A group decision making method based on double hesitant linguistic preference relations

A simple decision method is proposed to solve the group decision making problems in which the weights of decision organizations are unknown and the preferences for alternatives are provided by double hesitant linguistic preference relations. First, double hesitant linguistic elements are defined as representing the uncertain assessment information in the process of group decision making accurately and comprehensively, and the double hesitant linguistic weighted averaging operator is developed based on the defined operational laws for double hesitant linguistic elements. Then, double hesitant linguistic preference relations are defined and a means to objectively determine the weights of decision organizations is put forward using the standard deviation of scores of preferences provided by the individual decision organization for altematives. Finally the correlation coefficient between the scores of preferences and the scores of preferences are provided by the other decision organizations. Accordingly, a group decision method based on double hesitant linguistic preference relations is proposed, and a practical example of the Jiudianxia reservoir operation alternative selection is used to illustrate the practicability and validity of the method. Finally, the proposed method is compared with the existing methods. Comparative results show that the proposed method can deal with the double hesitant linguistic preference information directly, does not need any information transformation, and can thus reduce the loss of original decision information.

On Turán type inequality with doubling weights and A weights

Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities under L^p norm for 0〈p≤∞. Our results essentially extend the result of Wang and Zhou （2002）, and the method used in this paper is simpler and more direct than that of Wang and Zhou （2002）. The results and methods have their own values in approximation theory and computation.

Composition operators on weighted Bergman spaces induced by doubling weights

Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.

Intelligent Voltage Control Method in Active Distribution Networks Based on Averaged Weighted Double Deep Q-network Algorithm

High penetration of distributed renewable energy sources and electric vehicles(EVs)makes future active distribution network(ADN)highly variable.These characteristics put great challenges to traditional voltage control methods.Voltage control based on the deep Q-network(DQN)algorithm offers a potential solution to this problem because it possesses humanlevel control performance.However,the traditional DQN methods may produce overestimation of action reward values,resulting in degradation of obtained solutions.In this paper,an intelligent voltage control method based on averaged weighted double deep Q-network(AWDDQN)algorithm is proposed to overcome the shortcomings of overestimation of action reward values in DQN algorithm and underestimation of action reward values in double deep Q-network(DDQN)algorithm.Using the proposed method,the voltage control objective is incorporated into the designed action reward values and normalized to form a Markov decision process(MDP)model which is solved by the AWDDQN algorithm.The designed AWDDQN-based intelligent voltage control agent is trained offline and used as online intelligent dynamic voltage regulator for the ADN.The proposed voltage control method is validated using the IEEE 33-bus and 123-bus systems containing renewable energy sources and EVs,and compared with the DQN and DDQN algorithms based methods,and traditional mixed-integer nonlinear program based methods.The simulation results show that the proposed method has better convergence and less voltage volatility than the other ones.

Adjusted Log-rank Test with Double Inverse Weighting under Dependent Censoring

It is a common issue to compare treatment-specific survival and the weighted log-rank test is the most popular method for group comparison. However, in observational studies, treatments and censoring times are usually not independent, which invalidates the weighted log-rank tests. In this paper, we propose adjusted weighted log-rank tests in the presence of non-random treatment assignment and dependent censoring. A double-inverse weighted technique is developed to adjust the weighted log-rank tests. Specifically, inverse probabilities of treatment and censoring weighting are involved to balance the baseline treatment assignment and to overcome dependent censoring, respectively. We derive the asymptotic distribution of the proposed adjusted tests under the null hypothesis, and propose a method to obtain the critical values. Simulation studies show that the adjusted log-rank tests have correct sizes whereas the traditional weighted log-rank tests may fail in the presence of non-random treatment assignment and dependent censoring. An application to oropharyngeal carcinoma data from the Radiation Therapy Oncology Group is provided for illustration.

OPERATORS ON CORNER MANIFOLDS WITH EXIT TO INFINITY

We study （pseudo-）differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y. The typical operators A are corner degenerate in a specific way. They are described Cmodulo ＇lower order terms＇） by a principal symbolic hierarchy σ（A） = （σψ （A）, σ∧ CA）, σ∧ （A））, where σψ is the interior symbol and σ∧（A） （y, η）, （y, η） ∈ T＊Y／0, the Coperator-valued） edge symbol of ＇first generation＇, cf. [1]. The novelty here is the edge symbol σ∧ of ＇second generation＇, parametrised by （z, ζ） ∈ T＊Z ／ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.

On the Multi-Dimensional Duality Principle of Sawyer Type

A multi-dimensional version of the duality principle of Sawyer type [1] is obtained whenever the corresponding weight satisfies some doubling property.