Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set(SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging(SNNPWA) operator, simplified neutrosophic number power weighted geometric(SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging(SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric(SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multiattribute group decision making(MAGDM) within the framework of SNSs is developed by the above aggregation operators.Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

Multi-criteria linguistic interval group decision-making approach

For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria＇s weights and the decision-makers＇ preference information might take the form of linguistic grade, or might be between two continuous linguistic grades, or might be linguistic interval, or might be default. In this method, all linguistic values are transformed into two-tuple, and an aggregative decision-making matrix is obtained by using interval operation. The group aggregative values of each criterion on alternatives are computed by using a WC-OWA operator, the aggregative values on alternatives are worked out, and transformed into two-tuple. And the rank of the alternatives is obtained by using the order property of two-tuple. An example shows the feasibility and effectiveness of the proposed method.

Multi-criteria group decision making with fuzzy data:an extension of the VIKOR method

The VIKOR method is a multi-criteria decision making aid, which employs linear normalization to offer compromise solu- tions and has been successfully applied to various group decision making problems. However, the conventional VIKOR techniques used to integrate group judgments and the information loss arising from defuzzification are problematic and distort final outcomes. An improved integration method, which is optimization-based, is proposed. And it can handle fuzzy criteria values and weights. The precondition for accurately defuzzifying triangular fuzzy num- bers is identified. Several effective defuzzification procedures are proposed to improve the extant VIKOR, and a comprehensive evaluation framework is offered to aid multi-criteria group decision making. Finally, a numerical example is provided to illustrate the practicability of the proposed method.

Dynamic programming methodology for multi-criteria group decision-making under ordinal preferences

A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.

A Frame Work of Multistage Decision Making

This research has objective to analyze some tools which are used to support decision maker to make a decision in multi stage and systematic way. And also in making decision, there are a qualitative type and quantitative type. In order to get an optimum decision making, the decision maker needs systematic way. There is the frame work which is based on combination of some existing methods and challenges emerging in organizational activities, including social organizations as well as business organisations. To formulate the framework, this research conducted focus group discussion consisting of some organizational managers as participants. There are five components of proposed frame work： （1） Criteria Identification through Focus Group Discussion （FGD）; （2） Criteria Selection; （3） Focus Group for Criteria Verification; （4） Multicriteria Decision Making based Analytic Hierarchy Process （AHP）; and （5） Impact Analysis. This research resulted in an effective approach of decision making which allows decision maker to have objective and rational reason in each step of its decision-making process. Strength of the proposed framework is to provide rational and objective approach in group decision making. However, it takes longer time to conduct decision making due to more steps and participants involved. As a conclusion, the proposed research has been successful in establishing a multi stage and rational decision-making process.

群体决策可靠性的分层反馈与多级度量

为了提高群体决策质量,获得更加可靠的决策结果,结合语言环境下考虑专家自信度的异构多属性群决策问题,建立了群体决策可靠性的分层反馈机制与多级度量模型。利用三支决策思想将各方案各属性下对应子群体中的专家按照自信度的高、中、低划分成三类,进而,依次从子群体的专家构成、自信度以及共识度3个层次对决策可靠性进行量化分析,建立由粗到细、逐层细化的反馈机制,为决策过程的可靠性调整和控制提供途径;综合考虑子群体中高、中自信度专家的占比以及自信度和共识度等影响因素,构建多级可靠性度量模型,并形成针对方案级决策和整体决策的两级可靠性判定规则,有效提升决策结果的可解释性。在此基础上,提出一种可靠性驱动的异构多属性群决策方法,通过供应商选择实例分析并验证了所提方法的可行性和有效性。

属性权重动态更新的自适应群体共识决策方法

为了提高不确定语言环境下异构多属性群决策的质量、效率及可解释性,提出一种属性权重动态更新的自适应群体共识决策方法。首先,定义不确定语言变量与中间值之间的转换函数,发展多级共识测度,建立计算属性初始权重的双目标优化模型;进而,构建包含群体共识自动达成规则和属性权重动态更新机制的自适应共识模型,实现待调整值的精准定位和自动修改,在优化属性权重的同时进一步提升群体共识水平;然后,对于达成共识的群体决策矩阵,先利用转换函数将中间值转换为不确定语言变量,再使用属性权重和集结算子得到各方案的综合评价结果;最后,通过供应商选择实例和实验比较分析验证所提方法的有效性和可行性。本文研究结果为灵活、高效地求解复杂环境下的多属性群决策问题提供了有效途径。

基于GRA-GCRITIC和改进加权双向投影的区间Fermatean模糊多属性群决策方法

针对司法案件决策环境的复杂性及评价信息的模糊性,提出一种基于GRA-GCRITIC(grey relational analysis-group criteria importance through intercriteria correlation)和改进加权双向投影的区间Fermatean模糊Hamacher-TODIM多属性群决策方法。首先考虑到各位专家对各评价方案下各指标评价信息的差异性,提出一种GRA-GCRITIC方法,该方法将灰色关联融入到CRITIC中,以确定指标综合权重比单一获取的指标权重更加客观可靠;其次,结合信任关系对加权双向投影法进行改进,兼顾主客观关系,利用专家个体与群体评价信息的隶属度及非隶属度矩阵间的相似度得到专家权重;最后,考虑到决策者的损失规避心理,将融合了Hamacher算子的TODIM方法拓展至区间Fermatean模糊环境中,通过具体算例可得到其综合优势度及排序,验证了所提方法的可行性及灵活性。

基于决策者偏好构造的概率语言型Z-number多属性决策方法

由于决策环境的日益复杂,专家评价信息往往会包含专家偏好,因此有必要对专家偏好进行识别与处理。针对这一情况,提出了基于决策者偏好构造的概率语言型Z-number并应用于多属性决策问题中。首先,针对专家偏好未知的情况,提出了一种基于修正的平均得分距离,由专家评价信息确定专家偏好。然后,依据得到的专家偏好,利用GOWPA算子与最大熵生成概率语言型Z-number。同时,获得专家评价信息的可信度,由专家可信度聚合专家信息并采用TODIM方法对方案进行排序。最后,在国家大力提倡节能减排的背景下,将所提方法应用于国家绿色矿山试点企业的选取上,验证了所提方法的有效性和可行性。

计及群体压力和群体极化的PDHFSs-TODIM多属性群体决策算法

在概率对偶犹豫模糊环境下的多属性决策中,针对决策过程一般未考虑决策专家在讨论中所受的群体压力和群体极化的问题,提出了一种计及群体压力和群体极化的概率对偶犹豫模糊集-拓扑判别目标间方法(probabilistic discriminative heterogeneous fuzzy sets-topological discriminative inter-objective method,PDHFSsTODIM)的多属性群体决策算法。首先,定义了考虑群体压力的决策信息修正公式,有效削弱群体压力对专家决策信息的影响;然后,搭建了一种考虑群体极化现象的决策模型,该模型充分考虑了专家的主观性,为专家讨论和修正决策提供了机会,通过分配动态决策权重提高决策的置信度,并通过群体极化阈值约束群体的极化效应;进一步,将计算得到的决策数据输入改进的TODIM算法,得到最终决策结果。将算法运用于储能电池综合性能评估分析,通过与其他先进决策算法做对比,验证了所提算法的可靠性与准确性。

三角模糊不完备三支群决策及其在糖尿病诊断中的应用

为同时应对不确定信息表示与风险信息融合对群决策带来的挑战,构建一种三角模糊不完备三支群决策方法,并将其应用于糖尿病诊断决策。首先,针对信息不确定性蕴含的模糊性和不完备性,分别引入三角模糊集和不完备信息系统的概念。通过与多粒度三支决策结合,构建了可调多粒度三角模糊概率粗糙集模型。然后,根据离差最大化法计算属性权重与专家权重,结合ELECTRE(elimination et choice translating reality)方法建立了三角模糊多属性群决策方法。最后,通过对糖尿病患者数据的案例分析和评估,验证了所提方法的可行性和有效性。该方法不仅从不确定信息表示、风险信息融合和最优粒度选择的视角丰富了多粒度三支群决策理论,而且推动了糖尿病智能诊断方面的应用。

基于从众行为和移情关系的区间直觉模糊多属性群决策

在现实群决策中,决策者常因信息不完全或社会排斥风险而表现出从众行为,同时通过情感移情效应感知他人情感,并将其观点纳入决策之中。但目前群决策研究鲜少考虑从众行为与移情关系的因素。为了拓展群决策的研究范畴和应用领域,提出一种多属性群决策方法,揭示了从众行为和移情关系对群决策的影响规律。首先,构建一个序贯决策分析框架,有效表达决策者从众行为对群决策的影响机制。随后,引入移情网络,对决策者的移情关系、感召力和知识能力三方面信息进行界定,进而探讨这些因素在决策过程中的作用效果。评估阶段的从众关系综合考虑了移情关系、感召力和知识能力;集结阶段的决策者权重受到感召力的影响,而时间点权重则由知识能力决定;在共识阶段,利用移情关系提出意见调整建议。最后通过实例研究说明,所提方法能够取得可靠且稳定的结果,并且相较于传统群决策方法,能更为高效地达成群体共识。

Picture模糊数的改进得分函数在多属性群决策中的应用

针对picture模糊环境下专家权重和属性权重信息未知的多属性群决策问题进行研究.首先,针对现有picture模糊数的得分函数存在一些不足问题,提出了一种新的得分函数.通过分析其相关性质,并与现有得分函数进行比较,说明其更具合理性,能更好地处理模糊决策信息.其次,提出了基于得分函数的picture模糊环境下的多属性群决策方法,根据每位专家给出的picture模糊评价信息的不精确程度及不同专家给出信息的差异程度,从个体和群体两方面综合得到决策者权重;利用得分函数构造不同属性的灰靶贡献度,从而确定属性权重.最后,通过实例比较分析验证了所提方法的可行性和有效性.

基于梯形模糊数的动态混合多属性群决策方法

基于梯形模糊数信息环境,研究动态混合多属性群决策问题.给出梯形模糊数的转化方法及梯形模糊数信息的加权综合集结方法,定义动态梯形模糊加权几何算子;提出不同类别权重的确定方法,利用决策专家的赋值离差和最小化方法确定决策者的权重,运用离差最大化模型确定属性权重,基于熵权法和Orness测度赋权法计算时间权重;在此基础上,利用VIKOR(多准则妥协解排序)法提出一种基于梯形模糊数的动态混合多属性群决策方法,并通过算例验证其可行性与有效性.

基于毕达哥拉斯模糊多属性群决策的卷烟烟支质量评估方法

随着卷烟工业企业数字化进程的快速推进,精确恰当的卷烟烟支质量评估方法直接影响卷烟生产质量和效率。根据卷烟烟支质量评估中指标信息具备的多属性、不确定性、模糊性等特点,提出了一种基于毕达哥拉斯模糊多属性群决策的卷烟烟支质量评估方法。运用毕达哥拉斯模糊集对指标信息进行表述和处理,在专家权重和指标权重未知的情况下,构建综合距离模型和知识测度模型确定权重信息;通过相对距离和信息可靠性定义毕达哥拉斯模糊数排序新方法,并计算各方案集结算子进行排序。最后,通过应用实例对该方法进行验证分析。结果表明,方法可以有效运用于卷烟烟支的质量评估,决策结果更加准确客观。

基于模糊多属性群决策理论的课堂教学质量评价研究

考虑学生给定评价信息时的犹豫特性、学生主体之间的差异性以及信息共享的关联性,采用直觉梯形模糊数转换学生群体给定的评价信息,引入模糊测度和Shapley函数值处理存在关联性学生群体的客观权重,并由此构建基于模糊多属性群决策理论的教师课堂教学评价模型,以便于科学、合理地对高校教师课堂教学进行综合评价。