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41.
G. M. Ustinov 《Mathematical Notes》1999,65(5):610-619
The property of a space to be an existence subspace is studied for subspacesE ofC(Q) such that eitherE orC(Q)/E is a Lindenstrauss space. For a Chebyshev subspaceL⊂C(Q)1 an analytic representation of the nearest element in terms of the annihilatorL
┴ is obtained.
Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 726–737, May, 1999. 相似文献
42.
This paper presents an extension of the comprehensive (overall) concordance index of ELECTRE methods, which takes the interaction between criteria into account. In real-world decision-aiding situations, it is reasonable to consider only the interaction between a small number of criterion pairs. Three types of interaction have been considered: mutual strengthening, mutual weakening, and antagonistic. The new concordance index correctly takes into account such types of interactions, by imposing such conditions as boundary, monotonicity, and continuity. We demonstrate that the generalized index is able to take the three types of interaction, or dependencies, between criteria into account satisfactorily, first using quasi-criteria and then using pseudo-criteria. We also examine the links between the new concordance index and the Choquet integral. 相似文献
43.
44.
H.P. Kirschner 《Journal of multivariate analysis》1976,6(1):159-166
For statistical decision problems, there are two well-known methods of randomization: on the one hand, randomization by means of mixtures of nonrandomized decision functions (randomized decision rules) in the game “statistician against nature,” on the other hand, randomization by means of randomized decision functions. In this paper, we consider the problem of risk-equivalence of these two procedures, i.e., imposing fairly general conditions on a nonsequential decision problem, it is shown that to each randomized decision rule, there is a randomized decision function with uniformly the same risk, and vice versa. The crucial argument is based on rewriting risk-equivalence in terms of Choquet's integral representation theorem. It is shown, in addition, that for certain special cases that do not fulfill the assumptions of the Main Theorem, risk-equivalence holds at least partially. 相似文献
45.
46.
Michel Grabisch Jacques Duchêne Frédéric Lino Patrice Perny 《Fuzzy Optimization and Decision Making》2002,1(3):287-312
We study the modelling of the subjective sensation of discomfort for subjects seated during a long time, in terms of local discomforts. The methodology uses fuzzy measures and integrals in a multicriteria decision making process, which enables the modelling of complex interaction between variables. Results of the experiment are detailed, giving models with respect to different kinds of discomfort, and to different macro-zones of the body. 相似文献
47.
针对属性值为区间数,属性权重完全未知,但给出方案的主观偏好值,部分属性偏好关系以及属性交互类型的属性关联多属性决策问题给出决策方法.首先建立期望值目标规划模型,确定出属性集的M(o|¨)bius表达式以及属性权重,然后利用扩展的区间Choquet积分算子对决策信息进行集结,计算出各方案的区间模糊综合评价值,再利用比较区间数的期望值方法,从而得到方案的最终排序.最后给出了分析实例以说明所提出方法的有效可行性. 相似文献
48.
In this paper, we extend the concept of tail subadditivity (Belles-Sampera et al., 2014a; Belles-Sampera et al., 2014b) for distortion risk measures and give sufficient and necessary conditions for a distortion risk measure to be tail subadditive. We also introduce the generalized GlueVaR risk measures, which can be used to approach any coherent distortion risk measure. To further illustrate the applications of the tail subadditivity, we propose multivariate tail distortion (MTD) risk measures and generalize the multivariate tail conditional expectation (MTCE) risk measure introduced by Landsman et al. (2016). The properties of multivariate tail distortion risk measures, such as positive homogeneity, translation invariance, monotonicity, and subadditivity, are discussed as well. Moreover, we discuss the applications of the multivariate tail distortion risk measures in capital allocations for a portfolio of risks and explore the impacts of the dependence between risks in a portfolio and extreme tail events of a risk portfolio in capital allocations. 相似文献
49.
A motivation for this paper comes from the role of Choquet capacities in the study of semilinear elliptic partial differential equations. In particular, the recent progress in the classification of all positive solutions of Lu=uα in a bounded smooth domain E⊂Rd was achieved by using, as a tool, capacities on a smooth manifold ∂E. Either the Poisson capacities (associated with the Poisson kernel in E) or the Bessel capacities (related to the Bessel kernel) have been used. In this and many other applications there is no advantage in choosing any special member in a class of equivalent capacities. (Two capacities are called equivalent if their ratio is bounded away from 0 and ∞.) In the literature Bessel capacities are considered mostly in the space Rd. We introduce two versions of Bessel capacities on a compact N-dimensional manifold. A class Cap?,p of equivalent capacities is defined, for ?p?N, on every compact Lipschitz manifold. Another class CB?,p is defined (for all ?>0, p>1) in terms of a diffusion process on a C2-manifold. These classes coincide when both are defined. If the manifold is the boundary of a bounded C2-domain E⊂Rd, then both versions of the Bessel capacities are equivalent to the Poisson capacities. 相似文献
50.
In the context of multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones. 相似文献