Operators on separable L1-predual spaces

We give an extension of the classical Bartle–Dunford–Schwartz theorem for weakly compact operators on a $C(K)$ space, to weakly compact operators on a separable $L^1$-predual space. Using this we show that for operators on these spaces, the set of weakly compact operators that attain their norm is dense in the space of weakly compact operators. For operators from the space of affine continuous functions on a metrizable Choquet simplex with values in an uniformly convex space, we show that the operator theoretic version of the Bishop–Phelps–Bollobás property is valid. This gives an extension of some recent work of Kim and Lee.     

基于2-可加模糊测度的NPD项目复杂性评价

针对NPD项目复杂性各因素间具有的关联性以及传统评价方法的局限性,提出一种基于关联多属性的2-可加模糊测度方法来对NPD项目复杂性进行评价。在界定项目复杂性内涵的基础上,从产品复杂性、环境复杂性、组织复杂性和技术复杂性四个方面构建了NPD项目复杂性评价指标体系。从模糊测度、默比乌斯变换和交互作用系数间的转化关系出发,基于最大Marichal熵原则,提出了一种确定2-可加模糊测度值的新方法。利用Choquet积分作为集结算子,自下而上计算各候选方案的综合评价值。最后,通过具体算例说明了该方法的可行性和有效性。     

一种基于Choquet积分的多属性直觉模糊决策方法

研究了决策者对方案的主观偏好值以及属性值均为直觉模糊数的且属性间存在关联的多属性决策问题.利用Choquet模糊积分作为集结算子,构建了基于属性关联的M OD和SOD模型.通过求解模型获得属性的权重,进而给出了一种新的直觉模糊多属性决策方法.最后通过一个算例说明了该决策方法的有效性和可行性.     

Lebesgue-Stieltjes形式的Choquet积分Ⅱ

研究了Lebesgue-Stieltjes形式的Choquet积分的收敛性定理,如单调收敛定理、法都引理、控制收敛定理等.     

Possibilistic signal processing: How to handle noise?

We propose a novel approach for noise quantifier at each location of a signal. This method is based on replacing the conventional kernel-based approach extensively used in signal processing by an approach involving another kind of kernel: a possibility distribution. Such an approach leads to interval-valued resulting methods instead of point-valued ones. We propose a theoretical justification to this approach and we show, on real and artificial data sets, that the length of the obtained interval and the local noise level are highly correlated. This method is non-parametric and has an advantage over other methods since no assumption about the nature of the noise has to be made, except its local ergodicity. Besides, the propagation of the noise in the involved signal processing method is direct and does not require any additional computation.     

Choquet-based optimisation in multiobjective shortest path and spanning tree problems

This paper is devoted to the search of Choquet-optimal solutions in finite graph problems with multiple objectives. The Choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives. We first present a condition on preferences (name hereafter preference for interior points) that characterizes preferences favouring compromise solutions, a natural attitude in various contexts such as multicriteria optimisation, robust optimisation and optimisation with multiple agents. Within Choquet expected utility theory, this condition amounts to using a submodular capacity and a convex utility function. Under these assumptions, we focus on the fast determination of Choquet-optimal paths and spanning trees. After investigating the complexity of these problems, we introduce a lower bound for the Choquet integral, computable in polynomial time. Then, we propose different algorithms using this bound, either based on a controlled enumeration of solutions (ranking approach) or an implicit enumeration scheme (branch and bound). Finally, we provide numerical experiments that show the actual efficiency of the algorithms on multiple instances of different sizes.     

On the Choquet Charge of δ-superharmonic Functions

Let u v be positive superharmonic functions in a general potential-theoretic setting, where these functions have a Choquet-type integral representation by minimal such functions with Choquet charges (i.e. representing measures) and , respectively. We show that on the contact set {u – v = 0} of the -superharmonic function u – v, if this set is properly interpreted as the set of those minimal superharmonic functions s which satisfy lim sup _{T s} v/u = 1 for the co-fine neighborhood filter T _s associated with s. In the setting of classical potential theory for Laplace's equation this result improves on results obtained by Fuglede in 1992.     

基于单值中智集Choquet积分算子的群决策方法

单值中智集不仅能描述现实决策系统中不完整信息而且能描述不确定性和不一致信息,已有关于单值中智集的决策方法只能用来解决属性间相互独立的多属性决策问题.考虑到Choquet积分算子的特点,将Choquet积分算子应用到单值中智集中,用以解决属性间有关联关系的多属性群决策问题.首先应用单值中智集余弦相似度比较方法,提出了单值中智集Choquet积分算子,研究了其性质.然后建立了基于单值中智集Choquet积分算子的多属性群决策方法.最后通过实例分析说明了算法的可行性和有效性.     

Baire spaces, Tychonoff powers and the Vietoris topology

In this paper, we show that if the Tychonoff power of a quasi-regular space is Baire, then its Vietoris hyperspace is also Baire. We also provide two examples to show (i) the converse of this result does not hold in general, and (ii) the Baireness of finite powers of a space is insufficient to guarantee the Baireness of its hyperspace.