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1.
用模糊集合描述模糊信息无效的原因是,把原本是论域与状态空间上二元函数的模糊隶属函数看成是论域上的一元函数,用模糊集合描述的模糊信息,不能支持模糊集合转换;使得通过模糊集合转换处理模糊信息的模糊数学,不得不借用不是数学计算、无缘数学模型的"取大取小"实现模糊集合转换;结果是背离数学计算的模糊数学,不能为处理模糊信息提供算法支持,导致大量需要处理的模糊信息滞留至今.还原模糊信息是高维状态空间上分类数据的真实面目,把处理模糊信息明确为由指标隶属度确定目标隶属度的隶属度转换,是模糊数学回归数学的唯一正确途径.  相似文献   

2.
现有的计算贴近度的方法,都是建立在模糊集合的隶属函数基础之上的.在很多情况下,当隶属函数很难解析表达时,这时就很难用这些方法计算贴近度.为此,在结构元理论的基础上,提出并构造了模糊数的贴近度(称之为元贴近度).当隶属函数很难解析表达时,用其他方法无法得到的贴近度,此时,用元贴近度的方法往往可以得到,并且计算非常简捷.最后,通过一个模式识别例子,表明该方法的有效性.  相似文献   

3.
将模糊数学理论应用到合作博弈中,用精确的数学表达式来表示实际生活中的模糊事件,又将模糊结构元理论应用到模糊合作博弈中,将模型中的模糊数用模糊结构元表示,以往基于扩张原理的模糊Shapley值的隶属函数非常复杂,本文给出其求解方法,使其得到解析表达.通过一个算例,来说明该模型的具体应用,与支付函数用区间数表示等研究方法相比较,该模型不仅保证了隶属函数的连续性,还给出区间上每个取值的隶属度,可以为管理者提供更精确的信息.  相似文献   

4.
相关系数在模糊决策领域发挥着重要的作用,但是其定义一直存在着问题。1985年,Murthy等~([1])提出了连续模糊集相关系数的两个计算公式,第一个公式与统计学中的相关系数具有相似的意义,但是其连续模糊隶属函数的均值定义是错误的。为此,借助于积分中值定理,定义了连续模糊隶属函数的均值以及方差和协方差,继而定义了连续模糊隶属函数的相关系数,从而彻底解决了Murthy等~([1])定义的第一个相关系数计算公式存在的问题。该相关系数与Chiang~([2])提出的离散隶属函数的相关系数一起,构成了完整的模糊集相关性理论。数值例子说明了,与Murthy~([1])第二个公式,Yu~([4])和Chaudhuri~([5])等提出的相关系数相比,我们提出的相关系数更合理有效。然后,将连续模糊隶属函数的相关系数概念推广到连续直觉模糊集,通过计算连续隶属函数以及连续非隶属函数的相关系数的平均值,定义了连续直觉模糊集的相关系数,该定义与Hung~([23])定义的离散直觉模糊集相关系数一起,构成了完整的直觉模糊集相关系数理论。最后,通过两个数值例子说明了连续直觉模糊集相关系数有效可行。  相似文献   

5.
定义了幂模糊数和幂模糊数方程,基于结构元方法研究了幂模糊数运算和幂模糊数方程的求解,给出了隶属函数的表达式.同时,利用区间[-1,1]上的单调函数将二次模糊方程的求解问题转化为经典参数方程组的求解问题,给出了二次模糊方程解存在的充要条件,并辅以数值例子.  相似文献   

6.
流行的似然方法不合适数据先验分布(即信源)可变场合。为此,我们把Zadeh的隶属函数看做预测模型,用隶属函数和可变信源产生似然函数,用平均对数标准(normalized)似然度定义语义信息测度。这样可以保证:(1)坚持使用最大似然准则;(2)预测模型适合信源可变场合;(3)得到的语义贝叶斯预测兼容贝叶斯定理;(4)预测模型能表达语义,便于理解。一组隶属函数构成一个语义信道,优化隶属函数就是使语义信道匹配Shannon信道,产生多标签模糊分类。文中介绍了通过两种信道相互匹配求解最大似然度的迭代算法。几个例子显示这种算法用于检验、估计和混合模型时,收敛快速且可靠。  相似文献   

7.
应用模糊数学方法解决实际问题的关键在于建立符合实际情况的隶属函数.常用计算模糊隶属函数的模糊统计法建立在大量调查数据和函数图形分析法的基础上,巨大的运算量和复杂的过程限制了模糊技术的实际应用.本文从统计学的角度提出了一种基于概率统计的模糊隶属函数计算方法,该方法相对简单并且能适应多种情况的隶属函数计算.最后通过实际算例对两种算法得到的隶属函数曲线进行了比对,验证了本文的方法具有较好的精度.  相似文献   

8.
基于新精确函数的区间直觉模糊多属性决策方法   总被引:1,自引:0,他引:1  
基于区间直觉模糊数隶属度和非隶属度构成的二维几何图形特征给出区间直觉模糊数精确函数的新定义,并将其作为区间直觉模糊数的排序指标,区间直觉模糊数的精确函数值越大,则区间直觉模糊数就越大,进而提出一种权重信息不完全确定的区间直觉模糊多属性决策方法.通过算例分析说明所提出排序指标的有效性和决策方法的可行性.  相似文献   

9.
针对不确定性多冲突环境,建立了多个具有模糊目标的多目标双矩阵对策的综合集结模型.在假定局中人各模糊目标的隶属函数为线性函数的情形下,基于总体模糊目标的可达度,给出了纳什均衡解的定义,并应用粒子群优化算法对集结模型求解.最后,给出一个军事例子说明了模型的实用有效性和粒子群优化算法求解的高效性.  相似文献   

10.
模糊逻辑系统用模糊集合描述模糊信息、用模糊集合转换处理模糊信息.阐述支撑模糊集合转换的模糊逻辑为什么是伪逻辑的原因.指出定义在论域一个空间上的模糊集合,因为破坏了集合中元素的"不可分割性",所以模糊集合描述的模糊信息不能用数学计算通过模糊集合转换处理.实际应用中的模糊信息定义在论域与状态空间两个空间上,其正确表达方式是满足"归一化"条件的隶属度向量;处理的正确途径是,研究基于状态转移矩阵的隶属度转换;支撑隶属度转换的是近似推理逻辑,目的是使构建的隶属度转换模型是当前条件下人们可能构建的"最优"近似模型.  相似文献   

11.
Hesitant fuzzy sets (HFSs), which allow the membership degree of an element to a set represented by several possible values, can be considered as a powerful tool to express uncertain information in the process of group decision making. We derive some correlation coefficient formulas for HFSs and apply them to clustering analysis under hesitant fuzzy environments. Two real world examples, i.e. software evaluation and classification as well as the assessment of business failure risk, are employed to illustrate the actual need of the clustering algorithm based on HFSs, which can incorporate the difference of evaluation information provided by different experts in clustering processes. In order to extend the application domain of the clustering algorithm in the framework of HFSs, we develop the interval-valued HFSs and the corresponding correlation coefficient formulas, and then demonstrate their application in clustering with interval-valued hesitant fuzzy information through a specific numerical example.  相似文献   

12.
In the past, the choices of β values to be applied to find the β-reducts in VPRS for an information system are somewhat arbitrary. In this study, a systematic method which bridges the fuzzy set methodology and probabilistic approach of RS to solve the threshold value β determination problem in variable precision rough sets (VPRS) is proposed. Different from the existing probabilistic methods, the proposed method relies on the fuzzy membership degrees of each attribute of the objects to calculate β. The proposed method gives the membership degrees and fuzzy aggregation operators the probabilistic interpretations. Based on the probabilistic interpretations, the threshold value β of VPRS is directly derived from fuzzy membership degree by Implication Relations and Fuzzy Algorithms, in which the membership degrees are obtained by the standard Fuzzy C-means method. The argument is that errors of system classification would occur in the fuzzy-clustering phase prior to information classification, therefore the threshold value β should be constrained by the probability of belongingness of an object to the fuzzy clusters, i.e., through the values of membership functions. A few examples are given in the paper to demonstrate the differences with other β-determining methods.  相似文献   

13.
A dual hesitant fuzzy set (DHFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain, and can handle two kinds of hesitancy in this situation. It can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we propose a correlation coefficient between DHFSs as a new extension of existing correlation coefficients for hesitant fuzzy sets and intuitionistic fuzzy sets and apply it to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted correlation coefficient between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, a practical example of investment alternatives is given to demonstrate the practicality and effectiveness of the developed approach.  相似文献   

14.
Fuzzy linear regression models can provide an estimated fuzzy number that has a fuzzy membership function. If a point that has the highest membership value from the estimated fuzzy number is not within the support of the observed fuzzy membership function, a decision-maker can have high risk from the estimate. In this study a modification of fuzzy linear regression analysis based on a criterion of minimizing the difference of the fuzzy membership values between the observed and estimated fuzzy numbers is proposed. Two numerical examples are used to evaluate the fuzzy regression models.  相似文献   

15.
本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.  相似文献   

16.
模糊Bayes检验   总被引:1,自引:1,他引:0  
本文对原假设和备择假设中参数是模糊子集的假设检验问题,引入了模糊Bayes检验的概念,对简单模糊假设,给出了求模糊Bayes检验的方法,讨论了它的性质,并针对一类特殊的隶属函数,得出了检验的具体公式。最后,通过几个数值实例,表明了模糊Bayes检验的优良性。  相似文献   

17.
The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.  相似文献   

18.
A soft set theory is a new general mathematical tool to dealing with imprecision. The theory differs from traditional mathematical tools to dealing with uncertainties in which many mathematical theories failed. In this paper, we proposed the concept of Bell shaped fuzzy soft set and its application in medical diagnosis using arithmetic operations of discrete- Gaussian fuzzy number, triangular-Cauchy fuzzy number and Gaussian-Cauchy fuzzy number. As an integral part of this paper, we discuss the parametric form of Gaussian membership function is discussed with some important properties.  相似文献   

19.
Hesitant fuzzy information aggregation in decision making   总被引:2,自引:0,他引:2  
As a generalization of fuzzy set, hesitant fuzzy set is a very useful tool in situations where there are some difficulties in determining the membership of an element to a set caused by a doubt between a few different values. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy information. We first discuss the relationship between intutionistic fuzzy set and hesitant fuzzy set, based on which we develop some operations and aggregation operators for hesitant fuzzy elements. The correlations among the aggregation operators are further discussed. Finally, we give their application in solving decision making problems.  相似文献   

20.
Fuzzy variables     
The purpose of this study is to explore a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed. The approach we propose is analogous to the sample space concept of probability theory. A fuzzy variable is a mapping from an abstract space (called the pattern space) onto the real line. The membership function is obtained as the extension of a special type of capacity (called a scale) from the pattern space to the real line via the fuzzy variable. In essence we are proposing an entirely new definition of a fuzzy set on the line as a mapping to the line rather than on the line. The current definition of a transformation of a fuzzy set is obtained as a derived result of our model. In addition, we derive the membership function of sums and products of fuzzy sets and present an example which reinforces the credibility of our approach.  相似文献   

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