Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

In this paper, we extend the Bonferroni mean (BM) operator with the picture fuzzy numbers (PFNs) to propose novel picture fuzzy aggregation operators and demonstrate their application to multicriteria decision making (MCDM). On the basis of the algebraic operational rules of PFNs and BM, we introduce some aggregation operators: the picture fuzzy Bonferroni mean, the picture fuzzy normalized weighted Bonferroni mean, and the picture fuzzy ordered weighted Bonferroni mean. Then, a new picture fuzzy MCDM method is proposed with the help of the proposed operators. Lastly, a practical application of proposed model is given to verify the developed model and related results of the proposed model is compared with the results of the existing models to indicate its applicability.     

基于系统矩阵有序实Schur分解的模型降阶

对复杂高阶系统进行模型简化，为研究与设计系统提供了方便的条件。对系统模型的降阶是控制系统设计与仿真工作者的一个重要研究课题，对高阶复杂系统的分析、设计、仿真等具有重要的理论意义和工程实用价值。针对目前比较成熟的基于系统矩阵的有序实Schur分解方法，提出了采用时矩输出拟合来改善降阶系统输出响应逼近程度的改进方法，从而使简化模型具有输出误差更小、计算简便等优点，通过给出的实例仿真证实了这一点。     

The magnetic structure of TbNiSiD1.78

TbNiSiD_1.78 has been studied by powder neutron diffraction below 100 K. The compound takes the hexagonal room temperature structure at 100 and 50 K (P6₃/mmc). At 2 K, below the antiferromagnetic ordering temperature of 10 K, there is a small orthorhombic distortion of the lattice. The refined unit-cell dimensions at 2 K (space group Pnma) are a=7.9505(2), b=4.02502(14), c=6.9823(2) Å. The magnetic moments of Tb are 8.71(6) μ_B, and are ordered antiferromagnetically along a.     

Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

关于Smarandache可乘函数的均值研究

本文的主要目的是利用初等方法研究Smarandache可乘函数在简单数集中的均值性质,并给出一个有趣的渐近公式。     

An LP-based heuristic procedure for the generalized assignment problem with special ordered sets

The generalized assignment problem with special ordered sets (GAPS2), is the problem of allocating n tasks to m time-periods, where each task must be assigned to a time-period, or shared between two consecutive time-periods. For reasonably large values of m and n the NP-hard combinatorial problem GAPS2 becomes intractable for standard mathematical programming software, hence there is a need for heuristic algorithms to solve such problems. It will be shown how an LP-based heuristic developed previously for the well-established generalized assignment problem can be modified and extended to solve GAPS2. Encouraging results, in terms of speed and accuracy, in particular when compared to an existing heuristic for GAPS2, are described.