共查询到18条相似文献,搜索用时 45 毫秒
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利用n维模糊集截集理论和模糊点与n维模糊集的邻属关系,并利用n+1-值Lukasiewicz蕴涵,首先给出(α,β)-n维凸模糊集的定义,然后对(∈,∈)-n维凸模糊集和(∈,∈Vq)-n维凸模糊集这两种非常有意义的n维凸模糊集进行了讨论,最后得到了一些有意义的结果.这将为n维凸模糊分析理论研究打下基础. 相似文献
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利用n维模糊集截集理论和模糊点与n维模糊集的邻属关系,并利用n+1-值Lukasiewicz蕴涵,首先给出(α,β)-n维凸模糊集的定义,然后对(∈,∈)-n维凸模糊集和(∈,∈∨q)-n维凸模糊集这两种非常有意义的n维凸模糊集进行了讨论,最后得到了一些有意义的结果。这将为n维凸模糊分析理论研究打下基础。 相似文献
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定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。 相似文献
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研究了分组0-1背包问题,提出了一种动态规划解决方法,在物品总数为n个和背包承重量为W时,递推过程的复杂度为O(nW),回溯过程的复杂度为O(n).计算实例表明利用该方法易于找到最优解. 相似文献
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本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理. 相似文献
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为研究平面或空间模糊几何问题的需要,在平面或空间模糊点的背景下,给出了O型模糊数的概念,它是一类二维实数域上的模糊集,同时给出了O型模糊数的二维模糊结构元表示方法.二维模糊数的结构元方法,可以使O型模糊数的运算变成普通实数与模糊结构元之间的运算,使得过去必须依赖扩张原理和表现定理来刻画的模糊数运算变得更加简单与直观,不仅仅为模糊分析计算的简化提供了工具,也为二维实数域上模糊分析理论与应用的研究开创了一条新的途径. 相似文献
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《European Journal of Operational Research》2001,135(1):158-176
This paper investigates knapsack problems in which all of the weight coefficients are fuzzy numbers. This work is based on the assumption that each weight coefficient is imprecise due to the use of decimal truncation or rough estimation of the coefficients by the decision-maker. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve this problem. Our work intends to extend the original knapsack problem into a more generalized problem that would be useful in practical situations. As a result, our study shows that the fuzzy knapsack problem is an extension of the crisp knapsack problem, and that the crisp knapsack problem is a special case of the fuzzy knapsack problem. 相似文献
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This paper investigates solving the knapsack problem with imprecise weight coefficients using genetic algorithms. This work is based on the assumption that each weight coefficient is imprecise due to decimal truncation or coefficient rough estimation by the decision-maker. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve this problem. We investigate the possibility of using genetic algorithms in solving the fuzzy knapsack problem without defining membership functions for each imprecise weight coefficient. The proposed approach simulates a fuzzy number by distributing it into some partition points. We use genetic algorithms to evolve the values in each partition point so that the final values represent the membership grade of a fuzzy number. The empirical results show that the proposed approach can obtain very good solutions within the given bound of each imprecise weight coefficient than the fuzzy knapsack approach. The fuzzy genetic algorithm concept approach is different, but gives better results than the traditional fuzzy approach. 相似文献
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The 0-1 knapsack problem with fuzzy data 总被引:1,自引:0,他引:1
The 0-1 knapsack problem with imprecise profits and imprecise weights of items is considered. The imprecise parameters are
modeled as fuzzy intervals. A method of choosing a solution under the uncertainty is proposed and two methods for solving
the constructed models are provided. 相似文献
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This paper proposes a parametric programming approach to analyze the fuzzy maximum total return in the continuous knapsack problem with fuzzy objective weights, in that the membership function of the maximum total return is constructed. The idea is based on Zadeh’s extension principle, α-cut representation, and the duality theorem of linear programming. A pair of linear programs parameterized by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy maximum total return at α, through which the membership function of the maximum total return is constructed. To demonstrate the validity of the proposed procedure, an example studied by the previous studies is investigated successfully. Since the fuzzy maximum total return is completely expressed by a membership function rather than by a crisp value reported in previous studies, the fuzziness of object weights is conserved completely, and more information is provided for making decisions in real-world resource allocation applications. The generalization of the proposed approach for other types of knapsack problems is also straightforward. 相似文献
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The fractional knapsack problem to obtain an integer solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. A modification of the Dinkelbach's algorithm [3] is proposed to exploit the fact that good feasible solutions are easily obtained for both the fractional knapsack problem and the ordinary knapsack problem. An upper bound of the number of iterations is derived. In particular it is clarified how optimal solutions depend on the right hand side of the constraint; a fractional knapsack problem reduces to an ordinary knapsack problem if the right hand side exceeds a certain bound. 相似文献
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Hisatoshi Suzuki 《Mathematical Programming》1978,15(1):162-176
The ordinary knapsack problem is to find the optimal combination of items to be packed in a knapsack under a single constraint on the total allowable resources, where all coefficients in the objective function and in the constraint are constant.In this paper, a generalized knapsack problem with coefficients depending on variable parameters is proposed and discussed. Developing an effective branch and bound algorithm for this problem, the concept of relaxation and the efficiency function introduced here will play important roles. Furthermore, a relation between the algorithm and the dynamic programming approach is discussed, and subsequently it will be shown that the ordinary 0–1 knapsack problem, the linear programming knapsack problem and the single constrained linear programming problem with upper-bounded variables are special cases of the interested problem. Finally, practical applications of the problem and its computational experiences will be shown. 相似文献
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The knapsack problem (KP) is generalized taking into account a precedence relation between items. Such a relation can be represented by means of a directed acyclic graph, where nodes correspond to items in a one-to-one way. As in ordinary KPs, each item is associated with profit and weight, the knapsack has a fixed capacity, and the problem is to determine the set of items to be included in the knapsack. However, each item can be adopted only when all of its predecessors have been included in the knapsack. The knapsack problem with such an additional set of constraints is referred to as the precedence-constrained knapsack problem (PCKP). We present some dynamic programming algorithms that can solve small PCKPs to optimality, as well as a preprocessing method to reduce the size of the problem. Combining these, we are able to solve PCKPs with up to 2000 items in less than a few minutes of CPU time. 相似文献