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。     

直觉犹豫模糊集的相关系数在群推荐中的应用

在直觉犹豫模糊集描述的群推荐系统中,首先,针对直觉犹豫模糊距离公式计算相似性问题中存在的不足,提出了直觉犹豫模糊集相关系数的概念;其次,给出直觉犹豫模糊集相关系数的聚类算法,并分析采用直觉犹豫模糊集相关系数公式与距离公式计算相似性的区别;最后,利用直觉犹豫模糊集相关系数对电影进行推荐,结论表明了直觉犹豫模糊集相关系数方法的实用性和有效性。     

q阶犹豫模糊集及其在决策中的应用

定义q阶模糊集的数乘、算术、几何等基本运算,研究运算的性质.结合犹豫模糊集与q阶模糊集,提出q阶犹豫模糊集的概念,定义q阶犹豫模糊集的一些运算并研究基本性质,提出q阶犹豫模糊集的得分函数和精确函数,实现q阶犹豫模糊集的对比.基于q阶犹豫模糊集的基本运算法则,构建q阶犹豫模糊集的多属性群决策模型,并通过实例验证此决策模型的可行性和有效性.     

加权犹豫模糊集的群决策方法

对于犹豫模糊元中的不同隶属度值赋予不同的权重,由此构造出一种应用范围更广、更符合实际需要的犹豫模糊集合 ----- 加权犹豫模糊集合.针对加权犹豫模糊集中的加权犹豫模糊元,定义了加权犹豫模糊集合和加权犹豫模糊元的并、交、余、数乘和幂等运算及其运算法则,并讨论它们的运算性质;同时,给出加权犹豫模糊元的得分函数和离散函数,进而给出一种比较加权犹豫模糊元的排序法则.在此基础上,提出两类集成算子:加权犹豫模糊元的加权算术平均算子和加权犹豫模糊元的加权几何平均算子,并针对专家权重(已知和未知)的两种情形,将加权犹豫模糊集合应用于群决策,给出两种基于加权犹豫模糊集合的群决策方法.最后,通过一个应用实例表明所提出的群决策方法的有效性和实用性.     

犹豫模糊软集的相关系数及其在决策中的应用

犹豫模糊软集结合了Torra(2010)的犹豫模糊集理论和Molodtsov(1999)的软集理论.鉴于相关系数是数据分析中应用最广泛的指标之一,提出一种犹豫模糊软集相关系数,同时给出犹豫模糊软集的平均值和方差的定义,基于这些概念给出犹豫模糊软集相关系数的计算公式.新的犹豫模糊软集相关系数的值在区间[$-1,1$]上,而不是[$0,1$]上,这与统计学中经典相关系数一致,因此克服了已有犹豫模糊软集相关系数中存在的缺陷.为了提升其应用的广泛性,提出犹豫模糊软集加权相关系数的概念.最后,通过医院评估的实例验证所提出的犹豫模糊软集相关系数的适用性和有效性.     

区间值对偶犹豫模糊集的相关系数及其应用

区间值对偶犹豫模糊集因其可能隶属度与可能非隶属度均采用区间的形式而更具有一般性,因而得到广泛的应用。相关系数可以用来度量两个模糊信息之间的相关关系。基于区间值对偶犹豫模糊集相关系数提出了一种新的多属性群决策方法。在对偶犹豫模糊集的基础上给出了区间值对偶犹豫模糊集的定义及其基本运算;给出了区间值对偶犹豫模糊集的相关系数的定义及相应的计算公式;构造了确定权重的优化模型;基于区间值对偶犹豫模糊集的相关系数和确定权重的优化模型,提出一种属性权重部分未知的模糊多属性群决策方法,并通过实例说明该方法的有效性和可行性。     

基于混合型相关系数的概率犹豫模糊集识别方法

针对现有概率犹豫模糊集相关系数研究中存在的缺陷,如未考虑隶属度个数以及存在反直觉现象等,提出新的混合型相关系数.混合型相关系数能够综合反映概率犹豫模糊集之间的个体和整体相关性,相比已有的相关系数更为全面、合理.首先,综合考虑概率犹豫模糊数中元素的整体性、分布和长度3个因素,分别定义均值、方差和长度率3个基本相关系数,在此基础上集成得到混合型相关系数,并证明其满足相关系数公理化定义的基本准则,实例分析结果表明,混合型相关系数能够克服现有概率犹豫模糊相关系数存在的缺陷;然后,基于混合型相关系数,进一步设计概率犹豫模糊环境下的多属性决策方法;最后,通过案例分析验证所提出相关系数的有效性和合理性.     

加权犹豫三角模糊距离度量及其在群决策中的应用

对于犹豫三角模糊元中不同的元素作为隶属度的重要性不同,提出加权犹豫三角模糊元和加权犹豫三角模糊集的概念,研究了决策值为加权犹豫三角模糊元的群决策问题。首先,给出了加权犹豫三角模糊距离公式;其次,基于计算方便且不改变三角模糊数作为隶属度的重要性,提出一种对加权犹豫三角模糊元添加元素的方法;最后,提出加权犹豫三角模糊距离度量的群决策方法,并应用于加权犹豫三角模糊环境下的群决策。数值实例表明,加权犹豫三角模糊距离度量在群决策中具有合理性和可行性。     

毕达哥拉斯犹豫模糊集成算子及其决策应用

针对毕达哥拉斯犹豫模糊多属性决策中,集成算子的重要作用以及集成算子不完善的情况,较为系统地研究了毕达哥拉斯犹豫模糊集成算子。为此,在毕达哥拉斯模糊数的运算和运算法则基础上,定义了毕达哥拉斯犹豫模糊有序加权平均算子（PHFOWA）、广义有序加权平均算子（GPHFOWA）和混合平均算子（PHFHA）,以及毕达哥拉斯犹豫模糊有序加权几何平均算子（PHFOWG）、广义有序加权几何平均算子（GPHFOWG）和混合几何平均算子（PHFHG）,并结合数学归纳法,分别给出了它们的计算公式,讨论了它们的有界性、单调性和置换不变性等性质。建立了基于毕达哥拉斯犹豫模糊集成算子的多属性决策方法,并应用算例和相关方法比较说明了决策方法的可行性与有效性。     

毕达哥拉斯犹豫模糊集的相关测度

毕达哥拉斯犹豫模糊集,既能描述隶属度与非隶属度之和超过1、而平方和不超过1的模糊现象,又能表达决策者在隶属度和非隶属度上的犹豫不决,因此它是表达不确定现象的一个强有力工具.考虑到相关测度在统计学和管理科学中发挥着重要的作用,在模糊集、直觉模糊集以及毕达哥拉斯模糊集等相关测度基础上,研究毕达哥拉斯犹豫模糊集的相关测度.为此,定义毕达哥拉斯犹豫模糊集的信息能量、相关指标以及相关系数,证明相关系数的性质.由于决策中经常要考虑到属性权重,定义毕达哥拉斯犹豫模糊集的加权相关系数,并讨论其性质.最后,通过求出每个方案与正理想方案之间的加权相关系数,实现方案的排序择优,并通过算例表明其可行性与有效性.     

时序犹豫模糊软集及其在决策中的应用

针对犹豫模糊软集的信息随着时间动态变化的情形,引入时间参数,将犹豫模糊软集推广为时序犹豫模糊软集。基于时序犹豫模糊软集的概念,定义了其基本的运算法则,分析对应的运算结果并讨论其运算性质。给出了时序犹豫模糊软集的一种决策方法,并通过实例表明了该方法的有效性与可行性。     

Uncertain linguistic hesitant fuzzy sets and their application in multi‐attribute decision making

To denote the quantitative and qualitative fuzzy information simultaneously, this paper introduces a new type of fuzzy sets called uncertain linguistic hesitant fuzzy sets, which are denoted by an uncertain linguistic variable with several possible interval membership degrees. Considering the application of this type of fuzzy sets, several basic operational laws are defined, and several properties are studied. Meanwhile, an ordered relationship is introduced. Then, two types of uncertain linguistic hesitant fuzzy aggregation operators are defined. One uses additive measures, and the other is based on λ‐fuzzy measures. Then, a similarity measure is presented, by which models for the optimal weight vector are constructed. After that, an approach to uncertain linguistic hesitant fuzzy multi‐attribute decision making is developed. Finally, an illustrative example for evaluating corporate environmental performance is offered to show the concrete practicality of the procedure.     

Fermatean fuzzy linguistic set and its application in multicriteria decision making

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter in the proposed distance measure is also discussed.     

A novel hesitant fuzzy linguistic hybrid cloud model and extended best-worst method for multicriteria decision making

Developing effective and accurate model to handle complex uncertainties of linguistic assessments in multicriteria decision making (MCDM) has important theoretical significance and practical value of engineering. This paper proposes a novel hesitant fuzzy linguistic hybrid cloud (HFLHC) model that integrates hesitant fuzzy linguistic term set and cloud model to handle the hesitancy, fuzziness, and randomness of linguistic expression. The normal cloud and trapezium cloud are integrated to represent hybrid-length linguistic variables of HFLHC model, which can effectively avoid evaluation information loss and distortion. Aiming at applying HFLHC model to MCDM, some hybrid operations for normal cloud and trapezium cloud are developed. Moreover, an improved method for aggregating multiple linguistic concepts into an integrated trapezium cloud in HFLHC model is proposed, with consideration of the different representation region of each linguistic concept. Furthermore, a novel HFLHC-based best-worst method is proposed to obtain optimal criteria weights with developing a HFLHC optimization programming model and a modified consistency ratio. Finally, an illustrative example of sustainable supplier selection is presented. Several comparative analyses demonstrate that our method can provide more consistency and greater reliability.     

基于梯形模糊隶属函数的复合语言多目标决策

对于一些复杂的决策问题, 使用比较语言比单一语言更能准确地表达专家的看法. 据此, 提出一种同时使用单一语言和比较语言的新算法. 根据上下文无关文法将比较语言表达转换为犹豫模糊语言术语集(HFLTS), 并应用有序加权算子(OWA) 计算出由梯形隶属函数表示的模糊语言术语集的模糊包络, 有效地简化了基于HFLTS 的词计算过程. 最后应用逼近理想解排序(TOPSIS) 方法进行决策.

     

Assessment of traffic congestion with ORESTE method under double hierarchy hesitant fuzzy linguistic environment

With the new generation of information technology development and the promotion of the Internet, local governments turn their attention to the construction of intelligent transportation systems. More and more cities began building intelligent transportation which has been widely used to monitor urban traffic. Experts can evaluate urban traffic congestion based on the information collected from the big data of intelligent transportation. In recent two years, double hierarchy hesitant fuzzy linguistic term set has been widely used to depict explicit evaluation information, which is straightforward and broad-spectrum. When evaluating traffic congestion in a city, decision makers can utilize double hierarchy hesitant fuzzy linguistic term sets to express vague information. Moreover, the ORESTE method is an applicative method which can select a reliable alternative by subdividing alternatives and reduce the loss of information in the conversion process. In this paper, we propose a double hierarchy hesitant fuzzy linguistic ORESTE method and a new score function of double hierarchy hesitant fuzzy linguistic term set. The method raises a new perspective to reduce the error from other methods and the new score function derives a robust decision-making result. Then, we apply the double hierarchy hesitant fuzzy linguistic ORESTE method to solve a practical case involving choosing the congested city by evaluating the 5S traffic congestion model. Finally, we compare the double hierarchy hesitant fuzzy linguistic ORESTE method with other methods such as the classical ORESTE method and the double hierarchy hesitant fuzzy linguistic MULTIMOORA to illustrate the advantages of our method.     

The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making

In this paper, the cross-entropy of intuitionistic hesitant fuzzy sets (IHFSs) is developed by integrating the cross-entropy of intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs). First, several measurement formulae are discussed and their properties are studied. Then, two approaches, which are based on the developed intuitionistic hesitant fuzzy cross-entropy, are proposed for solving multi-criteria decision-making (MCDM) problems within an intuitionistic hesitant fuzzy environment. For both methods, an optimisation model is established in order to determine the weight vector for MCDM problems with incomplete information on criteria weights. Finally, an example is provided in order to illustrate the practicality and effectiveness of the proposed approaches.