基于乘型一致性的毕达哥拉斯模糊偏好关系

在乘型一致性区间值模糊偏好关系和乘型一致性直觉模糊偏好关系启发下,研究了乘型一致性毕达哥拉斯模糊偏好关系。首先,将毕达哥拉斯模糊偏好关系转化为两个等价的区间值模糊偏好关系,通过区间值模糊偏好关系的乘型一致性,定义了毕达哥拉斯模糊偏好关系的乘型一致性。其次,研究了乘型一致性毕达哥拉斯模糊偏好关系的若干性质。然后,研究了毕达哥拉斯模糊偏好关系的排序向量,以及求解乘型一致性和非乘型一致型毕达哥拉斯模糊偏好关系排序向量的方法。最后,通过实例说明了求解排序向量的方法是可行有效的。     

加型一致性毕达哥拉斯模糊偏好关系

在模糊偏好关系两种等价的加型一致性概念基础上,通过简单的数学证明,分析了区间值模糊偏好关系、直觉模糊偏好关系的相应的两种加型一致性并不是等价的.然后,在加型一致性直觉模糊偏好关系的启发下,构造了可以与毕达哥拉斯模糊偏好关系相互转换的两个区间值模糊偏好关系,并利用它们的加型一致性,定义了加型一致性毕达哥拉斯模糊偏好关系,并分析了其与杨艺等定义的加型一致性毕达哥拉斯模糊偏好关系的关系.其次,研究了加型一致性毕达哥拉斯模糊偏好关系的性质以及毕达哥拉斯模糊偏好关系的满意一致性,并给出满意一致性毕达哥拉斯模糊偏好关系下的方案优劣排序算法.最后,通过两个计算实例说明了排序算法可行有效.     

一种新的区间数多属性决策权重信息集结方法

针对属性权重以区间数形式给出的多属性决策问题,在充分分析区间数向量的性质后,给出了一种决策模型。模型首先利用区间数权重向量得到决策偏好,然后在离差最大化思想指导下解决此带有决策偏好的决策问题。最后,通过一个实例说明了方法的可行性。     

区间值映射的半连续性与凸性

首先给出了区间数空间子集的有界性及确界等概念,并给出了确界的存在性定理;然后讨论了区间值映射的半连续性问题,给出了区间值映射的半连续性概念及相关性质;最后讨论了半连续区间值映射的凸性问题,给出了半连续区间值映射为凸区间值映射的两个充分条件.     

T-S-Ferrers性质与区间序指标

集中于T-S-Ferrers性质指标以及与之相关的区间序指标的研究。首先给出T-S-Ferrers性质指标的性质,包括T-S-Ferrers性质指标的等价形式、T-S-Ferrers性质指标与S-强完全指标的关系以及大偏好关系与严格偏好关系的T-S-Ferrers性质指标之间关系。然后定义区间序指标,并讨论区间序指标的性质以及T-S-Ferrers性质与区间序指标之间的关系。     

基于方案偏好值的属性关联区间多属性决策

针对属性值为区间数,属性权重完全未知,但给出方案的主观偏好值,部分属性偏好关系以及属性交互类型的属性关联多属性决策问题给出决策方法.首先建立期望值目标规划模型,确定出属性集的M(o|¨)bius表达式以及属性权重,然后利用扩展的区间Choquet积分算子对决策信息进行集结,计算出各方案的区间模糊综合评价值,再利用比较区间数的期望值方法,从而得到方案的最终排序.最后给出了分析实例以说明所提出方法的有效可行性.     

一种具有不确定偏好序评价信息的群决策方法

针对具有不确定偏好序评价信息的群决策问题,提出了一种决策方法。首先,描述了不确定偏好序的概念,并将它转化为概率向量,同时给出概率向量加权算子;然后,给出了概率向量两两比较的可能度的定义及性质分析;依据概率向量加权算子及可能度,建立了方案两两比较的可能度矩阵;基于可能度矩阵及互补判断矩阵的权重公式,计算方案的优先权重并对方案进行优选;最后,通过一个算例说明了该方法的可行性和有效性。     

基于区间值对偶犹豫模糊集的多属性决策方法

基于区间值对偶犹豫模糊集的基本定义,提出了区间值对偶犹豫模糊熵与相似性测度的概念。给出了区间值对偶犹豫模糊熵的定义及公式,在此基础上构造了熵权重模型;由距离与相似性测度的关系给出三种区间值对偶犹豫模糊集的距离公式。由此基于区间值对偶犹豫模糊集的熵和相似性测度提出一种新的区间值对偶犹豫模糊集的决策方法。最终给出此方法的计算步骤,通过实例验证该方法的有效性。     

一致性区间数判断矩阵的性质及排序

讨论了具有序传递性的区间数判断矩阵的性质,给出了一致性区间数判断矩阵具有序传递性的一个充要条件.在此基础上,证明了一致性区间效判断矩阵的权值可行域中所有向量的分量在不劣于的次序关系下具有完全相同的排列次序.因此,用权值可行域的顶点的算术平均或几何平均作为一致性区间数判断矩阵的排序向量是合理的.     

基于三维模糊向量的一种模糊决策方法

首先从三维模糊向量出发,给出了三维模糊向量的区间值截函数的定义,讨论了截函数的性质。然后利用区间值截函数给出了两个三维模糊向量比较可能度的定义,并利用这种可能度建立了基于三维模糊集的一种新的模糊决策方法。     

区间直觉模糊判断矩阵群决策中的逆判问题

研究了区间直觉模糊判断矩阵的群决策问题.定义了两种区间直觉模糊集相似度公式,给出两种与决策群体意见一致性程度最高的理想区间直觉模糊判断矩阵构造优化方法.利用矩阵对不同专家判断矩阵中相同位置元素的一致性进行分析,并对不同专家的判断信息进行整体相似程度分析,最后通过算例说明了该方法的有效性和实用性.     

考虑决策者风险偏好的区间直觉模糊多属性群决策方法

提出了一种考虑决策者风险偏好且属性权重信息不完全的区间直觉模糊数多属性群决策方法。同时考虑相似度和接近度,确定每一属性的决策者权重。为了考虑决策者风险偏好对决策结果的影响和避免区间直觉模糊矩阵的渐进性,引入了决策者风险偏好系数,将集结后的综合决策矩阵转换成区间数矩阵。然后,为了客观地求出属性权重信息不完全环境下属性的权重,构建了基于区间直觉模糊交叉熵的属性权重目标规划模型,该模型不仅考虑了评价值的偏差,也强调了评价值自身的可信度。最后,通过研发项目选择问题的实例分析说明了所提方法的合理性和优越性。     

A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.     

Consistency analysis of triangular fuzzy reciprocal preference relations

In order to simulate the uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. Based on the reciprocity property, this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations. The new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by Buckley (1985). The properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail. In addition, the shortcomings of the proof procedure of the proposition given by Wang and Chen (2008) are pointed out. And the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations. Finally, using the (n − 1) restricted comparison ratios, a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed, and an algorithm is shown to make a consistent decision ranking. Numerical results are further calculated to illustrate the new definition and the obtained algorithm.     

A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations

Decision makers (DMs)’ preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations. This paper proposes a chi-square method (CSM) for obtaining a priority vector from multiplicative and fuzzy preference relations. The proposed CSM can be used to obtain a priority vector from either a multiplicative preference relation (i.e. a pairwise comparison matrix) or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures. Theorems and algorithm about the CSM are developed. Three numerical examples are examined to illustrate the applications of the CSM and its advantages.     

区间犹豫模糊ELECTRE多属性决策方法及应用

近年来,多属性决策问题一直是广大学者研究的重点,然而基于ELECTRE方法的区间犹豫模糊多属性决策问题的研究并不多见。因此,结合区间犹豫模糊集的信息表达优势和ELECTRE方法的思想,提出了一种区间犹豫模糊ELECTRE(IVHF ELECTRE)多属性决策新方法。首先构造了区间犹豫模糊决策矩阵,引入得分函数和可能度的概念,构造属性优势集和属性劣势集。然后通过设定阈值得到综合优先判定矩阵,从而得到各方案间的优先顺序。为了进一步得到各方案的整体排序,引入TOPSIS方法,通过计算各方案与正负理想点的相对距离来构造综合优先矩阵,从而得到各方案的总体排序。最后通过具体实例验证了该方法的可行性和合理性。     

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。     

On consistency measures of linguistic preference relations

Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.     

Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection

This paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations. The proposed approach that is analytical in nature assesses the weights by minimizing the sum of squared distances between any two weighted fuzzy preference relations. Relevant theorems are offered in support of the proposed approach. Multiplicative preference relations are also incorporated into the approach using an appropriate transformation technique. An eigenvector method is introduced to derive the priorities from the collective fuzzy preference relation. The proposed aggregation approach is tested using two numerical examples. A third example involving broadband internet service selection is offered to illustrate that the proposed aggregation approach provides a simple, effective and practical way of aggregating multiple fuzzy preference relations in real-life situations.     

Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems

This paper investigates an approach for multi-criterion decision making (MCDM) problems with interval-valued intuitionistic fuzzy preference relations (IVIFPRs). Based on the novel interval score function, some extended concepts associated with IVIFPRs are defined, including the score matrix, the approximate optimal transfer matrix and the possibility degree matrix. By using these new matrixes, a prioritization method for IVIFPRs is proposed. Then, we investigate an interval-valued intuitionistic fuzzy AHP method for multi-criteria decision making (MCDM) problems. In the end, a numerical example is provided to illustrate the application of the proposed approach.