An efficient algorithm for low-order direct discrete-time implementation of fractional order transfer functions

Fractional order systems become increasingly popular due to their versatility in modelling and control applications across various disciplines. However, the bottleneck in deploying these tools in practice is related to their implementation on real-life systems. Numerical approximations are employed but their complexity no longer match the attractive simplicity of the original fractional order systems. This paper proposes a low-order, computationally stable and efficient method for direct approximation of general order (fractional order) systems in the form of discrete-time rational transfer functions, e.g. processes, controllers. A fair comparison to other direct discretization methods is presented, demonstrating its added value with respect to the state of art.     

基于增强算子的污染土雷达图像特征提取仿真

针对雷达图像特征提取效率低、精度不高等问题,提出一种基于增强算子的污染土雷达图像特征提取方法。首先使用多尺度非均匀滤波把含有噪声与不含噪声的像素点灰度值、构成因素及像素加权灰度密度三个特征进行划分,完成雷达图像去噪。其次提出增强算子方法,将图像数据转变至图像的空间域,以此判断污染土雷达图像内是否存在对比度不高区域和细微区域。最后采用灰色关联分析计算超像素之间的相似度,运用MLS增强算子对曲面进行拟合,通过高斯曲率与平均曲率构建出特征判断准则,提高图像特征提取完整性,实现污染土雷达图像特征的精准提取。仿真结果表明,与传统方法相比所提方法计算速度较快,雷达特征提取效率较高,可大幅提升污染土雷达图像特征提取准确率。     

The power average operator for unbalanced linguistic term sets

In order to aggregate linguistic values of unbalanced linguistic term sets, this paper introduces the linguistic proportional 2-tuple power average operator, which can reflect the relationship among the aggregated values by considering the support for each value from others. Its advantage regarding other linguistic power average operators enables it to be used in such cases in which the linguistic term sets are not necessarily to be balanced, and the membership functions of the linguistic terms are utilized in the computational processes. In this operator, a linguistic proportional 2-tuple is represented by a normalized numerical representation. Some properties of the operator are discussed. A group decision making model based on the proposed operator is introduced. Finally an illustrative example is presented.     

An improved partheno genetic algorithm for multi-objective economic dispatch in cascaded hydropower systems

The multi-objective economic dispatch (MOED) problem in cascaded hydropower systems is a complicated nonlinear optimization problem with a group of complex constraints. In this paper, an improved partheno genetic algorithm (IPGA) for resolving the MOED problem in hydropower energy systems based on the non-uniform mutation operator is proposed. In the new algorithm, the crossover operator is removed and only mutation operation is made, which makes it simpler than GA in the genetic operations and not generate invalid offspring during evolution. With the help of incorporating greedy selection idea into the non-uniform mutation operator, IPGA searches the solution space uniformly at the early stage and very locally at the later stage, which makes it avoid the random blind jumping and stay at the promising solution areas. Finally, the proposed algorithm is applied to a realistic hydropower energy system with two giant scale cascaded hydropower plants in China. Compared with other algorithms, the results obtained using IPGA verify its superiority in both efficiency and precision.     

Fermatean fuzzy linguistic set and its application in multicriteria decision making

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter in the proposed distance measure is also discussed.     

Exponential ergodicity of some Markov dynamical systems with application to a Poisson-driven stochastic differential equation

We are concerned with the asymptotics of the Markov chain given by the post-jump locations of a certain piecewise-deterministic Markov process with a state-dependent jump intensity. We provide sufficient conditions for such a model to possess a unique invariant distribution, which is exponentially attracting in the dual-bounded Lipschitz distance. Having established this, we generalize a result of J. Kazak on the jump process defined by a Poisson-driven stochastic differential equation with a solution-dependent intensity of perturbations.     

An interval-valued exceedance method in MCDM with uncertain satisfactions

Multicriteria decision-making problems have been applied to many applications for its practicality. Nevertheless, when the evaluated satisfactions are more complex, such as interval-valued distributions, how to reasonably obtain the aggregation results of alternatives is still an open issue. In this paper, an interval-valued exceedance method is proposed to solve such a question based on the Golden Rule representative value and probabilistic exceedance method. Due to good performance of expressing uncertain information, the Golden Rule representative value method is used to order interval-valued satisfactions after an effective normalization process. In addition, a quantifier-based ordered weighted averaging operator is also introduced to consider the preferences of decision makers. A realistic application of supplier selection is shown to illustrate the practicality of the proposed method.     

基于变异算子和邻域值自适应的MOEA/D算法

基于分解的多目标进化算法（MOEA/D）在解决多目标问题时，具有简单有效的特点。但多数MOEA/D采用固定的控制参数，导致全局搜索能力差，难以平衡收敛性和多样性。针对以上问题提出一种基于变异算子和邻域值自适应的多目标优化算法。该算法根据种群中个体适应度值的分散或集中程度进行判断，并据此对变异算子进行自适应的调节，从而增强算法的全局搜索能力；根据进化所处的阶段以及个体适应度值的集中程度，自适应地调节邻域值大小，保证每个个体在不同的进化代数都有一个邻域值大小；在子问题邻域中，统计子问题对应个体的被支配数，通过判断被支配数是否超过设定的上限，来决定是否将Pareto支配关系也作为邻域内判断个体好坏的准则之一。将提出的算法与传统的MOEA/D在标准测试问题上进行对比。实验结果表明，提出的算法求得的解集具有更好的收敛性和多样性，在求解性能上具有一定的优势。     

A RBF based finite difference method for option pricing under regime-switching jump-diffusion model

Abstract

In this article, we presented a method for option pricing problem under regime-switching jump-diffusion models. We have proposed a numerical method for solving a partial integro-differential equation (PIDE) for pricing European option and for solving linear complementarity problem (LCP), to evaluate the price of American options. We use implicit explicit method for time semi discretization, followed by radial basis function based finite difference (RBF-FD) method for spatial discretization to solve PIDE. The proposed method is further extended to solve the LCP by coupling it with operator splitting method. Numerical simulation is done for European and American option to demonstrate efficiency and accuracy of the proposed method.