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.

Multi-attribute group decision making method under 2-dimension uncertain linguistic variables

A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.

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.

Solution to multiple attribute group decision making problems with two decision makers

A kind of multiple attribute group decision making （MAGDM） problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.

A Confidence-based Consensus Model for Multi-Attribute Group Decision Making:Exploring the Bounded Trust Propagation and Personalized Adjustment Willingness

Social trust network(STN)and minimum cost consensus(MCC)models have been widely used to address consensus issues in multi-attribute group decision-making(MAGDM)problems with limited resources.However,most researchers have overlooked the decision maker‘(DMs)’confidence levels(CLs)and adjustment willingness implicit in their evaluations.To address these problems,this paper explores a confidence-based MCC model that considers DMs’adjustment willingness in the STN.The proposed model includes several modifications to the traditional trust propagation and consensus optimization models.Firstly,the improved method for measuring CLs of DMs and the confidence-based normalization approach are defined,respectively.Secondly,the bounded trust propagation operator is proposed,which considers the credibility of mediators to complete the STN.Thirdly,the identification rules based on the consensus index and CL are defined,and the MCC model with personalized cost functions and acceptable adjustment thresholds is built to automatically generate adjustment values for non-consensus DMs.Finally,a model to identify the non-cooperative behavior at the element level is established and the hybrid MCC model with persuasion strategies is provided.Finally,a case study is processed to verify the applicability of the proposed model,and comparison and sensitivity analysis are conducted to highlight its benefits.

基于IITFN输入的复杂系统关联MAGDM方法

区间直觉梯形模糊数(Interval-valued intuitionistic trapezoidal fuzzy number,IITFN)是刻画复杂系统不确定性的有效工具.基于进一步完善的IITFN运算规则,讨论其局部封闭性.由此定义IITFN几何Bonferroni平均算子,并验证该算子的相关性质.针对决策者及属性之间均存在关联作用且权重均未知的多属性群决策(Multi-attribute group decision making,MAGDM)问题,提出基于前景混合区间直觉梯形几何Bonferroni(Prospect hybrid interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni,PHIITFGB)平均算子的关联多属性群决策方法.该方法首先通过依次定义IITFN的前景效应、前景价值函数和前景价值,获取前景价值矩阵;其次,将前景价值矩阵转化为前景记分函数矩阵,并综合运用基于灰关联深度系数的客观属性权重极大熵模型和基于2-可加模糊测度与Choquet积分联合的决策者权重确定模型,获取决策者权重及属性权重;再次,利用PHIITFGB算子集结各决策者的方案评估信息,结合决策者权重即可获取相应于各方案的综合前景价值;最后,计算综合前景记分价值函数,基于IITFN的序关系判别准则确定方案排序.案例验证决策方法的有效性和可行性.

UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING

In multiple attribute group decision making （MAGDM） problems based on linguistic information, the granularities of linguistic label sets are usually different due to the differences of thinking modes and habits among decision makers. In order to deal with this inconvenience, the transformation relationships among multigranular linguistic labels （TRMLLs）, which are applied to unify linguistic labels with different granularities into a certain linguistic label set with fixed granularity, are presented in this paper. Furthermore, the reference tables are made according to TRMLLs so that the interrelated calculation will be less complicated, and the method of how to use them is explained in detail. At length, the TRMLLs are illustrated through an application example.

Optimized interval 2-tuple linguistic aggregation operator based on PGSA and its application in MAGDM

This study proposes a multiple attribute group decisionmaking(MAGDM)approach on the basis of the plant growth simulation algorithm(PGSA)and interval 2-tuple weighted average operators for uncertain linguistic weighted aggregation(ULWA).We provide an example for illustration and verification and compare several aggregation operators to indicate the optimality of the assembly method.In addition,we present two comparisons to demonstrate the practicality and effectiveness of the proposed method.The method can be used not only to aggregate MAGDM problems but also to solve multi-granularity uncertain linguistic information.Its high reliability,easy programming,and high-speed calculation can improve the efficiency of ULWA characteristics.Finally,the proposed method has the exact characteristics for linguistic information processing and can effectively avoid information distortion and loss.

Fuzzy distances based FMAGDM compromise ratio method and application

An extended compromise ratio method（CRM） based on fuzzy distances is developed to solve fuzzy multi-attribute group decision making problems in which weights of attributes and ratings of alternatives on attributes are expressed with values of linguistic variables parameterized using triangular fuzzy numbers.A compromise solution is determined by introducing the ranking index based on the concept that the chosen alternative should be as close as possible to the positive ideal solution and as far away from the negative ideal solution as possible simultaneously.This proposed method is compared with other existing methods to show its feasibility and effectiveness and illustrated with an example of the military route selection problem as one of the possible applications.

Spherical uncertain linguistic Hamacher aggregation operators and their application on achieving consistent opinion fusion in group decision making

Purpose-The aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers(SULNs).Design/methodology/approach-First,the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs.Furthermore,the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.Findings-The authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.Originality/value-In order to give an application of the introduced operators,the authors first constrict a system of multi-attribute decision-making algorithm.

一种基于多QoS注册中心和模型异构的WEB服务选择算法

多QoS注册中心并且QoS模型异构给服务选择带来巨大困难。借鉴多属性群决策(MAGDM)理论的基本思想,该文提出一种解决上述难题的多注册中心和模型异构的Web服务选择算法(MRHQ_WSSA)。MRHQ_WSSA算法能综合评估各QoS注册中心的QoS信息,从而获得QoS综合最优的服务组合计划。MRHQ_WSSA算法包括5个步骤:用户偏好规格化、群偏好确定、加权规格化决策矩阵、确定群理想方案、计算群贴近度。最后通过实验验证算法的优势和有效性。

一种QoS感知的语义Web服务组合群决策算法

针对QoS信息不确定和存在多个决策者的语义Web服务组合问题,基于多属性群决策理论给出了一个自治的语义Web服务组合群决策算法(AGSC)。该算法能够对以实数型、区间型和语言型数据描述的复杂的QoS信息进行综合评估,从而为多客户提供正确、高效的决策支持,为其优选出最佳的组合服务执行计划。利用真实Web服务的质量对该算法进行了实验验证,结果表明该算法具有优秀的决策灵敏性和稳定性,并能有效地反映决策群中个体角色的变化。

基于双犹豫模糊信息的灰靶群决策方法

考虑到现实决策环境的不确定性与复杂性,提出一类新的双犹豫模糊环境下基于正负靶心的灰靶多属性群决策问题。首先,将双犹豫模糊理想最优方案定义为正靶心,将理想最劣方案定义为负靶心,正负靶心距则通过正负靶心与双犹豫模糊集的归一化汉明距离确定。然后,提出一种新的综合靶心距,用来评估方案与正负靶心之间的距离。再以综合靶心距最小为目标,建立一个非线性优化模型来确定最优属性权重信息。最后,通过算例证明了所建模型的有效性和可行性。

基于混合QoS的大群用户服务选择

群体活动在日常生活中非常广泛,面向群体的信息服务提供是必需解决的问题。群体规模较大和混合数据类型QoS模型给Web服务选择带来巨大困难。基于混合QoS模型,借鉴多属性群决策理论,提出面向大群体用户的服务选择算法。包括5个步骤:群体偏好确定、族加权权重确定、构造族加权规格化决策矩阵、确定理想方案、计算贴进度。另外,还介绍了一种Web服务QoS模型,能够描述实数、区间数、直觉模糊数表示的QoS信息。实验数据表明,该算法能够很好地解决混合QoS模型的大规模群体用户的服务选择问题。

面向大群体用户的模糊服务选择

面向群体的服务选择在社会生活中应用非常广泛;而群体规模较大并且QoS需求个性化和模糊QoS给Web服务选择带来巨大困难。基于多属性群决策理论提出面向大群体用户的模糊服务选择(BGFWSS),其包括5个步骤:群体偏好确定、族加权权重确定、构造族加权规格化决策矩阵、确定理想方案、群体综合评价。另外,还介绍了一个新的Web服务QoS模型,其能够描述实数、区间数、直觉模糊数表示的QoS信息。实验数据表明,BGFWSS能够很好地解决模糊QoS的大规模群体用户的服务选择问题。

基于粗糙集定义区间数环境下专家权重的新方法（英文）

专家权重在多属性组决策问题中起到重要的作用,如何衡量专家的权重一直以来都是研究热点。提出一种基于粗糙集来定义区间数环境中专家权重的方法。首先建立一个粗糙群组下决策(LRGD)和一个粗糙群组上决策(URGD)。然后,定义LRGD的区间中值矩阵为下理想决策(Lower PIS),URGD的区间中值矩阵为上理想决策(Upper PIS)。正理想决策(PIS)是Lower PIS和Upper PIS的区间中值矩阵,同时,负理想决策(NIS)对正理想决策存在最远的欧式距离。之后,利用专家决策到PIS和NIS的欧式距离,得出专家权重。由"空气质量监测站"的算例来阐明提出方法的详细实施步骤。

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.

基于犹豫语言H-几何算子的信息安全系统选择

针对属性值为犹豫模糊语言信息且属性输入变量之间存在相互联系的多属性群决策问题,提出了一种基于犹豫语言Heronian几何算子的多属性群决策模型。基于Archimedean范数定义了新的犹豫模糊语言运算法则,并提出了犹豫语言Heronian几何(HLHG)算子;探讨了HLHG算子的一些优良性质,研究了HLHG算子的几种常见形式,引入了犹豫语言Heronian加权几何(HLHWG)算子;基于HLHWG算子构建了一种新的犹豫模糊语言多属性群决策模型,该群决策模型不仅考虑到了输入决策信息之间的相互联系,而且使得决策者能够依据自身偏好选择不同参数进行决策。结合信息安全系统选择实例验证了提出的群决策模型是可行的和有效的。