A novel approach for combination of individual and group decisions based on fuzzy best-worst method

The process of decision-making in an enterprise may either keep the business on track or derail it. Thus, a senior decision maker often use a group of experts as the supportive team to ensure appropriate decisions. The experts often have different expertise level regarding their knowledge, talent, proficiency, and experience. In this study, we first extend the best-worst method based on the linguistic preferences of decision-makers about importance of attributes. These preferences are converted into triangular fuzzy numbers to be utilized in the linear programming model. That is, in contrast with the original best-worst method in which the preferences towards the attributes are crisp, fuzzy preferences are considered in the proposed method to reflect the imprecise comments of experts. Second, we propose a novel group decision making approach based on the fuzzy best-worst method to combine the opinion of senior decision-maker and the opinions of the experts. Indeed, our model helps the senior decision-maker to make a significant trade-off between democratic and autocratic decision-making styles. From sensitivity analyses on two numerical examples, we show that, when there is conflict between senior decision-maker and group of decision-makers, the consistency of group decision-making (democracy) will increase as it tends to individual decision-making (autocracy).     

A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems

The multi-criteria group decision-making methods under fuzzy environments are developed to cope with imprecise and uncertain information for solving the complex group decision-making problems. A team of some professional experts for the assessment is established to judge candidates or alternatives among the chosen evaluation criteria. In this paper, a novel multi-criteria weighting and ranking model is introduced with interval-valued hesitant fuzzy setting, namely IVHF-MCWR, based on the group decision analysis. The interval-valued hesitant fuzzy set theory is a powerful tool to deal with uncertainty by considering some interval-values for an alternative under a set regarding assessment factors. In procedure of the proposed IVHF-MCWR model, weights of criteria as well as experts are considered to decrease the errors. In this regard, optimal criteria’ weights are computed by utilizing an extended maximizing deviation method based on IVHF-Hamming distance measure. In addition, experts’ judgments are taken into account for computing the criteria’ weights. Also, experts’ weights are determined based on proposed new IVHF technique for order performance by similarity to ideal solution method. Then, a new IVHF-index based on Hamming distance measure is introduced to compute the relative closeness coefficient for ranking the candidates or alternatives. Finally, two application examples about the location and supplier selection problems are considered to indicate the capability of the proposed IVHF-MCWR model. In addition, comparative analysis is reported to compare the proposed model and three fuzzy decision methods from the recent literature. Comparing these approaches and computational results shows that the IVHF-MCWR model works properly under uncertain conditions.     

基于前景理论的信息不完全的模糊多准则决策方法

针对准则权重不完全确定且方案的准则值为梯形模糊数的多准则决策问题,提出一种基于前景理论的模糊多准则决策方法.该方法将决策者的风险心理因素引入多准则决策,根据前景理论及模糊数距离公式,定义梯形模糊数的前景价值函数,并以此构建方案综合前景值最大化的非线性规划模型,求解模型得出最优权向量,最终确定出方案的排序.最后通过实例说明了该方法的有效性和可行性.     

基于Orness 测度约束的多阶段灰色局势群决策模型

研究多阶段灰色局势群决策模型。从决策专家各阶段的评价信息质量分析入手,给出了评价阶段质变和量变的定义;基于各阶段的评价信息和Orness测度,构建以相邻阶段信息偏差最小为目标的时间权重模型,分析了在保持最优局势不变的情况下Orness测度的取值范围,为决策专家Orness取值提供参考;研究基于群体差异最小的决策专家权重模型,提出一种多阶段灰色局势群决策评价信息集结方法。最后,通过一个具体的算例说明了该方法的有效性和可行性。     

Integrated group fuzzy multi-criteria model: Case of facilities management strategy selection

Managerial decisions should be made by taking into account the priorities and objectives of different stakeholders' groups. Their preferences are usually expressed in words and are fuzzy concepts. This article analyses the peculiarities of companies’ work and decision - making within a fuzzy market situation. It also presents a developed fuzzy multi-criteria group decision-making model for practical problem solving by taking into account cost-effective management. This case study presents a selection of rational criteria set to use in the weighted cost-effectiveness analysis for facilities management strategies, in which integrated fuzzy multi-criteria decision-making methods are applied. The main findings are: the model is adopted to real- life; the main criteria groups are identified by a three-step Delphi technique; a rational strategy is determined and integrated in one model by the concept of Minkowski distance and fuzzy TOPSIS method, ARAS-F and fuzzy weighted product method. The proposed model is versatile and therefore can be applied for various problems were the experts’ knowledge needed for decision–making.     

An integrated fuzzy multi criteria group decision making approach for ERP system selection

This paper aims to ease group decision-making by using an integration of fuzzy AHP (analytic hierarchy process) and fuzzy TOPSIS (technique for order preference by similarity to ideal solution) and its application to software selection of an electronic firm. Firstly, priority values of criteria in software selection problem have been determined by using fuzzy extension of AHP method. Fuzzy extension of AHP is suggested in this paper because of little computation time and much simpler than other fuzzy AHP procedures. Then, the result of the fuzzy TOPSIS model can be employed to define the most appropriate alternative with regard to this firm's goals in uncertain environment. Fuzzy numbers are presented in all phases in order to overcome any vagueness in decision making process. The final decision depends on the degree of importance of each decision maker so that wrong degree of importance causes the mistaken result. The researchers generally determine the degrees of importance of each decision maker according to special characteristics of each decision maker as subjectivity. In order to overcome this subjectivity in this paper, the judgments of decision makers are degraded to unique decision by using an attribute based aggregation technique. There is no study about software selection using integrated fuzzy AHP-fuzzy TOPSIS approach with group decision-making based on an attribute based aggregation technique. The results of the proposed approach and the other approaches are compared. Results indicate that our methodology allows decreasing the uncertainty and the information loss in group decision making and thus, ensures a robust solution to the firm.     

A multi-agent affective interactive MAGDM approach and its applications

Traditional multi-attribute group decision-making (MAGDM) methods focus on weights calculation of sub-attributes and experts' preferences, but lack the discussion on the decision-makers' affective interaction, and its influence on the decision preference and group consistency. To address this problem, the present study proposed a new multilayer affective computing model based on “personality–mood–emotion” pattern, under the multi-agent decision system framework. In addition, we introduced the group trending index and affection-preference incentive mechanism, which can help simulate MAGDM process and learn group experts' decision preferences. Further, we proposed a new multi-agent affective interactive MAGDM (MAAI-MAGDM) method, where we defined a novel group convergence index and an alternative decision entropy to explain the convergence process of decision and group consistency. Compared to the traditional MAGDM approaches, the proposed MAAI-MAGDM method fully considered the affective features of each expert, reduced the dependence on aggregation operators and weight analysis, alleviated the workload of group experts, and effectively reduced the complexity of decision-making calculation process. Finally, we verified that the proposed method can effectively assist the decision-making processes by employing two numerical cases.     

基于熵和风险态度的二型模糊多属性决策方法

针对属性权重信息完全未知的二型模糊多属性决策问题,提出了一种基于二型模糊熵和决策者风险态度的决策方法。首先,为了准确测度二型模糊集（T2FS）的不确定性,通过引入模糊因子和犹豫因子建立了二型模糊熵的公理化准则,并基于距离测度给出了对应的计算公式。其次,为了减少整体不确定信息对决策结果的影响,结合二型模糊熵构建非线性规划模型来确定属性权重。同时,将决策者的风险态度引入二型模糊信息的得分函数中并给出具体的决策步骤。最后,通过实例分析验证了该决策方法的可行性,并与现有文献对比发现该决策方法更具有灵活性。     

FAHP方法在信息安全风险评估中的研究

本文在分析影响信息安全风险的因素的基础上构建了信息安全风险分析的层次结构模型，提出了采用模糊层次分析法（Fuzzy-AHP）对风险进行量化分析的方法。该方法采用三角模糊数来表示基于群组决策的信息安全风险各因素的判断矩阵，并用层次分析法来对专家判断结果进行处理，为决策提供了更合理的数据。     

Hesitant fuzzy best-worst multi-criteria decision-making method and its applications

Best-worst method (BWM) is extended to uncertain situations, hesitant fuzzy best-worst method (HFBWM) is proposed by using hesitant fuzzy multiplicative preference relation for multiple-criteria group decision-making problems. The reference comparison of the best criterion and the worst criterion are described by the linguistic terms, which are expressed in hesitant fuzzy elements, of the decision makers. Weights of criteria are calculated by using score function. Using the concept of BWM, nonlinearly constrained optimization problems are formed to obtain hesitant fuzzy weights (HFWs) of different criteria and alternatives. To check the reliability of the HFBWM, consistency ratio is proposed. The advantage and suitability of the proposed HFBWM are determined by three case studies. The results indicate that the HFBWM, due to higher comparison consistency as compared to BWM, obtain plausible preference ranking for alternatives.     

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。     

A fuzzy group-preferences analysis method for new-product development

This paper reports a new idea-screening method for new product development (NPD) with a group of decision makers having imprecise, inconsistent and uncertain preferences. The traditional NPD analysis method determines the solution using the membership function of fuzzy sets which cannot treat negative evidence. The advantage of vague sets, with the capability of representing negative evidence, is that they support the decision makers with the ability of modeling uncertain opinions. In this paper, we present a new method for new-product screening in the NPD process by relaxing a number of assumptions so that imprecise, inconsistent and uncertain ratings can be considered. In addition, a new similarity measure for vague sets is introduced to produce a ratings aggregation for a group of decision makers. Numerical illustrations show that the proposed model can outperform conventional fuzzy methods. It is able to provide decision makers (DMs) with consistent information and to model situations where vague and ill-defined information exist in the decision process.     

A fuzzy group-preferences analysis method for new-product development

This paper reports a new idea-screening method for new product development (NPD) with a group of decision makers having imprecise, inconsistent and uncertain preferences. The traditional NPD analysis method determines the solution using the membership function of fuzzy sets which cannot treat negative evidence. The advantage of vague sets, with the capability of representing negative evidence, is that they support the decision makers with the ability of modeling uncertain opinions. In this paper, we present a new method for new-product screening in the NPD process by relaxing a number of assumptions so that imprecise, inconsistent and uncertain ratings can be considered. In addition, a new similarity measure for vague sets is introduced to produce a ratings aggregation for a group of decision makers. Numerical illustrations show that the proposed model can outperform conventional fuzzy methods. It is able to provide decision makers (DMs) with consistent information and to model situations where vague and ill-defined information exist in the decision process.     

Combining fuzzy weight average with fuzzy inference system for material substitution selection in electric industry

Material selection is a very important issue for an electronics company as it includes many qualitative or quantification factors. The material selection problem is associated with design and manufacturing problems which have been widely investigated. This study develops a hybrid fuzzy decision-making model which combines the fuzzy weight average (FWA) with the fuzzy inference system (FIS) for material substitution selection in the electronics industry. FWA is employed to select a substitute material in an uncertain environment, while FIS is used for reasoning purposes. FWA with α-cuts arithmetic (FWA_α-cut) is a popularly technology in decision-making problems. However, FWA_α-cut may result in the following unanticipated situations: (1) unclear decision situations; (2) undecided results expressed by fuzzy membership functions; and (3) high computational complexity. Therefore, a fuzzy weight average with the weakest t-norm (FWA_Tω) is designed as an alternative method for group decision making. In contrast to traditional FWA methods, FWA_Tω obtains more visible fuzzy results for decision makers with lower computational complexity, and can provide exacter estimation by the weakest t-norm operations in uncertain environment. Thus, the proposed hybrid fuzzy decision-making model imitates an expert’s experiences and can estimate substitution purchasing in various statuses. A real material substitution selection case is employed to examine the feasibility of the proposed model; experimental results reveal that the proposed model performs better than the traditional FWA model in coping with material substitution selection problems.     

Group decision-making based on pythagorean fuzzy TOPSIS method

Group decision-making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well-known method for multiple-criteria decision-making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision-making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF-TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF-TOPSIS are solved.     

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation (IFPR) is a suitable technique to express fuzzy preference information by decision makers (DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR, by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly, a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.      

基于犹豫模糊语言的多阶段多属性决策方法

针对不确定语言条件下的决策问题,考虑专家偏好的阶段性差异,提出基于犹豫模糊语言的多阶段多属性决策方法。首先为了更准确地表达专家在决策过程中的犹豫性,采用犹豫模糊语言来表达专家的评估信息;其次考虑阶段权重的波动性,运用基于专家阶段性偏好的信息熵方法构建阶段权重优化模型确定阶段权重;然后利用最大化偏差法来求解属性权重,并采用基于平均解距离评价(EDAS)方法对备选方案进行排序;最后以某企业选取物流商问题为例,验证该方法的有效性和可行性。     

A normal wiggly hesitant fuzzy linguistic projection-based multiattributive border approximation area comparison method

As a useful information representation tool, hesitant fuzzy linguistic term set (HFLTS) allows decision makers (DMs) to express their cognitive preferences in terms of several ordered and continuous linguistic terms. Considering the fact that much valuable information related to the cognitive behavior of DMs is hidden in the original evaluation information, this paper studies how to comprehensively mine uncertain information from original hesitant fuzzy linguistic evaluation information given by DMs. To address this objective, we present a new representation tool, normal wiggly hesitant fuzzy linguistic term set (NWHFLTS), which not only retains the original evaluation information, but also delivers and quantifies potential uncertain information, and can also help DMs express their evaluation information in a more complete manner. First, we develop the basic operations, score function, and comparison rule of NWHFLTS based on linguistic scale functions (LSFs), and propose the projection measure, the normal projection measure, and the normalized projection-based distance measure to describe the degree of deviation between two NWHFLTSs. Furthermore, for the case when the attribute weight is completely unknown, we combine the multiattributive border approximation area comparison (MABAC) method and develop a new method called as normal wiggly hesitant fuzzy linguistic projection-based MABAC to solve the multiattribute decision-making problems where attribute values are expressed in the form of NWHFLTS. Finally, through a practical example of marine ecological security situation, the specific calculation steps of this method are exemplified, the feasibility and advancement of the proposed method are demonstrated via a comprehensive comparative study.     

Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations

Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms.     

集对分析在不确定性智能决策中的应用

语言是思维的表达，智能决策是基于确定性与不确定性对立统一思维的一类高级决策。文章综述集对分析在纯自然语言决策，自然语言与数学混合语言决策，区间数决策和直觉模糊决策，集对分析粗糙集决策，联系数与马尔可夫链相结合的决策，赵森烽?克勤概率的贝叶斯决策，偏联系数的决策和同异反综合集成决策等方面的应用。特点是把基于确定性的决策建模与不确定性系统分析相结合，把系统宏观层次的分析与微观层次的分析相结合，把两种或多种决策方法综合集成，根据不确定性的具体情况给出决策建议，因而是一种立足于全局的智能决策，并认为集对分析的不确定性智能决策过程，在本质上是把决策系统中的信息能转换成智能的过程。