Vague集相似度量模型

Vague集的相似度量在模糊推理、模式识别、聚类分析、决策分析等领域的广泛运用,要求所建立的vague集相似度量模型具有较高的区分度及度量结果合乎人的直觉.基于此要求,首先对已有Vague值的相似度量模型在区分度上的不足进行了分析.然后,在分析地基础上,提出了vague值的相似度量建模须考虑的因素.最后建立了Vague集的相似度量模型.数值实验表明,新模型具有较好的区分度,能克服已有模型在区分度上的不足.     

基于误差传递的Vague值数据回归分析

Vague值数据是重要的符号数据,也是处理一类模糊问题的手段.基于误差传递的理论,提出了Vague值数据的回归分析方法.在分析原有Vague集相似性测度的基础上,提出了一种新的Vague集相似性测度,并以此来评价Vague值数据的回归模型.通过数值事例计算,验证了该回归模型的有效性.     

基于Vague集的群决策方法研究

首先介绍了Vague集的基本概念,将直觉模糊集的一些运算规则重新在Vague集上作了定义,提出用Vague值表示的九级语言术语集.接着指出衡量Vague集(值)相似度要考虑的三个因素,提出了新的度量方法.在同时考虑专家决策结果的一致性和专家权重的基础上,提出了汇总各专家Vague意见的方法.最后以一个案例说明了所提出的方法.     

基于Vague集的模糊多目标决策方法及应用

针对目前基于Vague集多目标决策中Vague值计算困难以及确定目标满意度的下界和不满意度的上界存在主观随意性问题.提出了一种基于Vague集的模糊多目标决策方法.利用属性数学中的属性集和属性测度理论构造目标的真隶属度函数、假隶属度函数和犹豫度函数,从而可计算出目标的Vague值;采用记分函数计算方案的多目标评分值,从而可以对方案进行排序并选择出最优方案.应用实例验证了该方法的有效性和实用性.     

基于vague集投影及距离的模糊多指标决策

提出了两个vague值投影和距离的概念,并在此基础上给出了考虑指标权重影响的基于vague集投影和距离的多指标模糊决策方法.在这个方法中,利用候选方案在理想方案上的投影和距离来求出最佳方案.此方法与文献现有的应用vague集相似度度量进行决策的方法相比较,新方法更加合理且弥补了现有方法的不足之处.最后对实例进行分析计算,算例验证了该方法的有效性.     

基于Vague集信息的多属性群决策专家水平评判方法

针对基于Vague集信息的多属性群决策专家水平评判问题提出了两种评判方法.首先引进了基于Vague集信息的多属性群决策信息体(即决策信息体)的相关概念,通过决策信息体构造了基于Vague集信息的一致性决策矩阵及模糊熵,其次利用Vague集信息的相似度量以及Vague集信息的模糊熵两种信息不确定性度量方法,对基于Vague集信息的多属性群决策专家水平评判问题提出了两种评判方法,即统计分析方法和模糊熵分析方法,对专家的评判水平进行排序.最后,通过一个算例说明两种方法的一致性、有效性和实用性.     

基于证据理论和Vague集的多属性群决策方法研究

为了解决人们在复杂环境中决策困难的问题,论文基于Vague集描述不确定事物的优势,通过证据理论对Vague集进行合成,得到一种信息集结的多属性群决策方法。该算法首先考虑专家评分的可信度,在分析Vague集与证据理论的数学关系后,使用证据理论将各方案在各属性下的专家集证据集结。然后通过Vague集记分函数进行属性权重的计算,将方案集在属性集下的Vague评价值进行加权修正,再通过证据理论将属性集证据集结得到各方案最终的Vague评价值。之后使用记分函数计算每一方案的得分来确定最优方案。最后通过算例进一步说明所提方法的可行性与有效性。文章给出的算法使决策者在不确定环境下可以进行理性决策,从而选出最优方案。     

基于Vague集的PROMETHEE-Ⅱ

PROMETHEE是应用广泛的多属性决策方法之一.研究了PROMETHEE-Ⅱ的Vague集方法,首先定义了Vague集的减法,然后提出了Vague集的PROMETHEE-Ⅱ,并给出具体的算例.     

一种Vague偏好群体决策方法

采用 Vague集理论来描述和处理不确定信息或含糊信息 ,比采用模糊集理论描述和处理不确定信息或含糊信息在很多情况下更贴近客观现实 .在诸学者对模糊群体决策研究的基础上 ,提出一种 Vague群体决策方法 ,采用 Vague值作为决策者对备选方案的评估值 ,通过对决策者的各备选方案偏好值的集结 ,最后根据集结值的效用值对备选方案排序 ,进行决策 .     

权重信息未知对方案有偏好的vague集多指标决策

就指标权重未知,且对方案有偏好的vague集多指标决策问题,提出了通过使决策者的主观偏好值与属性值的相离度最小来建立最优化模型,从而获得指标的权重.通过将vague值转化为模糊值来建立模糊值矩阵,由模糊值矩阵按各指标对应值的大小对方案进行排序,形成多个线性序,进而由线性序来构造模糊优先矩阵,对其进行截割,得到最优方案.最后通过一个实例说明此方法的具体决策过程.     

Vague指派问题的求解方法研究

Vague指派问题的特殊性在于用Vague值表述效益矩阵,进而反映了指派问题中存在的诸多不确定性和模糊性。论文根据Vague值的特点,提出了Vague指派问题的求解转化为经典指派问题思想,进而借助“马太效应”函数、特征值向量和Pareto三种方法实现问题的求解。最后,论文以参考文献中的一组数据为例,采用以上方法进行计算,得到了理想的结果。     

基于Vague集的最优路径选择方法（英文）

Optimal route selection is an important function of vehicle traffic flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting route. In this paper, subjective weighting method which relies on driver preference is used to determine the weight and the paper proposes the multi-criteria weighted decision method based on vague sets for selecting the optimal route. Examples show that, the usage of vague sets to describe route index value can provide more decision-making information for route selection.     

A distance-based statistical analysis of fuzzy number-valued data

Real-life data associated with experimental outcomes are not always real-valued. In particular, opinions, perceptions, ratings, etc., are often assumed to be vague in nature, especially when they come from human valuations. Fuzzy numbers have extensively been considered to provide us with a convenient tool to express these vague data. In analyzing fuzzy data from a statistical perspective one finds two key obstacles, namely, the nonlinearity associated with the usual arithmetic with fuzzy data and the lack of suitable models and limit results for the distribution of fuzzy-valued statistics. These obstacles can be frequently bypassed by using an appropriate metric between fuzzy data, the notion of random fuzzy set and a bootstrapped central limit theorem for general space-valued random elements. This paper aims to review these ideas and a methodology for the statistical analysis of fuzzy number data which has been developed along the last years.     

粗糙Vague集及其相似度量

对粗糙V ague集的基本操作和性质进行了研究。另外,对粗糙V ague集的相似度量问题进行研究,首先构造一种粗糙V ague值的相似度函数并给出其基本性质,然后给出一种粗糙V ague集的相似度函数以及一种粗糙V ague集的加权相似度函数。     

Vague集上的正规距离与正规相似度

距离与相似度是Vague集上的一对对偶概念,给出了Vague集上加强的距离的公理化定义,引入了正规距离与正规相似度的概念,提出了Vague集上距离的一个一般公式,通过对Vague值的探讨给出了该一般公式成为正规距离的充分条件,同时得到Vague集上的一个新的正规距离公式.最后通过数据分析得出由此正规距离公式生成的正规相似度是合理有效的.     

一种新的Vague集多准则决策评分函数

在基于Vague集的多准则决策过程中,评分函数是影响评价结果的决定性因素之一.现有评分函数对Vague集未知信息的处理都不恰当,有的忽略了未知信息对评价结果的影响,有的则夸大了未知信息的影响,所以都存在评价结果与人们直觉判断不符的问题.在总结和整合前人工作的基础上,提出了一种新的评分函数,可根据未知信息的多少决定其对评价结果的影响程度,有效地解决了评价结果与直觉判断不符的问题,并据此提出了一种计算Vague集相似度的新方法.     

Neuro-fuzzy based constraint programming

Constraint programming models appear in many sciences including mathematics, engineering and physics. These problems aim at optimizing a cost function joint with some constraints. Fuzzy constraint programming has been developed for treating uncertainty in the setting of optimization problems with vague constraints. In this paper, a new method is presented into creation fuzzy concept for set of constraints. Unlike to existing methods, instead of constraints with fuzzy inequalities or fuzzy coefficients or fuzzy numbers, vague nature of constraints set is modeled using learning scheme with adaptive neural-fuzzy inference system (ANFIS). In the proposed approach, constraints are not limited to differentiability, continuity, linearity; also the importance degree of each constraint can be easily applied. Unsatisfaction of each weighted constraint reduces membership of certainty for set of constraints. Monte-Carlo simulations are used for generating feature vector samples and outputs for construction of necessary data for ANFIS. The experimental results show the ability of the proposed approach for modeling constrains and solving parametric programming problems.     

Optimization of the number of components in the mixed model using multi-criteria decision-making

The distributions of empirical data are often complex. Such complexity cannot be sufficiently addressed by the individual theoretical statistical distribution function. Furthermore, the selection of the distribution function becomes more complicated when the empirical data present a multi-peak feature. In such a case, the multiple testing criteria and the mixed model must be considered during the selection of an appropriate distribution function. Aiming at this vague challenge, the present paper proposes a novel method for establishing a mixed model that can describe accurately the distribution characteristics of empirical data. Apart from combining the Akike and Bayesian information criteria to define the feasible solutions of the mixed model, this study also utilizes the root mean squared deviation, coefficient of determination, Kolmogorov–Smirnov test statistic, average deviation in cumulative distribution function, and average deviation in probability distribution function as the testing criteria. In addition, a non-linear programming is used to find the weighting factors of each criterion. The multi-criteria decision-making technology is adopted to comprehensively and objectively integrate these testing criteria into a synthetic indicator. Finally, an optimization algorithm is proposed to determine the optimal number of components in the mixed model. The illustrated results of the simulated data and measured signals confirm that this approach can estimate precisely the number of components as well as establish a highly accurate mixed model.     

Comparison of first aggregation and last aggregation in fuzzy group TOPSIS

The Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), one of the major multi attribute decision making (MADM) techniques, ranks the alternatives according to their distances from the ideal and the negative ideal solution. In real evaluation and decision making problems, it is vital to involve several people and experts from different functional areas in decision making process. Also under many conditions, crisp data are inadequate to model real-life situations, since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Therefore aggregation of fuzzy concept, group decision making and TOPSIS methods that we denote “fuzzy group TOPSIS” is more practical than original TOPSIS.