INGIOWGA算子的多属性决策方法及其应用

研究了方案的属性评估信息以模糊语言形式给出的多属性群决策问题，在导出的有序加权几何平均（IOWGA）算子理论的基础上，给出了一种区间数广义导出有序加权几何平均（INGIOWGA）算子，利用广义的导出有序加权平均（GIOWA）算子，对专家所给出的对应于各方案的属性评估信息进行了集结，并提出了一种基于模糊语言评估和GIOWA算子的多属性群决策方法。利用该算法对X射线实时成像检测系统方案选择中的判断信息进行集结，并且通过算例说明了该方法的有效性和实用性。     

C-POWGA算子及其在不确定多属性决策中的应用

为了降低不确定多属性决策中区间决策信息集成时的计算复杂度,将连续区间有序加权几何平均（C-OWGA）算子和Power几何平均算子相结合,提出一种连续区间Power有序加权几何平均（C-POWGA）算子,并提出了一种基于C-POWGA算子的不确定多属性群决策方法;通过某银行的员工绩效考核来说明该方法的可行性和有效性。     

基于Choquet 积分的直觉不确定语言信息集结算子及其应用

基于直觉不确定语言信息,针对属性间不严格相互独立且具有较大关联度的群决策问题,提出了两种基于直觉不确定语言信息的Choquet积分算子.首先,分析了因属性关联使得以往直觉不确定语言信息集结算子失效的现象,对此引入模糊测度,提出了直觉不确定语言的Choquet加权算术平均算子(IULCWA)和直觉不确定语言的Choquet加权几何平均算子(IULCGM);然后,证明了算子的相关性质,研究了属性间相关的、属性值为直觉不确定语言数的多属性群决策方法;最后,通过实例分析说明了以往直觉不确定语言信息集结算子的局限性以及新算子的有效性.     

区间直觉梯形模糊几何Heronian平均算子及应用

针对决策信息为区间直觉梯形模糊数（IVITFN）且属性间存在相互关联的多属性群决策（MAGDM）问题,提出了一种区间直觉梯形模糊几何加权Heronian平均算子（IVITFGWHM）的决策方法。基于IVITFN的运算法则和几何Heronian平均（GHM）算子,定义了IVITFGHM算子和IVITFGWHM算子。研究了这些算子的一些性质,建立基于IVITFGWHM算子的MAGDM模型,结合排序方法进行决策。通过MAGDM算例验证了该算子的有效性与可行性。     

犹豫模糊Einstein几何算子及应用

研究了属性权重信息已知条件下的犹豫模糊信息集结算子及其在多属性群决策问题中的应用。基于Einstein运算定义了犹豫模糊Einstein和、犹豫模糊Einstein积以及犹豫模糊Einstein幂运算,并且研究了犹豫模糊Einstein运算法则间的关系。提出了四种犹豫模糊信息集结算子,即犹豫模糊Einstein加权几何（HFEWG）算子、犹豫模糊Einstein有序加权几何（HFEOWG）算子、犹豫模糊Einstein混合几何（HFEHG）算子和犹豫模糊Einstein诱导有序加权几何（HFEIOWG）算子,并分析了这些算子的性质。给出了基于HFEIOWG算子的犹豫模糊多属性决策方法,并结合投资公司对金融产品的选择来验证提出的决策方法是可行有效的。     

区间直觉模糊几何Bonferroni平均算子及其应用

研究了决策信息为区间直觉模糊数（IVIFN）且属性间存在相互关联的多属性群决策（MAGDM）问题,提出一种基于区间直觉模糊几何加权Bonferroni平均（IVIFGWBM）算子的决策方法。介绍了IVIFN的概念和运算法则,基于这些运算法则和几何Bonferroni平均（GBM）算子,定义了区间直觉模糊几何Bonferroni平均（IVIFGBM）算子和IVIFGWBM算子。研究了这些算子的一些性质,建立基于IVIFGWBM算子的MAGDM模型,结合排序方法进行决策。将该方法应用在一个MAGDM问题中,结果表明了该方法的有效性与可行性。     

基于加权犹豫Frank几何算法的决策模型

加权犹豫模糊集是一种广义的犹豫模糊集,其可以更准确和全面地刻画决策信息。而Frank三角模运算能够挖掘多个输入参数值间的相互关系。基于Frank三角模思想,在加权犹豫模糊环境下,提出了一种加权犹豫Frank几何平均算法的群决策模型。首先,运用Frank三角模定义了加权犹豫模糊基本运算法则,并构建了新的得分函数;接着,提出了加权犹豫Frank几何平均（WHFGA）算子,分析了WHFGA算子关于参数[r]的相关性质;最后,基于提出的WHFGA算子,建立了加权犹豫模糊多属性决策模型,并通过算例进行分析。实验结果表明,WHFGA算子具有良好的内在一致性。     

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。     

多属性群决策理论信息安全风险评估方法研究

信息安全风险评估是信息系统安全工程的重要组成部分,是建立信息系统安全体系的基础和前提。针对信息系统安全评估中风险值计算难以量化、主观因素影响大的问题,提出了一种基于多属性群决策理论OWGA（有序加权几何平均）算子和CWGA（组合加权几何平均）算子的评估方法。采用该方法,解决了风险评估中评估要素属性的权重赋值问题,同时群决策理论的引入提高了风险评估的准确性和客观性。实例分析表明,该方法合理有效,可为信息系统安全风险评估提供新思路。另外,该方法比较适合于指导安全工程实践与评估软件系统的开发。     

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.     

An interval-valued 2-tuple linguistic group decision-making model based on the Choquet integral operator

The Choquet integral (IL) operator is an effective approach for handling interdependence among decision attributes in complex decision-making problems. However, the fuzzy measures of attributes and attribute sets required by IL are difficult to achieve directly, which limits the application of IL. This paper proposes a new method for determining fuzzy measures of attributes by extending Marichal's concept of entropy for fuzzy measure. To well represent the assessment information, interval-valued 2-tuple linguistic context is utilised to represent information. Then, we propose a Choquet integral operator in an interval-valued 2-tuple linguistic environment, which can effectively handle the correlation between attributes. In addition, we apply these methods to solve multi-attribute group decision-making problems. The feasibility and validity of the proposed operator is demonstrated by comparisons with other models in illustrative example part.     

Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets

In this paper, we present a new method to deal with fuzzy multiple attributes group decision-making problems based on ranking interval type-2 fuzzy sets. First, we propose a new method for ranking interval type-2 fuzzy sets. Then, we propose a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision-making process of the proposed method. The proposed method is simpler than the methods presented in [Chen and Lee, 2010a] and [Lee and Chen, 2010b] for fuzzy multiple attributes group decision-making based on interval type-2 fuzzy sets. It provides us with a useful way for dealing with fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets.     

基于Choquet积分的多属性灰靶群决策方法

针对属性间具有关联性且属性值为区间灰数的多属性群决策问题,提出一种基于Choquet 积分的多属性灰靶群决策方法.根据模糊测度和Choquet积分的性质,定义关于区间灰数的Choquet积分信息集成算子,并证明其相关性质;通过灰靶决策方法,对方案集的综合靶心距进行排序.仿真实例验证了所提出方法的合理性.     

Multiattribute group decision-making based on Pythagorean fuzzy Einstein prioritized aggregation operators

Pythagorean fuzzy set (PFS) is a powerful tool to deal with the imprecision and vagueness. Many aggregation operators have been proposed by many researchers based on PFSs. But the existing methods are under the hypothesis that the decision-makers (DMs) and the attributes are at the same priority level. However, in real group decision-making problems, the attribute and DMs may have different priority level. Therefore, in this paper, we introduce multiattribute group decision-making (MAGDM) based on PFSs where there exists a prioritization relationship over the attributes and DMs. First we develop Pythagorean fuzzy Einstein prioritized weighted average operator and Pythagorean fuzzy Einstein prioritized weighted geometric operator. We study some of its desirable properties such as idempotency, boundary, and monotonicity in detail. Moreover we propose a MAGDM approach based on the developed operators under Pythagorean fuzzy environment. Finally, an illustrative example is provided to illustrate the practicality of the proposed approach.     

改进加权支持度的Pythagorean模糊交叉幂均群决策方法

针对毕达哥拉斯环境下的多属性群决策问题,首先,将毕达哥拉斯模糊数和幂均算子相结合,创造性地拓展了一种新的改进加权支持度;然后,基于此提出了改进加权支持度的毕达哥拉斯模糊交叉幂均算子,并讨论了该算子的性质,进而建立一种毕达哥拉斯模糊背景下能够反映决策属性间相互作用的决策方法;最后,将其应用于智慧城市的评价中。实例分析表明,该方法可以解决实际的多属性群决策问题,并可以进一步应用到智慧物流、模式识别、人工智能等领域。     

概率区间值直觉犹豫模糊Maclaurin对称平均算子及决策方法

在概率区间值直觉犹豫模糊集(PIVIHFS)的基础上,引入Maclaurin对称平均算子和Archimedean范数,构建一种基于概率区间值直觉犹豫模糊Maclaurin对称平均(PIVIHFMSM)算子的多属性决策模型,用来刻画决策专家输入多个参数值的决策信息,决策者可根据风险偏好等主观意识选择合适的参数值进行决策,同时能保证决策信息的有效性和完整性,避免决策过程中的不确定性和决策信息缺失问题.首先,回顾PIVIHFS的定义和排序方法以及Archimedean范数;其次,提出概率区间值直觉犹豫模糊Maclaurin对称平均(PIVIHFMSM)算子,研究其优良性质及常见形式;最后,提出一种基于PIVIHFWMSM算子的多属性决策方法,并进行比较分析,通过实例验证该方法的可行性和有效性.拓展PIVIHFS理论和应用领域,为决策属性具有相关性和决策信息有可能缺失提供新思路.     

Correlation Coefficient of Interval-Valued Intuitionistic Uncertain Linguistic Sets and Its Application

With respect to multiattribute group decision-making with interval-valued intuitionistic uncertain linguistic information, correlation and correlation coefficient are defined. To obtain the optimal weight vector, models based on the introduced correlation coefficient are constructed. Furthermore, two aggregation operators called the interval-valued intuitionistic uncertain linguistic Shapley averaging operator and the interval-valued intuitionistic uncertain linguistic Shapley geometric operator are defined, which are used to aggregate the interval-valued intuitionistic uncertain linguistic information. Moreover, an approach to multiattribute group decision-making under interval-valued intuitionistic uncertain linguistic environment is developed. Finally, an illustrative example is selected to verify the practicality and feasibility of the proposed procedure.     

A novel outranking sorting approach based on interval-valued Pythagorean uncertain linguistic Euclidean distance for material supplier grading

Multiple attribute linguistic group decision making (MALGDM) is one of the important research topics in decision-making theory. The material supplier grading involves multiple attributes and forms a typical MALGDM problem. In this paper, based on interval-valued Pythagorean uncertain linguistic Euclidean distance (IVPUL-Euclidean distance) and IVPUL aggregation operators, we develop a new outranking sorting approach, which can cope with MALGDM problems in IVPUL environment. The proposed IVPUL-Euclidean distance defines a novel outranking relation, and it introduces three parameters that can adjust outranking sorting result according to various decision-making situations. Meanwhile, the IVPUL aggregation operators are introduced to aggregate the IVPUL information. Eventually, we give a numerical example concerning the comprehensive assessment of material supplier to illustrate validity and applicability of the proposed approach and compare the proposed method with different generalized aggregation operators to perform its flexibility.