Combining compound linguistic ordinal scale and cognitive pairwise comparison in the rectified fuzzy TOPSIS method for group decision making

Group decision making is the process to explore the best choice among the screened alternatives under predefined criteria with corresponding weights from assessment of a group of decision makers. The Fuzzy TOPSIS taking an evaluated fuzzy decision matrix as input is a popular tool to analyze the ideal alternative. This research, however, finds that the classical fuzzy TOPSIS produces a misleading result due to some inappropriate definitions, and proposes the rectified fuzzy TOPSIS addressing two technical problems. As the decision accuracy also depends on the evaluation quality of the fuzzy decision matrix comprising rating scores and weights, this research applies compound linguistic ordinal scale as the fuzzy rating scale for expert judgments, and cognitive pairwise comparison for determining the fuzzy weights. The numerical case of a robot selection problem demonstrates the hybrid approach leading to the much reliable result for decision making, comparing with the conventional fuzzy Analytic Hierarchy Process and TOPSIS.     

A fuzzy closeness approach to fuzzy multi-attribute decision making

The aim of this paper is to develop a new fuzzy closeness (FC) methodology for multi-attribute decision making (MADM) in fuzzy environments, which is an important research field in decision science and operations research. The TOPSIS method based on an aggregating function representing “closeness to the ideal solution” is one of the well-known MADM methods. However, while the highest ranked alternative by the TOPSIS method is the best in terms of its ranking index, this does not mean that it is always the closest to the ideal solution. Furthermore, the TOPSIS method presumes crisp data while fuzziness is inherent in decision data and decision making processes, so that fuzzy ratings using linguistic variables are better suited for assessing decision alternatives. In this paper, a new FC method for MADM under fuzzy environments is developed by introducing a multi-attribute ranking index based on the particular measure of closeness to the ideal solution, which is developed from the fuzzy weighted Minkowski distance used as an aggregating function in a compromise programming method. The FC method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum individual regret for the “opponent”. A real example of a personnel selection problem is examined to demonstrate the implementation process of the method proposed in this paper.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

Group decision making based on novel fuzzy modified TOPSIS method

The aim of this paper is to present a novel fuzzy modified technique of order preference by a similarity to ideal solution (TOPSIS) method by a group of experts, which can select the best alternative by considering both conflicting quantitative and qualitative evaluation criteria in real-life applications. The proposed method satisfies the condition of being the closest to the fuzzy positive ideal solution and also being the farthest from the fuzzy negative ideal solution with multi-judges and multi-criteria. The performance rating values of alternatives versus conflicting criteria as well as the weights of criteria are described by linguistic variables and are transformed into triangular fuzzy numbers. Then a new collective index is introduced to discriminate among alternatives in the evaluation process with respect to subjective judgment and objective information. This paper shows that the proposed fuzzy modified TOPSIS method is a suitable decision making tool for the manufacturing decisions with two examples for the robot selection and rapid prototyping process selection.     

基于有序梯形模糊灰色关联TOPSIS的多属性决策方法

研究了有序梯形模糊数来表示不确定语言环境下的灰色关联TOPSIS多属性决策问题。首先应用有序梯形模糊数标度方案属性偏好信息,在传统梯形模糊数基础上增加了一个方向属性,使得决策信息的表示更加细腻;提出了有序梯形模糊环境下多属性决策灰色关联TOPSIS综合优选算法,引入了距离和灰色关联度相结合的综合贴近度公式,实现最优方案与理想方案的位置与曲线形状的一致性;最后通过制造系统内流动控制实例说明了所提出有序梯形模糊灰色关联TOPSIS方法的可行性和有效性。     

区间犹豫模糊ELECTRE多属性决策方法及应用

近年来,多属性决策问题一直是广大学者研究的重点,然而基于ELECTRE方法的区间犹豫模糊多属性决策问题的研究并不多见。因此,结合区间犹豫模糊集的信息表达优势和ELECTRE方法的思想,提出了一种区间犹豫模糊ELECTRE(IVHF ELECTRE)多属性决策新方法。首先构造了区间犹豫模糊决策矩阵,引入得分函数和可能度的概念,构造属性优势集和属性劣势集。然后通过设定阈值得到综合优先判定矩阵,从而得到各方案间的优先顺序。为了进一步得到各方案的整体排序,引入TOPSIS方法,通过计算各方案与正负理想点的相对距离来构造综合优先矩阵,从而得到各方案的总体排序。最后通过具体实例验证了该方法的可行性和合理性。     

Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment

TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.     

基于区间直觉梯形模糊数的改进TOPSIS多属性决策方法

研究了属性权重完全未知的区间直觉梯形模糊数的多属性决策问题,结合TOPSIS方法定义了相对贴近度及总贴近度公式.首先由区间直觉梯形模糊数的Hamming距离给出了每个方案的属性与正负理想解的距离,基于此,给出了相对贴近度矩阵,根据所有决策方案的综合贴近度最小化建立多目标规划模型,从而确定属性的权重值,然后根据区间直觉梯形模糊数的加权算数平均算子求出各决策方案的总贴近度,根据总贴近度的大小对方案进行排序;最后,通过实例分析说明该方法的可行性和有效性.     

基于新型区间直觉三角模糊熵的多属性决策方法

在进行区间直觉模糊多属性决策时,有时属性权重是未知的,针对这一问题,提出一种新型区间直觉三角模糊熵的决策方法.首先,给出该新型区间直觉三角模糊熵定义和相关定理,应用该区间直觉三角模糊熵确定属性的权重.然后,基于逼近理想解排序法(TOPSIS)的思想,采用改进的加权欧几里得距离,进行区间直觉模糊群决策,并给出决策步骤.最后,将该方法应用在供应链选择的群决策问题中,通过算例实验验证了该方法的有效性与可行性.     

An extension of TOPSIS for group decision making

An extension of TOPSIS (technique for order performance by similarity to ideal solution), a multi-attribute decision making (MADM) technique, to a group decision environment is investigated. TOPSIS is a practical and useful technique for ranking and selection of a number of externally determined alternatives through distance measures. To get a broad view of the techniques used, we provide a few options for the operations, such as normalization, distance measures and mean operators, at each of the corresponding steps of TOPSIS. In addition, the preferences of more than one decision maker are internally aggregated into the TOPSIS procedure. Unlike in previous developments, our group preferences are aggregated within the procedure. The proposed model is indeed a unified process and it will be readily applicable to many real-world decision making situations without increasing the computational burden. In the final part, the effects of external aggregation and internal aggregation of group preferences for TOPSIS with different computational combinations are compared using examples. The results have demonstrated our model to be both robust and efficient.     

基于模糊证据推理及改进TOPSIS的多属性群决策方法

针对不同识别框架多属性群决策问题属性准则度量的不确定性、随机性,定义基于梯形模糊数表征的属性准则评价等级相似度量,求解专家决策权重的最优解。对公共识别框架备选方案属性准则采用模糊证据推理过程综合专家评价等级置信度信息;利用可严格区分属性准则评价等级的相似度量,改进TOPSIS方法中备选方案属性准则评价等级置信度距离因子,获取备选方案逼近正负理想解的贴近度。实例分析以某通信企业电信产品市场竞争力评估为例,说明基于模糊证据推理、改进TOPSIS的多属性群决策问题求解过程,从属性准则专家模糊评价等级置信度集中获取直观的待评估产品市场竞争力排序结果,验证该方法解决此类决策问题的可行性与有效性。     

模糊多属性格序决策的冗余指标的消除策略

在模糊多属性决策中,属性权重的确定对于整个评价工作有十分重要的意义.如果评价属性数量过多,指标间的相关性将影响评价的科学性和公平性.本文建立了评价值为梯形模糊数的"相似"概念和模糊相似评价模型,并基于格序决策的理论,得到了一种新的模糊格序决策方法.结合传统的TOPSIS方法,通过计算将各方案的属性值的中心进行加权后与正负理想中心的贴近度的大小,实现备选方案的格序化排序.实例分析的结果表明:方法合理、易行.     

Fuzzy prioritized operators and their application to multiple attribute group decision making

In this paper, we investigate the triangular fuzzy multiple attribute group decision making (MAGDM) problem in which the attributes and experts are in different priority level. Motivated by the ideal of prioritized aggregation operators (R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263–274.), we develop some prioritized aggregation operators for aggregating triangular fuzzy information, and then apply them to develop some models for triangular fuzzy multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

模糊多属性决策的直觉模糊集方法

基于直觉模糊集理论,提出了一种新的TOPSIS方法来研究模糊多属性决策问题。首先,根据直觉模糊集的几何意义,定义了两个直觉模糊集之间的距离,且每个备选方案的评价值用直觉模糊值表示;然后,根据TOPSIS原理,通过计算备选方案到直觉模糊正理想解和负理想解的距离,来确定备选方案的综合评价指数,以此判断方案的优劣次序。最后,通过一个具体实例说明该方法的有效性和具体应用过程。     

Approach to group decision making based on determining the weights of experts by using projection method

The aim of this paper is to present a new approach for determining weights of experts in the group decision making problems. Group decision making has become a very active research field over the last decade. Especially, the investigation to determine weights of experts for group decision making has attracted great interests from researchers recently and some approaches have been developed. In this paper, the weights of experts are determined in the group decision environment via projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, the weight of expert is determined by the projection of individual decision on the ideal decision. By using the weights of experts, all individual decisions are aggregate into a collective decision. Then an ideal solution of alternatives of the collective decision, expressed by a vector, is determined. Further, the preference order of alternatives are ranked in accordance with the projections of alternatives on the ideal solution. Comparisons with an extended TOPSIS method are also made. Finally, an example is provided to illustrate the developed approach.     

Combining grey relation and TOPSIS concepts for selecting an expatriate host country

As international corporate activities increase, their staffing involves more strategic concerns. However, foreign assignments have many differences, and dissatisfaction with the host country is a known cause of expatriate failure. From the point of view of an expatriate candidate, the decision of whether to take an expatriate assignment can be regarded as a FMCDM (fuzzy multiple criteria decision making) problem. This paper describes a fuzzy AHP (fuzzy analytic hierarchy process) to determine the weighting of subjective judgments. Using the Sugeno integral for λ-fuzzy measure, and using the nonadditive fuzzy integral technique to evaluate the synthetic utility values of the alternatives and the fuzzy weights, then the best host country alternative can be derived with the grey relation model. The authors further combine the grey relation model based on the concepts of TOPSIS (technique for order preference by similarity to ideal solution) to evaluate and select the best alternative. A real case of expatriate assignment decision-making was used to demonstrate that the grey relation model combined with the ideas of TOPSIS results in a satisfactory and effective evaluation.     

Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making

The intuitionistic uncertain fuzzy linguistic variable can easily expressthe fuzzy information, and the power average (PA) operator is a usefultool which provides more versatility in the information aggregation procedure.At the same time, Einstein operations are a kind of various t-normsand t-conorms families which can be used to perform the corresponding intersectionsand unions of intuitionistic fuzzy sets (IFSs). In this paper, wewill combine the PA operator and Einstein operations to intuitionistic uncertainlinguistic environment, and propose some new PA operators. Firstly,the definition and some basic operations of intuitionistic uncertain linguisticnumber (IULN), power aggregation (PA) operator and Einstein operationsare introduced. Then, we propose intuitionistic uncertain linguistic fuzzypowered Einstein averaging (IULFPEA) operator, intuitionistic uncertain linguisticfuzzy powered Einstein weighted (IULFPEWA) operator, intuitionisticuncertain linguistic fuzzy Einstein geometric (IULFPEG) operator and intuitionisticuncertain linguistic fuzzy Einstein weighted geometric (IULFPEWG)operator, and discuss some properties of them in detail. Furthermore, we developthe decision making methods for multi-attribute group decision making(MAGDM) problems with intuitionistic uncertain linguistic information andgive the detail decision steps. At last, an illustrate example is given to showthe process of decision making and the effectiveness of the proposed method.     

基于TOPSIS的模糊群体多属性决策方法

针对模糊群体多属性决策问题,给出一种基于理想点法(TOPSIS)的多属性决策方法.方法先用三角模糊数的形式表示专家评价值的模糊性和不确定性,而后考虑了专家在不同评价属性中的重要程度和意见的相似度,并将专家意见进行集结得到专家群体关于方案集的模糊决策矩阵,最后定义了三角模糊数形式的正负理想方案,通过计算各方案与正负理想方案的距离以及各方案与理想点的相对接近度,最终确定最优方案.通过实例分析说明了该方法的可行性和有效性.     

TOPSIS for bi-level MODM problems

TOPSIS (technique for order preference by similarity to ideal solution) is a multiple criteria method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. This paper proposes a fuzzy TOPSIS algorithm to solve bi-level multi-objective decision-making (BL-MODM) problems, and in which the objective function at each level are non-linear functions which are to be maximized. The proposed model for getting the satisfactory solution of the BL-MODM problems includes the membership functions for the upper level decision variables vector with possible tolerances, the membership function of the distance function from the positive ideal solution (PIS) and the membership function of the distance function from the negative ideal solution (NIS). A numerical illustrative example is given to clarify the proposed TOPSIS approach of this paper.     

基于TOPSIS的区间直觉模糊多属性决策法

对基于区间直觉模糊信息的多属性决策问题进行了研究。给出了区间直觉模糊数之间的距离公式,并定义了区间直觉模糊正、负理想点,进而提出了一种基于TOPSIS的区间直觉模糊多属性决策方法。最后进行了实例分析。