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991.
Eric C.K. Cheung 《Insurance: Mathematics and Economics》2011,48(3):384-397
In a general Sparre Andersen risk model with surplus-dependent premium income, the generalization of Gerber-Shiu function proposed by Cheung et al. (2010a) is studied. A general expression for such Gerber-Shiu function is derived, and it is shown that its determination reduces to the evaluation of a transition function which is independent of the penalty function. Properties of and explicit expressions for such a transition function are derived when the surplus process is subject to (i) constant premium; (ii) a threshold dividend strategy; or (iii) credit interest. Extension of the approach is discussed for an absolute ruin model with debit interest. 相似文献
992.
The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm. 相似文献
993.
本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件. 相似文献
994.
In this paper, we prove that strongly convex space and almost locally uniformly rotund space, very convex space and weakly almost locally uniformly rotund space are respectively equivalent. We also investigate a few properties of k-strongly convex space and k-very convex space, and discuss the applications of strongly convex space and very convex space in approximation theory. 相似文献
995.
Zhi Kong Lifu WangZhaoxia Wu 《Journal of Computational and Applied Mathematics》2011,236(6):1521-1530
There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems. 相似文献
996.
997.
开集条件是分形几何的一个重要概念,弱分离条件(WSC)在研究有重叠的迭代函数系统(IFS)中扮演着重要角色.本文考虑满足弱分离条件的自共形迭代函数系统,并给出确定其不变集的Hausdorff维数的一种方式. 相似文献
998.
Pedro Terán 《International Journal of Approximate Reasoning》2011,52(9):1243-1256
This paper aims at formalizing the intuitive idea that some points are more central in a probability distribution than others. Our proposal relies on fuzzy events to define a fuzzy set of central points for a distribution (or a family of distributions, including imprecise probability models). This framework has a natural interpretation in terms of fuzzy logic and unifies many known notions from statistics, including the mean, median and mode, interquantile intervals, the Lorenz curve, the halfspace median, the zonoid and lift zonoid, the coverage function and several expectations and medians of random sets, and the Choquet integral against an infinitely alternating or infinitely monotone capacity. 相似文献
999.
Duoqian Miao Can Gao Nan Zhang Zhifei Zhang 《International Journal of Approximate Reasoning》2011,52(8):1103-1117
Rough set theory is an effective supervised learning model for labeled data. However, it is often the case that practical problems involve both labeled and unlabeled data, which is outside the realm of traditional rough set theory. In this paper, the problem of attribute reduction for partially labeled data is first studied. With a new definition of discernibility matrix, a Markov blanket based heuristic algorithm is put forward to compute the optimal reduct of partially labeled data. A novel rough co-training model is then proposed, which could capitalize on the unlabeled data to improve the performance of rough classifier learned only from few labeled data. The model employs two diverse reducts of partially labeled data to train its base classifiers on the labeled data, and then makes the base classifiers learn from each other on the unlabeled data iteratively. The classifiers constructed in different reduct subspaces could benefit from their diversity on the unlabeled data and significantly improve the performance of the rough co-training model. Finally, the rough co-training model is theoretically analyzed, and the upper bound on its performance improvement is given. The experimental results show that the proposed model outperforms other representative models in terms of accuracy and even compares favorably with rough classifier trained on all training data labeled. 相似文献
1000.
This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology. 相似文献