两个空间之间复合映射的不动点集和Reidemeister数

设X,Y为拓扑空间,f:X→Y,g:y→X．该文证明了下列结论:对每一自然数n, (1)f(Fix((g o,f)n))=Fix((f o g)n),g(Fix((f og )n))=Fix(g o f)n),且#Fix((g o f)n)= #Fix((f o g)n);(2)R((g o f)n)=R((f o g)n)．     

On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem

In this paper a comparison is made between two decomposition techniques to solve a staff scheduling problem with column generation. In the first approach, decomposition takes place on the staff members, whereas in the second approach decomposition takes place on the activities that have to be performed by the staff members. The resulting master LP is respectively a set partitioning problem and a capacitated multi-commodity flow problem. Both approaches have been implemented in a branch-and-price algorithm. We show a trade-off between modeling power and computation times of both techniques.     

Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study

In this paper, locating some warehouses as distribution centers (DCs) in a real-world military logistics system will be investigated. There are two objectives: finding the least number of DCs and locating them in the best possible locations. The first objective implies the minimum cost of locating the facilities and the latter expresses the quality of the DCs locations, which is evaluated by studying the value of appropriate attributes affecting the quality of a location. Quality of a location depends on a number of attributes; so the value of each location is determined by using Multi Attribute Decision Making models, by considering the feasible alternatives, the related attributes and their weights according to decision maker’s (DM) point of view. Then, regarding the obtained values and the minimum number of DCs, the two objective functions are formed. Constraints imposed on these two objectives cover all centers, which must be supported by the DCs. Using Multiple Objective Decision Making techniques, the locations of DCs are determined. In the final phase, we use a simple set partitioning model to assign each supported center to only one of the located DCs.     

Necessary optimality conditions for bilevel set optimization problems

Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative due to Clarke or Michel-Penot. Using a certain regularity condition Karush-Kuhn-Tucker conditions are obtained.      

基于单调包含度的模糊决策信息系统的知识约简

知识约简是机器学习,模式识别,信号处理等领域的主要问题之一。本文介绍了基于单调包含度的模糊决策信息系统的知识约简。证明了模糊决策信息系统的约简即是其对应信息系统的约简,从而为该种模糊决策信息系统的知识约简提供了简单直接的方法。     

连续论域上Fuzzy集的信息熵

在文献[1]的基础上,把模糊熵从离散论域推广到连续论域,给出连续论域上Fuzzy集的偏熵、关联熵等概念。对其主要性质进行讨论,取得了一些令人满意的结果。拓宽信息熵的研究领域,对不确定复杂系统的信息处理、知识学习、归纳学习、模糊信息学的进一步研究打下一定基础。     

(∈,∈∨ q(λ,μ))-凸模糊集

给出(∈,∈∨q(λ,μ))-凸模糊集的定义,讨论它们的一些基本性质。     

基于优势关系下不协调目标信息系统的分布约简

在基于优势关系下的不协调目标信息系统中引入了分布约简和最大分布约简的概念,并讨论了二者之间的关系,而且得到了分布和最大分布约简的判定定理以及辨识矩阵,建立了不协调目标信息系统的分布和最大分布约简的具体方法,同时通过实例验证了该方法的有效性,从而进一步丰富了粗糙集理论。     

基于Type-2型模糊集的动态生态位模型

复杂生态系统中,由于生物进化的高度非线性,使生物更容易适应环境的变化,生物与环境的交流要求用动态的观点来描述生态位及其相关概念。本文利用T ype-2型模糊集合的“宽带”效应,给出了具有动态特性的生态位模型,并相应的给出宽度和重叠的计算公式。应用于植物的生态位宽度和重叠的计算,与已有公式结果的比较,本文提出的模型可以全面的给出了物种在每个资源状态下的情形,同时反应了物种与环境之间的互动交流。为生物系统的应用研究和理论研究提出统一的数学模型。