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【期刊论文】Iteration algorithms for solving a system of fuzzy linear equations☆
哈明虎, Xizhao Wang a, *, Zimian Zhong b, Minghu Ha a
Fuzzy Sets and Systems 119(2001)121-128,-0001,():
-1年11月30日
In this paper, we discuss the solution of a system of fuzzy linear equations, X =AX+U, and its iteration algorithms where A is a real n×n matrix, the unknown vector X and the constant U are all vectors consisting of n fuzzy numbers, and the addition, scale-multiplication are defined by Zadeh's extension principle. After introducing a metric between two fuzzy vectors, we prove that the system has unique solution if ‖A‖∞<1. We also give the convergence and the error estimation for using simple iteration to obtain the solution. Finally, we give the convergence and the error estimation of successive iteration sequence for obtaining the solution.
Algebra, Numerical algebra, Fuzzy numbers, Systems of fuzzy linear equations, Iteration algorithms
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【期刊论文】经济系统中的模糊递推规划模型①——模糊递推规划模型的结构、定义与实例
哈明虎, 李双杰, 张峰
数量经济技术经济研究,2001,(11):48~51,-0001,():
-1年11月30日
递推规划为解决复杂经济系统的描述问题提供了一种有效的“分解—综合”的方法,但它却不能处理存在于经济系统中的模糊信息。基于此,本文提出了模糊递推规划方法,对带有模糊信息的经济系统建立了模糊递推规划模型,并给出了一个应用模糊递推规划模型的实例。
递推规划, 模糊信息, 模糊递推规划模型
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哈明虎, 王瑞省, 宋士吉, 李法朝
运筹与管理,2003,12(5):6~12,-0001,():
-1年11月30日
由于模糊信息在现实世界中的大量存在及鞍点规划在管理科学、系统科学等诸多领域中的重要应用,本文提出了模糊鞍点规划。根据模糊鞍点规划数学模型的特点确定了。模糊目标隶属函数形式,通过推广的多变量模糊决策,将模糊鞍点规划转化为一个普通的非线性规划问题。
运筹学, 模糊鞍点规划, 模糊优化, 鞍点规划
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【期刊论文】Sequences of (S) fuzzy integrable functions☆
哈明虎, Minghu Ha∗, Xizhao Wang, Lanzhen Yang, Yan Li
Fuzzy Sets and Systems 138(2003)507-522,-0001,():
-1年11月30日
A new concept of the fuzzy mean fundamental convergence is introduced, and the relations among several convergences ofsequences of(S) fuzzy integrable functions are discussed. Further, the equivalent relation between fuzzy mean fundamental convergence and fundamental convergence in fuzzy measure of sequences of (S) fuzzy integrable functions is proved. Three new definitions of uniform sequence, uniform weak and absolute continuous sequence, and uniform bounded sequence of (S) fuzzy integrable functions are also given, and the properties ofsequences of(S) fuzzy integrable functions are discussed. Moreover, the equivalent relation between the uniform sequence and the uniform bounded sequence of (S) fuzzy integrable functions is shown.
Generalized measure and integral, Sequences of (, S), fuzzy integrable functions, Fuzzy mean fundamental convergence, Fundamental convergence in fuzzy measure
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