基于概率犹豫模糊熵的多属性决策方法

针对概率犹豫模糊元的多个隶属度和其概率各不相同的特点,提出基于概率犹豫模糊熵的多属性决策方法.首先,定义3种新的概率犹豫模糊熵:模糊熵、犹豫熵和总熵,以分别测量概率犹豫模糊元的模糊性、犹豫性和整体不确定性;然后给出3种熵测度的公理化定义和表达式;最后,根据概率犹豫模糊元的3种熵,构建能够解决属性权重完全未知的多属性决策模型,并通过案例和对比分析验证所提模型的有效性和合理性.     

基于符号距离和交叉熵的概率犹豫模糊多属性决策方法

针对概率犹豫模糊环境下属性权重完全未知的多属性决策问题,提出基于符号距离和交叉熵的多属性决策方法.首先,定义用于测量决策者犹豫程度的3种概率犹豫模糊元的犹豫度:数值犹豫度,信息不完全度和总犹豫度,基于3种犹豫度提出概率犹豫模糊符号距离;然后,为了避免人为添加元素,定义调和概率犹豫模糊元,并结合信息不完全度提出概率犹豫模糊元的交叉熵;最后,根据概率犹豫模糊元的符号距离和交叉熵构建多属性决策模型,并通过算例验证了该模型的有效性和合理性.     

改进的犹豫模糊语言熵的一般公式与生成算法

由于现有的扩展犹豫模糊语言术语集的熵无法区分与补集相等的扩展犹豫模糊语言术语集的不确定性，并且对犹豫模糊语言信息中的犹豫性考虑得相对较少，无法全面地反映犹豫模糊语言信息的不确定性。改进了扩展犹豫模糊语言术语集的熵的定义，从模糊性和犹豫性两方面刻画了扩展犹豫模糊语言术语集的不确定性，分别定义了扩展犹豫模糊语言术语集的模糊熵和犹豫熵，给出了模糊熵和犹豫熵的一般公式与生成算法。定义了一个扩展犹豫模糊语言术语集的总熵，给出了总熵的一般公式。最后给出了一个基于犹豫模糊语言熵的高校教授晋升优选评估的多属性决策算例，通过比较分析说明了决策方法的可行性与有效性。     

基于可达概率区间的不确定决策树

针对不确定数据的概率分布难以获取的客观实际,讨论了缺失概率分布的值不确定离散对象的决策树。定义了(条件)概率区间,并证明了(条件)概率区间是可达概率区间;基于可达概率区间,定义了(条件)熵区间,并给出了求解(条件)熵区间的上/下界的方法;采用条件熵区间作为属性选择度量,提出了一种新的不确定决策树,将以0-1划分对象的决策树扩展到以概率区间分配对象的决策树,这样不仅可以处理缺失概率分布的值不确定离散对象,也可以处理确定离散对象。通过在基于UCI数据集的不确定数据集上的实验,证实了不确定决策树是有效的。     

模糊语言多属性群决策的客观综合赋权方法

针对一类属性及专家权重完全未知且评价值为直觉不确定语言数的多属性群决策问题,提出一种基于客观综合赋权模型的模糊群决策方法。通过定义直觉不确定语言数的不确定度和距离测度,对单个专家内部以及专家群体之间的评价值进行分析,分别建立基于离差最大化和熵值的属性综合赋权模型以及基于不确定度和偏离度的专家综合赋权模型,提出一种基于客观综合权重的直觉不确定语言多属性群决策方法。通过实例分析表明了该方法的可行性和实用性。     

混合型概率犹豫模糊熵和交叉熵测度

针对已有概率犹豫模糊熵测度构造复杂、区分能力弱等缺点,提出一种混合型概率犹豫模糊熵测度.混合型熵测度能够综合反映概率犹豫模糊元所具有的个体不确定性和整体不确定性,具有结构简单、物理意义明确、区分能力强等优势.在概率犹豫模糊元规范化的基础上,基于混合型熵测度的构造理念所设计的混合型交叉熵测度,能够克服已有交叉熵测度的设计缺陷,综合反映两个概率犹豫模糊元之间的个体区分度和整体区分度,且具有自然的对称性.基于混合型熵测度和交叉熵测度,进一步设计概率犹豫模糊环境下的多属性决策方法,并将其应用于无人机集群作战效能评估.数值和理论分析结果表明,所提出的混合型概率犹豫模糊熵和交叉熵测度能够成对设计,互为印证,具有广泛的应用前景.     

一种基于前景理论的毕达哥拉斯犹豫模糊不确定语言ELECTRE多属性决策方法

针对属性权重已知、属性值为毕达哥拉斯犹豫模糊不确定语言变量的多属性决策问题,提出一种前景理论和消去与选择转换法(ELECTRE)相结合的多属性决策方法.首先给出毕达哥拉斯犹豫模糊不确定语言集的 定义,包括得分函数、距离测度和运算法则;然后将前景理论引入该决策环境下,构建前景价值矩阵,运用传统ELECTRE法求得一致矩阵和矛盾矩阵,并对其进行转化构建前景优/劣势判断矩阵,进而求得总优/劣势值以确定备选方案的优劣排序;最后通过算例分析验证所提出方法的有效性和可行性,并与该决策环境下的传统ELECTRE法进行对比,表明了该方法的优越性和实用性.     

基于前景理论的犹豫模糊TOPSIS多属性决策方法

针对属性权重未知、属性值为犹豫模糊集的决策问题,提出一种前景理论和逼近理想解(TOPSIS)相结合的多属性决策方法.考虑到决策者对指标集的不同偏好,利用犹豫模糊熵的相关理论,提出一种基于犹豫模糊熵的熵权法确定属性权重.将决策者的风险心理因素引入犹豫模糊多属性决策中,定义了犹豫模糊数的前景价值函数,并以此将犹豫模糊决策矩阵转化为价值矩阵,计算出各方案的收益损失比值.最终应用TOPSIS的基本思路,确定备选方案的优劣排序,并通过算例分析验证了所提出方法的有效性.     

对偶犹豫模糊集的相关系数及其应用

对偶犹豫模糊集因其可以给决策者提供更多的决策信息成为模糊决策的热点研究问题,相关性指标可以用来度量两个模糊信息之间的相关关系,熵可以用来度量模糊信息的不确定程度。提出了一种基于对偶犹豫模糊集相关系数和熵的模糊多属性群决策方法。定义了对偶犹豫模糊集相关系数的概念,讨论了其基本性质;提出了两种对偶犹豫模糊集的熵,在此基础上,给出了模糊多属性群决策的权重确定方法;基于对偶犹豫模糊集相关系数和熵,提出了一种属性权重完全未知条件下的模糊多属性群决策方法;通过案例分析说明了该方法的有效性和可行性。     

基于广义直觉语言算子的多属性群决策方法

针对属性权重未知,属性值为直觉语言数的多属性决策问题,提出了一种基于直觉语言熵和广义直觉语言算子的群决策方法.定义了直觉语言熵,并利用直觉语言熵确定属性权重,提出了三种直觉语言算子:广义直觉语言加权几何平均(GILWGA)算子、广义直觉语言有序加权几何(GILOWG)算子及广义直觉语言混合几何(GILHG)算子.利用GILWGA和GILHG算子集结信息,采用基于直觉语言数的得分函数及精确函数进行方案排序与择优,最后通过一个算例说明了该方法的有效性和合理性.     

考虑决策者心理行为的概率语义术语集多属性决策方法

概率语义术语集可以通过给语义赋予概率以表达不同程度偏好,采用概率语义术语集获取专家犹豫和不确定的评价信息。针对传统多属性决策中指标权重确定没有考虑指标间相互影响关系的问题,采用概率语义DEMATEL方法分析指标间的相互影响关系,其中采用二元语义将指标间关联关系概率语义术语集的得分函数转换为精确数值,得到指标的权重。考虑决策者的不同偏好和心理行为,采用改进的概率语义TODIM方法对决策对象进行排序。最后以某班轮公司的综合竞争力评估为例,验证了所提方法的有效性。     

Probabilistic linguistic information fusion: A survey on aggregation operators in terms of principles,definitions, classifications,applications, and challenges

The probabilistic linguistic term set is a flexible and efficient tool to represent the cognitive complex information of experts. It has attracted many scholars’ attention since it was proposed. Information fusion over the cognitive complex information is a significant issue for decision-making problems. Over the past years, more than 40 aggregation operators have been proposed to fuse the probabilistic linguistic term sets. The aim of this paper is to survey the existing probabilistic linguistic aggregation operators from the perspectives of principles, definitions, classifications, and applications. To do so, first, we summarize the present normalization techniques and operations of probabilistic linguistic term sets. Afterward, this study classifies the existing probabilistic linguistic aggregation operators into 12 kinds. Then, the application areas of these probabilistic linguistic aggregation operators are outlined. Future research directions with interests are proposed to tackle present challenges.     

q-Rung orthopair uncertain linguistic partitioned Bonferroni mean operators and its application to multiple attribute decision-making method

A q-rung orthopair uncertain linguistic set can be served as an extension of an uncertain linguistic set (ULS) and a q-rung orthopair fuzzy set, which can also be treated as a generalized form of the existing intuitionistic ULS and Pythagorean ULS. The new linguistic set uses the uncertain linguistic variable to express the qualitative evaluation information and allows decision makers to provide their true views freely in a larger membership grade space. In this paper, we investigate the Bonferroni mean under the q-rung orthopair uncertain linguistic environment, then we propose the q-rung orthopair uncertain linguistic Bonferroni mean and its weighted form. Furthermore, considering the specific partition pattern among the attributes, the q-rung orthopair uncertain linguistic partitioned Bonferroni mean and its weighted form are developed. Meanwhile, we discuss several representative cases and attractive properties of our proposed operators in depth. Subsequently, a novel multi-attribute decision-making method is developed based on the above-mentioned aggregation operators. In the end, a comprehensible case is performed to analyze the superiority of the developed method by comparing with other typical studies.     

基于概率语言术语集的云服务选择

为了解决云服务评估决策中QoS(Quality of Service,服务质量)属性的动态性刻画不足以及传统决策方法中用户主观因素过强的缺点,提出了一种基于概率语言术语集(Probabilistic Linguistic Term Set,PLTS)的选择方法.通过相似性权重与可靠性权重结合获取推荐权重,加入决策矩阵中...     

基于概率语言术语信息的前景决策方法

针对属性值为概率语言术语、属性权重完全未知的多属性决策问题,提出一种基于概率语言术语信息的前景决策方法.首先,为解决语言决策信息的群集结问题,通过power语言集结算子把一组语言术语集集结为概率语言术语,最大程度保留决策信息;其次,考虑概率语言术语集现有距离公式分辨率不高,定义一种新的距离公式;再次,鉴于决策者主观风险态度,引入前景理论至概率语言环境中,结合新的距离公式,构建前景决策矩阵;进而,综合主客观因素,构建组合赋权模型计算属性权重;最后,结合前景理论决策模型和指标权重求得综合前景值以此排序得最优方案,并通过算例验证其有效性.     

Z‐uncertain probabilistic linguistic variables and its application in emergency decision making for treatment of COVID‐19 patients

Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z‐uncertain probabilistic linguistic variables (Z‐UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z‐UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z‐uncertain probabilistic linguistic (Z‐UPL) environment. Finally, an emergency decision‐making case of COVID‐19 patients and comparative analysis illustrate the necessity and effectiveness of this method.     

Operators and comparisons of probabilistic linguistic term sets

The probabilistic linguistic term sets (PLTSs) allow experts to express their preferences regarding one linguistic term over another. Nowadays, multicriteria decision-making methods for PLTSs are very popular, and Bai et al’s multicriteria decision-making method based on the possibility degree formula for PLTSs cannot be ranked in some situations. In this paper, we first propose a new possibility degree method for PLTSs and state their properties, and we use this new possibility degree method to solve the drawbacks of Bai et al’s possibility degree method. Second, we propose a probabilistic linguistic weight average (PLWA) and probabilistic linguistic order weight average (PLOWA) operator and state their properties. Then, based on the new possibility degree method and the PLWA (PLOWA) operator, we propose a multicriteria decision-making method based the PLWA (PLOWA) operator. Finally, we utilize an example to illustrate the interrelationships between our method and Bai et al’s method. The result shows that our multicriteria decision-making method is more rational.     

Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations

Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms.     

Inclusion measures of probabilistic linguistic term sets and their application in classifying cities in the Economic Zone of Chengdu Plain

The probabilistic linguistic term set is a powerful tool to express and characterize people’s cognitive complex information and thus has obtained a great development in the last several years. To better use the probabilistic linguistic term sets in decision making, information measures such as the distance measure, similarity measure, entropy measure and correlation measure should be defined. However, as an important kind of information measure, the inclusion measure has not been defined by scholars. This study aims to propose the inclusion measure for probabilistic linguistic term sets. Formulas to calculate the inclusion degrees are put forward Then, we introduce the normalized axiomatic definitions of the distance, similarity and entropy measures of probabilistic linguistic term sets to construct a unified framework of information measures for probabilistic linguistic term sets. Based on these definitions, we present the relationships and transformation functions among the distance, similarity, entropy and inclusion measures. We believe that more formulas to calculate the distance, similarity, inclusion degree and entropy can be induced based on these transformation functions. Finally, we put forward an orthogonal clustering algorithm based on the inclusion measure and use it in classifying cities in the Economic Zone of Chengdu Plain, China.