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1.
A survey of credibility theory   总被引:26,自引:0,他引:26  
This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.  相似文献
2.
Fuzzy Random Variables: A Scalar Expected Value Operator   总被引:24,自引:5,他引:19  
Fuzzy random variable has been defined in several ways in literature. This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables. Some properties concerning the measurability of fuzzy random variable are also discussed. In addition, the concept of independent and identically distributed fuzzy random variables is introduced. Finally, a type of law of large numbers is proved.  相似文献
3.
模糊数据的线性回归模型   总被引:5,自引:0,他引:5  
研究观测数据为模糊数据的统计线性回归模型 ,由该模型所得回归系数非模糊 ,易于应用。对于对称三角模糊数据一元线性回归给出最优解的解析表达式 ;将对称三角模糊数多元线性回归问题给出转化为一类二次规划问题的方法 ;证明了最优解的存在性和估计量的无偏性。  相似文献
4.
The aim of this paper is to deal with a multiobjective linear programming problem with fuzzy random coefficients. Some crisp equivalent models are presented and a traditional algorithm based on an interactive fuzzy satisfying method is proposed to obtain the decision maker’s satisfying solution. In addition, the technique of fuzzy random simulation is adopted to handle general fuzzy random objective functions and fuzzy random constraints which are usually hard to be converted into their crisp equivalents. Furthermore, combined with the techniques of fuzzy random simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy random multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.  相似文献
5.
动态模糊随机信息处理的数学方法   总被引:1,自引:1,他引:0  
本文系统地概述了我们近年来提出的动态模糊随机信息处理的数学方法,内容包括模糊随机变量、模糊随机过程和模糊随机微分方程的基本解法等方面的基本概念、基本定义和某些重要的定理,以及动态系统的模糊随机响应与可靠性分析的方法等。这些方法是为我们研究工程实际问题的需要逐步发展起来的,对于处理某些类型的问题简便实用。  相似文献
6.
This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.  相似文献
7.
基于随机模糊参数预测烧结法氧化铝生产中碱液成分   总被引:1,自引:1,他引:0  
针对来自许多实际过程中数据变化的多态不确定性,提出一类新的预测方法。为了反映数据的多态不确定性,设计了一种分段推断算法来对样本数据的分布函数进行推断,在假设总体服从一类模糊随机变量的条件下,由该方法得到总体的分布函数的解析式。基于这种预测方法,对烧结法氧化铝生产过程中碱液成分进行了预测。预测结果表明新方法具有广泛的应用价值。  相似文献
8.
Fuzzy random variables   总被引:1,自引:0,他引:1  
9.
One Machine Scheduling Problem with Fuzzy Random Due-Dates   总被引:1,自引:0,他引:1  
In many classical or basic scheduling models, jobs processing times and due-dates are crisp values. Recently, they have been formulated as uncertain values in some more actual models. That is the introduction of fuzziness. However, in a real situation of decision making, there exists uncertainty that can not be described only by fuzziness. In this paper, we propose an n-job, one machine scheduling model, where due-dates for jobs are fuzzy random variables. In the model, jobs processing times are crisp, and we assign satisfaction levels to jobs completion times according to membership functions. They are non-increasing functions, but their support positions depend upon the expected due-dates, which are exponentially distributed random variables.  相似文献
10.
Kolmogorov's strong law of large numbers for fuzzy random variables   总被引:1,自引:0,他引:1  
In this paper, Kolmogorov's strong law of large numbers for sums of independent and level-wise identically distributed fuzzy random variables is obtained.  相似文献
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