Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

Multimodel Ensemble Forecast of Global Horizontal Irradiance at PV Power Stations Based on Dynamic Variable Weight

In the present study,multimodel ensemble forecast experiments of the global horizontal irradiance(GHI)were conducted using the dynamic variable weight technique.The study was based on the forecasts of four numerical models,namely,the China Meteorological Administration Wind Energy and Solar Energy Prediction System,the Mesoscale Weather Numerical Prediction System of China Meteorological Administration,the China Meteorological Administration Regional Mesoscale Numerical Prediction System-Guangdong,and the Weather Research and Forecasting Model-Solar,and observational data from four photovoltaic(PV)power stations in Yangjiang City,Guangdong Province.The results show that compared with those of the monthly optimal numerical model forecasts,the dynamic variable weight-based ensemble forecasts exhibited 0.97%-15.96%smaller values of the mean absolute error and 3.31%-18.40%lower values of the root mean square error(RMSE).However,the increase in the correlation coefficient was not obvious.Specifically,the multimodel ensemble mainly improved the performance of GHI forecasts below 700 W m^(-2),particularly below 400 W m^(-2),with RMSE reductions as high as 7.56%-28.28%.In contrast,the RMSE increased at GHI levels above 700 W m^(-2).As for the key period of PV power station output(02:00-07:00),the accuracy of GHI forecasts could be improved by the multimodel ensemble:the multimodel ensemble could effectively decrease the daily maximum absolute error(AE max)of GHI forecasts.Moreover,with increasing forecasting difficulty under cloudy conditions,the multimodel ensemble,which yields data closer to the actual observations,could simulate GHI fluctuations more accurately.

Evaluation on Fuzzy Variable Weight of Cultivated Land Fertility Based on GIS

[Objective] The modified variable weights based on constant weight and in- troduced theory of equalization function would better incorporate authentic index weights and make evaluation results of fertility more scientific. [Method] In Gaozhou City, the final weights of influential factors can be determined with the help of GIS and as per AHP and theory of variable weights. In addition, farmland fertility was e- valuated in an automatic and quantitative way and the spatial distribution pattern was analyzed as per fuzzy comprehensive evaluation. [Result] For farmlands at 58 505.027 8 hm2 in the city, farmlands from grade 1 to grade 8 account for 3.62%, 18.27%, 33.15%, 26.96%, 13.66%, 3.29%, 0.81% and 0.24%, respectively, which is in consistent with local condition. [Conclusion] These results have been applied di- rectly in test regions and constitute a rewarding exploration for fertility evaluation in South China.

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces

In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extend some known results.

Using Fuzzy Theory and Variable Weights for Water Quality Evaluation in Poyang Lake, China

Achieving water purity in Poyang Lake has become a major concern in recent years, thus appropriate evaluation of spatial and temporal water quality variations has become essential. Variations in 11 water quality parameters from 15 sampling sites in Poyang Lake were investigated from 2009 to 2012. An integrative fuzzy variable evaluation(IFVE) model based on fuzzy theory and variable weights was developed to measure variations in water quality. Results showed that: 1) only chlorophyll-a concentration and Secchi depth differed significantly among the 15 sampling sites(P < 0.01), whereas the 11 water quality parameters under investigation differed significantly throughout the seasons(P < 0.01). The annual variations of all water quality variables except for temperature, electrical conductivity, suspended solids and total phosphorus were considerable(P < 0.05). 2) The IFVE model was reasonable and flexible in evaluating water quality status and any possible ′bucket effect′. The model fully considered the influences of extremely poor indices on overall water quality. 3) A spatial analysis indicated that anthropogenic activities(particularly industrial sewage and dredging) and lake bed topography might directly affect water quality in Poyang Lake. Meanwhile, hydrological status and sewage discharged into the lake might be responsible for seasonal water quality variations.

Risk assessment of floor water inrush in coal mines based on MFIM-TOPSIS variable weight model

Floor water inrush is one of the main types of coal mine water hazards.With the development of deep mining,the prediction and evaluation of floor water inrush is particularly significant.This paper proposes a variable weight model,which combines a multi-factor interaction matrix(MFIM)and the technique for order performance by similarity to ideal solution(TOPSIS)to implement the risk assessment of floor water inrush in coal mines.Based on the MFIM,the interaction between seven evaluation indices,including the confined water pressure,water supply condition and aquifer water yield property,floor aquifuge thickness,fault water transmitting ability,fracture development degree,mining depth and thickness and their influence on floor water inrush were considered.After calculating the constant weights,the active degree evaluation was used to assign a variable weight to the indices.The values of the middle layer and final risk level were obtained by TOPSIS.The presented model was successfully applied in the 9901 working face in the Taoyang Mine and four additional coal mines and the results were highly consistent with the engineering situations.Compared with the existing nonlinear evaluation methods,the proposed model had advantages in terms of the weighting,principle explanation,and algorithm structure.

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

A variable weight approach for evidential reasoning

A variable weight approach was proposed to handle the probability deficiency problem in the evidential reasoning （ER） approach. The probability deficiency problem indicated that the inadequate information in the assessment result should be less than that in the input. However, it was proved that under certain circumstances, the ER approach could not solve the probability deficiency problem. The variable weight approach was based on two assumptions： 1） the greater weight should be given to the rule with more adequate information; 2） the greater weight should be given to the rules with less disparate information. Assessment results of two notional case studies show that 1） the probability deficiency problem is solved using the proposed variable weight approach, and 2） the information with less inadequacy and more disparity is provided for the decision makers to help reach a consensus.

Gray weighted algorithm for variable voltage CT reconstruction

In conventional computed tomography （CT） reconstruction based on fixed voltage, the projective data often ap- pear overexposed or underexposed, as a result, the reconstructive results are poor. To solve this problem, variable voltage CT reconstruction has been proposed. The effective projective sequences of a structural component are obtained through the variable voltage. The total variation is adjusted and minimized to optimize the reconstructive results on the basis of iterative image using algebraic reconstruction technique （ART）. In the process of reconstruction, the reconstructive image of low voltage is used as an initial value of the effective proiective reconstruction of the adjacent high voltage, and so on until to the highest voltage according to the gray weighted algorithm. Thereby the complete structural information is reconstructed. Simulation results show that the proposed algorithm can completely reflect the information of a complicated structural com- ponent, and the pixel values are more stable than those of the conventional.

Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

Let T be the singular integral operator with variable kernel, T＊ be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator D^γ on the weighted Morrey spaces.

Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables

By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.

The Boundedness of the Singular Integral Operator with Variable Calder′on-Zygmund Kernel on Weighted Morrey Spaces

In this paper, we will study the boundedness of the singular integral operator with variable Calder′on-Zygmund kernel on the weighted Morrey spaces Lp,κ(ω) for q′≤ p < ∞and 0 < κ < 1. Furthermore, the boundedness for the commutator with BMO functions is also obtained.

Nonlinear combined forecasting model based on fuzzy adaptive variable weight and its application

In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using conceptions of the relative error,the change tendency of the forecasted object,gray basic weight and adaptive control coefficient on the basis of the method of fuzzy variable weight.Based on Visual Basic 6.0 platform,a fuzzy adaptive variable weight combined forecasting and management system was developed.The application results reveal that the forecasting precisions from the new nonlinear combined forecasting model are higher than those of other single combined forecasting models and the combined forecasting and management system is very powerful tool for the required decision in complex industry system.

TLBO with variable weights applied to shop scheduling problems

The teaching–learning-based optimisation (TLBO) algorithm is a population-based metaheuristic inspired on the teaching–learning process observed in a classroom. It has been successfully used in a wide range of applications. In this study, the authors present a variant version of TLBO. In the proposed version, different weights are assigned to students during the student phase, with higher weights being assigned to students with better solutions. Three different approaches to assign weights are investigated. Numerical experiments with benchmark instances of the flow-shop and the job-shop scheduling problems are carried out to investigate the performance of the proposed approaches. They compare the proposed approaches with the original TLBO algorithm and with two variants of TLBOs proposed in the literature in terms of solution quality, convergence speed and simulation time. The results obtained by the application of a Friedman statistical test showed that the proposed approaches outperformed the original version of TLBO in terms of convergence, with no significant losses in the average makespan. The additional simulation time required by the proposed approaches is small. The best performance was achieved with the approach of assigning a fixed weight to half the students with the best solutions and assigning zero to other students.

Information Security Testing Model Based on Variable Weights Fuzzy Comprehensive Evaluation

Nowadays,clear evaluation models and methods are lacking in classified protection of information system,which our country is making efforts to promote.The quantitative evaluation of classified protection of information system security is studied.An indicators system of testing and evaluation is established.Furthermore,a model of unit testing and evaluation and a model of entirety testing and evaluation are presented respectively.With analytic hierarchy process and two-grade fuzzy comprehensive evaluation,the subjective and uncertain data of evaluation will be quantitatively analyzed by comprehensive evaluation.Particularly,the variable weight method is used to model entirety testing and evaluation.It can solve the problem that the weights need to be adjusted because of the relationship role which enhances or reduces security of information system.Finally,the paper demonstrates that the model testing and evaluation can be validly used to evaluate the information system by an example.The model proposed in this paper provides a new valuable way for classified protection of information system security.

ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W(L^(p(x)), L_m^q)

In [4], a new family W（L^p（x）, Lm^q） of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p（x） （R） and the global component is a weighted Lebesgue space Lm^q （R）. This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W （L^p（x）, Lm^q） = L^q （R）. Later we give some characterization of Wiener amalgam space W （L^p（x）, Lm^q）.In Section 3 we define the Wiener amalgam space W （FL^p（x）, Lm^q） and investigate some properties of this space, where FL^p（x） is the image of L^p（x） under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces.

A comprehensive evaluation of enterprise emergency management capacity （EEMC） based on variable weight gray cluster

On the basis of the initial definition of Enterprise Emergency Management Capacity（EEMC）, the paper has established evaluation index system of EEMC, and provided a method to calculate index weight, with the regard to subjectivity existing in the comprehensive evaluation of EEMC multi-indicators, in accordance with the principle of Variable weight Gray Cluster, which makes the weight of indicators generate automatically in the evaluation process and not judged by human, thus decreasing subjective factors during the evaluation.