基于结构元理论的模糊数综合排序指标

文章在分析了基于结构元理论的五个模糊数排序指标(自然序、加权序、左序、右序和组合序等)的基础上,定义了模糊数排序综合指标,使得前五个模糊数排序指标是其特殊情况。综合指标同时考虑了决策者对元素权重分配的主观态度和风险偏好。数据例子表明,模糊数的排序,对不同风险偏好的决策者将有不同的结论。     

基于决策者风险偏好的直觉模糊数排序方法

决策者的风险偏好对决策有着重要的影响。本文通过引入反映决策者风险偏好程度的风险参数,基于直觉模糊数的隶属度、非隶属度和犹豫度,定义排序直觉模糊数的含风险参数的得分函数,并结合直觉模糊加权平均算子给出了一种属性值为直觉模糊数的多属性决策方法。通过算例阐明该方法的可行性和有效性。     

效用函数值的计算方法

效用函数值的计算是决策分析中的一个重要问题.由于不同决策者有不同偏好(Prefe-rence),以及同一决策者对不同抉择集合或同一抉择集合的不同子集也可能有不同偏好,故效用曲线具有近乎“捉摸不定”的多样性.多年来一直采用Standard Gamble Technique(SGT)绘制效用曲线,或按诸如边际效用递减原理等将对数函数或其它简单函数当作效用曲线,这些方法之繁琐或不严格性,使得效用理论的推广应用受到很大的局限.但也应看到,由于效用值一方面反映了决策者个人的偏好,另一方面也在一定程度上反映了决策后     

直觉模糊数风险偏好一致排序方法和决策

证明直觉模糊数的Hong排序法、刘华文排序法和陈东峰排序法都要求决策者的风险态度随直觉模糊数变化而变化,不满足风险偏好一致性,违背决策者的风险态度相对稳定的实际情况.提出基于风险偏好系数的直觉模糊数排序方法,它能保证决策者风险偏好一致;并且,面对相同的决策问题,不同风险偏好的决策者可能有不同的决策结果.最后,把基于风险偏好系数的直觉模糊数排序法应用于直觉模糊集多属性决策.     

基于合格值自适应后悔理论和证据理论的区间多属性决策方法

针对属性值和权重都用区间描述的不确定性多属性决策问题,文章提出了一种基于合格值自适应后悔理论和证据理论的决策方法.该方法定义属性合格参考值,表示决策者对方案的接受度在该值以下呈现快速下降趋势.之后依据后悔理论,定义基于属性合格参考值的后悔效用函数,改善传统后悔效用函数灵活性弱和对风险规避行为的描述能力不够强的缺点.之后扩展出基于区间的效用计算方法,并基于区间最优点得到感知效用值矩阵.然后将感知效用值转化为基本概率分配函数并据此进行基于权重的证据合成.该方法还通过设定偏好态度系数以反映决策者对评价高低的倾向性.最后,通过算例分析说明了该方法的可行性,合理性和稳定性.     

基于UTA方法的多目标优化模型

针对多目标线性优化问题进行研究,提出了一种基于效用加性方法(UTA)的多目标线性优化方法.利用不同目标值的组合给出训练方案,决策者针对训练方案给出一些偏好信息,据此推断决策者的效用函数,并进一步求解多目标线性优化模型.进一步给出了算例来说明方法的实施过程及验证可行性.方法较多的考虑了决策者对于决策的偏好,注重决策者的意见,为多目标决策问题提供了一种新的思路.     

区间二型模糊集效用函数和熵在风险决策中的应用

针对以区间二型模糊集(IT2FS)为信息环境的多属性决策(MADM)问题,引入IT2FS效用函数,并提出基于IT2FS效用函数,熵和风险因子的风险决策模型。首先基于截集思想提出两种IT2FS效用函数公式,有效提取了IT2FS全部信息,比以往的序值型公式更加科学有效。其次基于已提出的IT2FS三种不确定度量存在的问题提出三种新型不确定度量,并基于此三种不确定度量提出IT2FS熵公式弥补原有熵度量的不足。再次引入风险偏好因子反映决策者不同的风险态度,并改进风险偏好因子范围。构造基于效用函数,熵和风险偏好因子的风险决策模型。最后利用一个实例分析结果表明,该风险决策模型中决策者风险偏好对属性权重以及方案的排序存在影响,该决策思想对风险投资决策和风险管理决策均有一定的参考作用。     

基于后悔理论和概率犹豫模糊集的多属性决策方法

由于决策环境的不确定性以及决策问题的复杂性,决策者越来越难以处理不确定型多属性决策的相关问题.针对决策者评估时具有犹豫性和偏好性以及风险规避和后悔规避等特点,提出了一种基于后悔理论和概率犹豫模糊集的多属性决策方法.运用概率犹豫模糊集对专家的评价信息进行表述和处理,在权重属性完全未知的情况下,使用CRITIC法确定属性权重;通过定义决策者对方案的感知效用函数,计算各个方案的总感知效用值并进行排序.最后,通过算例对该方法进行验证分析.结果表明:方法可以更好地刻画决策者的实际心理,决策结果更加客观和科学.     

具有风险偏好的模糊网络最短路算法

运用结构元理论来求解具有风险偏好的、带有模糊权值的网络最短路问题.首先,简要介绍模糊结构元及相关定理.之后,提出了组合序,证明组合序是全序.组合序含有参数θ,随着θ的取值范围不同,序反映风险偏好的类型不同.在组合序和相关定理的基础上,证明了模糊网络最短路的判定定理,定理表明:求模糊网络最短路等价求一经典网络最短路,且风险偏好大小由θ的取值来确定.最后,通过一个例子来说明求解过程.     

基于模糊聚类的不同形式偏好信息的集结方法研究

针对具有5种不同形式偏好信息的群决策问题给出了一种分析方法.当专家给出的偏好信息是模糊互补判断矩阵、区间值、正互反矩阵、序关系值以及效用值时,首先把不同形式的偏好信息转化为模糊互补判断矩阵,然后,再根据模糊互补判断矩阵得出每个专家的方案排序值,据此对专家进行模糊聚类,根据聚类结果确定专家的权重,进而进行信息合成和方案选优,并用算例进行了验证.     

Fuzzy preference orderings in group decision making

In this paper, some use of fuzzy preference orderings in group decision making is discussed. First, fuzzy preference orderings are defined as fuzzy binary relations satisfying reciprocity and max-min transitivity. Then, particularly in the case where individual preferences are represented by utility functions (utility values), group fuzzy preference orderings of which fuzziness is caused by differences or diversity of individual opinions are defined. Those orderings might be useful for proceeding the group decision making process smoothly, in the same manner as the extended contributive rule method.     

Fuzzy expected utility

The aim of this paper is to state the foundations of fuzzy decision theory under uncertainty. Attention is focused on the analysis of a fuzzy expected utility.Given a fuzzy decision problem, which does not rest on a Borel field but on a weak Borel field, and according to the information available, we shall use successively the probability and the possibility of a fuzzy subset.When the imprecise preference structure of the decision maker verifies four axioms, we can determine a function of fuzzy expected utility. This latter is a numerical translation of the imprecise preferences of the decision maker, in an uncertain world.     

An integrated model-based interactive approach to FMAGDM with incomplete preference information

Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking, strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations, inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate the developed approach.     

基于直觉犹豫模糊集的TOPSIS法

直觉犹豫模糊集集成了直觉模糊集和犹豫模糊集的优势,能更有效地刻画决策者偏好不一致的情况。距离测度一直是研究的热点问题,但尚没有文献研究直觉犹豫模糊集间的距离测度,因此本文定义了直觉犹豫模糊集间的Hamming距离、Euclidean距离和广义距离,同时考虑每个元素的权重,定义了加权距离。犹豫度是直觉犹豫模糊集的重要特性,因此在考虑犹豫度的基础上,又定义了一些距离测度。这些距离测度不仅考虑了直觉犹豫模糊数间的差异,同时考虑了犹豫度的影响,决策者可以根据对直觉犹豫模糊数和犹豫度之间偏好的不同,设置不同的偏好值得到距离测度。然后基于这些距离测度,又提出了直觉犹豫模糊环境下的TOPSIS法。最后通过实例说明了所提出的TOPSIS法的合理性与实用性。     

三角直觉模糊数型VIKOR方法

针对备选方案的属性值为三角直觉模糊数且权重为实数的多属性决策问题,研究了三角直觉模糊数型VIKOR方法。首先,本文提出了一种基于偏好指标的三角直觉模糊数排序方法;其次,根据VIKOR方法的基本思想,提出了求解三角直觉模糊数型VIKOR方法的步骤,并在可接受优势和决策过程的稳定条件下对备选方案进行排序,得到折衷解;最后,在最大群体效用权重为0.5的情况下,用第三方物流服务商选择为例说明了该方法的有效性和可行性。     

A way to deal with fuzzy preferences in multi-criteria decision problems

This paper presents a special multiple criteria decision making approach for solving problems in context with fuzzy individual preferences.At first we briefly expose the proposed methodology. The individual preferences are explicitly given by a complete transitive relation R on a set of reference actions. The modelling of the decision-maker's preferences is obtained by means of fuzzy outranking relations. These fuzzy relations are based on a system of additive utility functions which are estimated by means of ordinal regression methods analysing the preference relation R.This is followed by a presentation of two real multicriteria problems which the proposed methodology has been applied to, i.e. a highway plan choice problem and a problem in marketing research dealing with the launching of a new product. In each application we tried to specify this method according to the specific structure of the problem considered.     

基于模糊语言判断矩阵和FIOWA算子的有限方案决策法

定义一种模糊的导出有序加权平均(FIOWA)算子，给出方案之间比较的模糊语言标度。运用模糊语言标度构造出模糊语言判断矩阵，并提出一种基于模糊语言判断矩阵和FIOWA算子的有限方案决策方法。该法利用FIOWA算子对模糊语言信息进行集结，并利用已有的三角模糊数排序公式求得决策方案的排序。     

Representing risk preferences in expected utility based decision models

Users of expected utility based decision models frequently find it useful or necessary to specify a functional form that represents the risk preferences of a decision maker. Having additional functional forms from which to choose would be helpful. The literature so far has provided several such functional forms for the utility function itself. The discussion presented here indicates that providing a functional form for the marginal utility function is an alternate and equally useful way to represent risk preferences. Furthermore, functional forms for marginal utility are easier to provide, and there exist functional forms for marginal utility that represent simple risk preferences for which there is no associated functional form for the utility function. Several functional forms for marginal utility are suggested, and the class of isoelastic risk preferences is identified and discussed.     

Fuzzy multi-criteria decision-making based on positive and negative extreme solutions

To encompass decision data vagueness, many researchers generalized multi-criteria decision-making (MCDM) methods in certain environment into fuzzy multi-criteria decision-making (FMCDM) methods under fuzzy environment. In these FMCDM methods, ranking fuzzy numbers based on fuzzy pair-wise comparison is normally essential, but the comparison is a complexity work. To avoid fuzzy pair-wise comparison, we propose a FMCDM method based on positive and negative extreme solutions of alternatives. In the proposed method, two extreme solutions of alternatives are obtained by MAX and MIN operations of fuzzy TOPSIS. Then weakness and strength matrices between alternatives and extreme solutions are derived by a difference function revised from fuzzy preference relation of Lee, and multiplied with weight matrix to be weighted weakness and strength indices. The two weighted indices are respectively transferred into positive and negative indices, and then the two indices integrated into a total performance index. Finally, alternatives can be sorted according to their related performance indices, and FMCDM problems are easily solved, not by fuzzy pair-wise comparison.