点负荷信息的变量转换为其随机集形式。基于随机集扩展准则,通过区间潮流计算将参数的不确定性映射到风险指标的不确定性,并利用随机集的信任测度和似真测度构造风险指标的上下累积概率分布函数。基于证据理论的随机集描述,利用Dempster-Shafer证据组合规则对所有系统状态下获得的基本概率分配(basic probability assignment,BPA)进行融合,获得系统风险水平的一致性描述。IEEE 39算例系统的计算结果证明了该方法的合理性。
