The author considers the possibility of generalizing the theory of classicalpolynomials to the higher dimensional case.The starting point is the splitting up ofthe second order differential operator of these polynomia...The author considers the possibility of generalizing the theory of classicalpolynomials to the higher dimensional case.The starting point is the splitting up ofthe second order differential operator of these polynomials into the derivation operator,considered as an operator between Hilbert spaces and its adjoint.In the case of severaldimensions the derivation operator is replaced by the Dirac operator.As however theset of polynomials in the vector variable x is not dense in the Hilbert modulesconsidered,first a decomposition of these modules in terms of spherical monogenicfunctions is proved.Then by applying the theory to each of the constituents,generalizations of the Gegenbauer and the Hermite polynomials are obtained.展开更多
直觉模糊集理论和可能性理论的融合是不确定问题领域的一个研究热点。文中提出了一种基于直觉模糊可能性分布的直觉模糊可能性测度(Intuitionistic Fuzzy Probability Measurement,IFPM),并在此基础上构建了三支决策模型。首先,定义了...直觉模糊集理论和可能性理论的融合是不确定问题领域的一个研究热点。文中提出了一种基于直觉模糊可能性分布的直觉模糊可能性测度(Intuitionistic Fuzzy Probability Measurement,IFPM),并在此基础上构建了三支决策模型。首先,定义了直觉模糊决策空间及该空间上的直觉模糊可能性分布,并对其性质进行了证明,给出了论域对象的隶属度和非隶属度可能性均值的计算方法。然后,讨论了论域对象的隶属度和非隶属度可能性均值与决策阈值的关系,分析了它们之间的概率分布情况。根据概率分布-可能性分布的转换关系,给出决策规则和三支决策模型,提出了一种基于直觉模糊可能性分布的IFPM决策风险计算方法。最后,考虑论域中对象的增减变化引起的IFPM变化,给出对应公式并对动态决策过程进行分析,同时通过实例验证了该模型的有效性。展开更多
文摘The author considers the possibility of generalizing the theory of classicalpolynomials to the higher dimensional case.The starting point is the splitting up ofthe second order differential operator of these polynomials into the derivation operator,considered as an operator between Hilbert spaces and its adjoint.In the case of severaldimensions the derivation operator is replaced by the Dirac operator.As however theset of polynomials in the vector variable x is not dense in the Hilbert modulesconsidered,first a decomposition of these modules in terms of spherical monogenicfunctions is proved.Then by applying the theory to each of the constituents,generalizations of the Gegenbauer and the Hermite polynomials are obtained.
文摘直觉模糊集理论和可能性理论的融合是不确定问题领域的一个研究热点。文中提出了一种基于直觉模糊可能性分布的直觉模糊可能性测度(Intuitionistic Fuzzy Probability Measurement,IFPM),并在此基础上构建了三支决策模型。首先,定义了直觉模糊决策空间及该空间上的直觉模糊可能性分布,并对其性质进行了证明,给出了论域对象的隶属度和非隶属度可能性均值的计算方法。然后,讨论了论域对象的隶属度和非隶属度可能性均值与决策阈值的关系,分析了它们之间的概率分布情况。根据概率分布-可能性分布的转换关系,给出决策规则和三支决策模型,提出了一种基于直觉模糊可能性分布的IFPM决策风险计算方法。最后,考虑论域中对象的增减变化引起的IFPM变化,给出对应公式并对动态决策过程进行分析,同时通过实例验证了该模型的有效性。
