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15 February 2019, Volume 36 Issue 1 Previous Issue    Next Issue

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Variable Selection Ensemble Methods ZHANG Chun-xia, LI Jun-li 2019, 36 (1):  1-17.  doi: 10.3969/j.issn.1005-3085.2019.01.001 Abstract ( 159 )   PDF (249KB) ( 277 )   Save With the emergence of massive high-dimensional data in many research and application fields, it is crucial to mine valuable information by using the sparsity of high-dimensional data. Being an effective tool for building an interpretative model, improving inference and prediction accuracy, variable selection plays an increasingly important role in statistical modelling of high-dimensional data. Because ensemble learning has advantages to significantly improve selection accuracy, to alleviate the instability of traditional selection methods, and to reduce falsely including noise variables, variable selection ensemble (VSE) methods have gained considerable interest in context of variable selection. In order to provide a systematic reference for researchers in related fields, this paper presents a detailed survey of the existing VSEs and categorizes them into two classes according to their different strategies. The main characteristics of the methods in each class are also analyzed. In the meantime, some simulated experiments are carried out to investigate the selection and prediction performance of some representative VSE techniques. Finally, several research directions of VSEs deserved to be further studied are discussed. Related Articles | Metrics

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Response Capability of Fuzzy Systems Based on Quintuple I Algorithm LI Jun-xia, LI De-chao 2019, 36 (1):  18-32.  doi: 10.3969/j.issn.1005-3085.2019.01.002 Abstract ( 146 )   PDF (184KB) ( 249 )   Save In order to apply the fuzzy system based on the QIP algorithm well in practice, research on responsiveness and general approximation of such fuzzy systems is of great significance. In this paper, the fuzzy inference expression of 5-I algorithm based on S implication and Zadeh implication is proposed. Furthermore, by using single-point fuzzification and gravity center defuzzification method, we find that for S implication and R implication, a single-input single-output (SISO) fuzzy system based on QIP algorithm has only step output conditions and can not approximates a function well. The preceding property does not necessarily exist in such fuzzy systems with Zadeh implication. In addition, in the multi-rule SISO fuzzy system based on QIP algorithm, fuzzy reasoning is independent of the order of aggregation under certain conditions. Finally, a concrete example is provided to demonstrate responsiveness and universal approximation of fuzzy systems based on the five-I algorithm. Related Articles | Metrics

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A Spatially Adaptive Edge-preserving Denoising Method for Seismic Data Based on Variational PDE WANG De-hua, GAO Jing-huai, ZHANG Li-li 2019, 36 (1):  33-42.  doi: 10.3969/j.issn.1005-3085.2019.01.003 Abstract ( 208 )   PDF (1567KB) ( 412 )   Save Seismic data denoising is a basic issue of seismic data processing, and its signal-to-noise ratio affects directly the reliability of seismic data and the accuracy of geological interpretation. In this paper, we firstly construct an edge detection function based on a nonlinear diffusion. On the basis, we establish a fractional adaptive edge-preserving denoising model in the variational framework, and calculate the fractional Euler-Lagrange equation for solving the proposed model. Finally, the proposed method is applied to synthetic seismic data and field seismic data denoising, and the effectiveness and practicability of the new method are verified by comparing with the traditional denoising method. Related Articles | Metrics

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The Comparative Research on Platform Pricing Model Between Loyalty Rewards with Uniform Pricing ZHU Zhu 2019, 36 (1):  43-58.  doi: 10.3969/j.issn.1005-3085.2019.01.004 Abstract ( 184 )   PDF (197KB) ( 280 )   Save The price strategy of platform pricing plays an important role in assisting managers who participate in platform competition. Amony different strategies, two important ones, loyalty rewarding and uniform pricing have their own emphasis. In this paper, a two-stage dynamic model for platform pricing is proposed, and the impact of price strategies on platform pricing and profit is comparably analyzed in the model, and then some propositions are obtained. The results show that the pricing of the platform at the second stage and the customer retention rate are positively correlated with the endogenous transfer costs generated by incentives to loyal customer. The equilibrium results of the unified pricing model show that the total profit changes of the two stages depend on the exogenous transfer cost and the expected discount coefficient of users. Related Articles | Metrics

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Approximating Multifunctions and Approximate Solutions in Set-valued Optimization KONG Xiang-yu, YU Guo-lin, LIU San-yang 2019, 36 (1):  59-70.  doi: 10.3969/j.issn.1005-3085.2019.01.005 Abstract ( 156 )   PDF (153KB) ( 343 )   Save Optimality conditions and duality are of great importance in vector optimization with set-valued mappings. The aim of this paper is to establish the sufficient optimality condition and duality theorems for a kind of generalized convex set-valued optimization problems. Based upon the concept of invexity in terms of cone-approximating multifunction for a set-valued map, a new kind of generalized invexities, termed subinvex set-valued mappings, is introduced, and optimality conditions and duality theorems are investigated for its constraint set-valued optimization. It also presents an example to illustrate their existence. By employing the analytic method, a sufficient optimality condition and weak, strong, converse duality theorems between Mond-Weir and Wolfe dual problems and the primal constraint set-valued optimization problems are proposed in sense of weakly approximate minimizers. The results  obtained in this note enrich and deepen the theory and applications of set-valued optimization. Related Articles | Metrics

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Existence of Solutions for Semilinear Delay Fuzzy Differential Equations LIU Juan, XIAO Jian-zhong, YAO Zhong-hao 2019, 36 (1):  71-84.  doi: 10.3969/j.issn.1005-3085.2019.01.006 Abstract ( 196 )   PDF (160KB) ( 284 )   Save Fuzzy differential equations are commonly used to describe the changing process with uncertain conditions. And its theory is widely applied to many different practical problems. The aim of this paper is to study the existence of solutions for semilinear delay fuzzy differential equations. We use a fixed point theorem of weakly contractive mappings to transform the existence of solutions into the existence of fixed points of an operator, and establish the theorem of existence of solutions for the equations. In addition, an example is given to illustrate the applicability of the theoretical results. Related Articles | Metrics

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A Nonstandard Numerical Methods for a Mathematical Model for Cholera LIAO Shu, YANG Wei-ming 2019, 36 (1):  85-98.  doi: 10.3969/j.issn.1005-3085.2019.01.007 Abstract ( 222 )   PDF (281KB) ( 565 )   Save By applying a nonstandard finite difference scheme, we construct and solve a discretized cholera epidemic model. The scheme can ensure that equilibrium points, the positivity and boundedness of solutions to the discrete model is the same as the original mathematical model. We have proved that when the basic reproduction number is less than 1, the disease-free equilibrium is locally and globally asymptotically stable. When the basic reproduction number is greater than 1, we prove that the endemic equilibrium is globally asymptotically stable by constructing a suitable Lyapunov function. Finally, the NSFD scheme can be well suited to numerically solve the cholera outbreak in Zimbabwe. Related Articles | Metrics

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Chaos Synchronization of Fractional-order Simple Pendulum Systems Based on Terminal Sliding Mode Control CHENG Chun-rui, ZHU Jun-hui, MAO Bei-xing 2019, 36 (1):  99-105.  doi: 10.3969/j.issn.1005-3085.2019.01.008 Abstract ( 140 )   PDF (644KB) ( 410 )   Save In this paper, a novel adaptive sliding mode approach for synchronization combining the fractional calculus with terminal sliding mode control is proposed. The scheme is applied to synchronize a class of fractional-order simple pendulum chaotic systems in the presence of model uncertainties and external disturbances. First, based on the fractional calculus a new nonsingular fractional-order terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is analytically proved using the fractional Lyapunov stability theorem. Then, for the case that the bounds of the uncertainties and external disturbances are assumed to be unknown in advance, appropriate adaptive laws are proposed. Afterwards, based on ideas of the adaptive laws and finite-time control, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite peroid. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, a numerical simulation is presented to demonstrate the applicability and effectiveness of the proposed scheme. Related Articles | Metrics

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An Algorithm for Linear Convolution Based on Generalized Discrete Fourier Transform DAI Yin-yun, YI Hua, YU Tao 2019, 36 (1):  106-114.  doi: 10.3969/j.issn.1005-3085.2019.01.009 Abstract ( 162 )   PDF (109KB) ( 440 )   Save Linear convolutions can be converted to circular convolutions so that a fast trans-form with a convolution property can be used to implement the computation, which method is known as the FFT-based fast algorithm of linear convolution. In this paper, a novel proof of the computation of linear convolution based on Generalized Discrete Fourier Transform (GDFT) is constructed. Firstly, a relationship of linear convolution and circular convolution is thoroughly analyzed. Secondly, the computation of the linear convolution is translated to the multiplication of a special Toeplitz matrix and the signal. Lastly, this multiplication is accomplished by the inverse GDFT of the product of the GDFTs of the signal and the filter. Furthermore, a new method about the computation of complex linear convolution is constructed by using the GDFT with parameter $-1$, which is not considered in the previous literatures. Related Articles | Metrics

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Equicontinuous of Fuzzy Dynamical Systems and Distal Fuzzy Dynamic System LU Han-chuan, FU Wen-qing, LI Sheng-gang 2019, 36 (1):  115-122.  doi: 10.3969/j.issn.1005-3085.2019.01.010 Abstract ( 129 )   PDF (114KB) ( 270 )   Save The equicontinuity has strong stability, it can be ensured within a pre-given error range if the error of its initial state is small enough. This dynamic behavior revealed by equicontinuity has high application value. Therefore, it has important research value in the theory of differential equation stability and topological dynamic system. Equicontinuity and distal are closely related to chaos and so on. In order to study them under the background of fuzzyness, a method of generalization is used to give the definition of the equicontinuity in fuzzy dynamic systems with establishing of fuzzy dynamic system. The following results were obtained: 1)~Equivalent propositions of the equicontinuity in fuzzy dynamic system; 2)~The equicontinuity is preserved under fuzzy uniform topologically conjugate mapping; 3)~The sufficient and necessary condition of two fuzzy dynamical systems to be distal. Related Articles | Metrics