Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.     

A criteria weighting approach by combining fuzzy quality function deployment with relative preference relation

In past, fuzzy multi-criteria decision-making (FMCDM) models desired to find an optimal alternative from numerous feasible alternatives under fuzzy environment. However, researches seldom focused on determination of criteria weights, although they were also important components for FMCDM. In fact, criteria weights can be computed through extending quality function deployment (QFD) under fuzzy environment, i.e. fuzzy quality function deployment (FQFD). By FQFD, customer demanded qualities expressing the opinions of customers and service development capabilities presenting the opinions of experts can be integrated into criteria weights for FMCDM. However, deriving criteria weights in FQFD may be complex and different to multiply two fuzzy numbers in real world. To resolve the tie, we will combine FQFD with relative preference relation on FMCDM problems. With the relative preference relation on fuzzy numbers, it is not necessary multiplying two fuzzy numbers to derive criteria weights in FQFD. Alternatively, adjusted criteria weights will substitute for original criteria weights through relative preference relation. Obviously, adjusted criteria weights are clearly determined and then utilized in FMCDM models.     

An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method.     

Logistics tool selection with two-phase fuzzy multi criteria decision making: A case study for personal digital assistant selection

Efficient logistics and supply chain management are enabled through the use of efficient information technologies (IT). The mobile logistics tools represent the IT interface in the supply chain. This paper aims to aid decision makers to identify the most appropriate mobile logistics tools and to achieve this aim, several evaluation criteria are identified to evaluate logistics tools, and a fuzzy axiomatic design (FAD) based group decision-making method is adopted to perform the evaluation in two phases. In the first phase of pre-assessment, alternatives that cannot meet basic requirements and the defined threshold are eliminated. In the second phase of selection, the remaining alternatives are more meticulously evaluated. Criteria weights are determined using fuzzy analytic hierarchy process (AHP) and another fuzzy multi-criteria decision-making (MCDM) technique, namely fuzzy technique for order preference by similarity to ideal solution (TOPSIS), is applied in the second phase to compare the outcome of FAD. A case study is provided in order to demonstrate the potential of the proposed methodology. Personal digital assistants (PDAs) with integrated barcode scanner that are available in the Turkish market are evaluated.     

R-WGA算子的构建及其在群决策分析中的应用

在群决策问题中,决策属性间与专家偏好间均可能存在关联,需定义新的集结算子来计算决策方案的综合评价值．为此,在传统加权几何平均（WGA）算子和模糊测度理论的基础上,构建关联加权几何平均（R—WGA）算子,探讨该算子的性质,给出基于R-WGA算子的群决策分析方法．研究表明,R—WGA算子是WGA算子的推广,与Choquet积分一样,R-WGA算子也可用于求解基于关联的决策问题．     

A hybrid approach for fuzzy multi-attribute decision making in machine tool selection with consideration of the interactions of attributes

Global economic competition has spurred the manufacturing sector to improve and invest in modern equipment to satisfy the needs of the market. In particular, machine tool selection is the most important problem; it plays a primary role in the improvement of productivity and flexibility in the manufacturing environment and involves the imprecise, vague and uncertain information. This paper presents the hybrid approach of the fuzzy ANP (Analytic Network Process) and COPRAS-G (COmplex PRoportional ASsessment of alternatives with Grey relations) for fuzzy multi-attribute decision-making in evaluating machine tools with consideration of the interactions of the attributes. The fuzzy ANP is used to handle the imprecise, vague and uncertain information from expert judgments and model the interaction, feedback relationships and interdependence among the attributes to determine the weights of the attributes. COPRAS-G is employed to present the preference ratio of the alternatives in interval values with respect to each attribute and calculate the weighted priorities of the machine alternatives. Alternatives are ranked in ascending order by priority. As a demonstration of the proposed model, a numerical example is implemented based on the collected data and the literature. The result is then compared with the rankings provided by other methods such as TOPSIS-G, SAW-G and GRA. Moreover, a sensitivity analysis is conducted to verify the robustness of the ranking. The result highlights that the hybrid approach of the fuzzy ANP and COPRAS-G is a highly flexible tool and reaches an effective decision in machine tool selection.     

Group consensus algorithms based on preference relations

In many group decision-making situations, decision makers’ preferences for alternatives are expressed in preference relations (including fuzzy preference relations and multiplicative preference relations). An important step in the process of aggregating preference relations, is to determine the importance weight of each preference relation. In this paper, we develop a number of goal programming models and quadratic programming models based on the idea of maximizing group consensus. Our models can be used to derive the importance weights of fuzzy preference relations and multiplicative preference relations. We further develop iterative algorithms for reaching acceptable levels of consensus in group decision making based on fuzzy preference relations or multiplicative preference relations. Finally, we include an illustrative example.     

A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS

This paper presents a new method for handling multicriteria fuzzy decision-making problems, in which the characteristics of the alternatives are represented by interval-valued fuzzy sets, and some techniques are developed to calculate the degree of similarity between interval-valued fuzzy sets. The proposed method is more flexible than the one we presented earlier (Chen et al., 1989) because it allows the criteria values of the alternatives to be represented by real intervals rather than crisp real values between zero and one.     

用区间直觉模糊集方法对属性权重未知的群求解其多属性决策

本文首先提出群区间直觉模糊有序加权几何(groupinterval-valuedintuitionistic fuzzy orderedweighted geometric,GIVIFOWG)算子和群区间直觉模糊有序加权平均(group interval-valued intuitionistic fuzzy ordered weighted averaging,GIVIFOWA)算子.利用GIVIFOWG算子或GIVIFOWA算子聚集群的决策矩阵以获得方案在属性上的综合区间直觉模糊决策矩阵(collectiveinterval-valuedintuitionistic fuzzy decision-matrix,CIVIFDM).然后定义了一个考虑犹豫度的区间直觉模糊熵(interval-valuedintuitionistic fuzzyentropy,IVIFE);通过熵衡量每个属性所含的信息来求解属性权重.最后,提出基于可能度的接近理想解的区间排序法(interval technique for order preference by similarity to an ideal solution,ITOPSIS)和区间得分函数法.在ITOPSIS法中,依据区间距离公式计算候选方案和理想方案的属性加权区间距离,进而采用ITOPSIS准则对各方案进行排序;在区间得分函数法中,算出CIVIFDM中各方案的得分值以及精确值,然后利用区间得分准则对各方案进行排序.实验结果验证了决策方法的有效性和可行性.     

对方案有偏好的直觉模糊多属性决策方法

对属性权重信息不完全、属性值和决策者对方案的偏好信息均以直觉模糊数表示的多属性决策问题提出一种决策方法。首先根据决策者对方案的偏好信息建立多目标规划模型,求出属性权重,接着利用觉模糊加权算术平均算子求出方案的综合属性值,由直觉模糊数的得分函数和精确函数确定方案的排序,最后通过实例证明了该方法的实用性和有效性。     

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method.     

A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information

Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decision-making processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relative-closeness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.     

Regret theory-based group decision-making with multidimensional preference and incomplete weight information

In this paper, we study fuzzy multi-attribute group decision-making (FMAGDM) problems with multidimensional preference information in the form of pairwise alternatives and incomplete weight information. We develop a new group decision-making (GDM) method considering regret aversion of the decision-makers (DMs). Firstly, we define a fuzzy regret/rejoice function and a computational formula for the perceived utility of alternative decisions. We propose a perceived utility value-based group consistency index (which reflects the total consistency) and a group inconsistency index (which represents the total inconsistency) for pairwise rankings of alternatives based on regret theory and an a priori multidimensional preference order given by the DMs. Then, under the circumstances of an unknown fuzzy ideal solution, we set up a mathematical programming model to determine the optimal attribute weights and a defuzzified fuzzy ideal solution with the idea of the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). We compute the DMs’ optimal comprehensive perceived utility values and obtain the ranking order of alternatives. Finally, we illustrate the application of the developed procedures with an air-fighter selection problem. The rationality and validity of the proposed method is demonstrated by comparing with two other GDM methods, including the fuzzy LINMAP (FLINMAP) method and the prospect theory-based GDM method.     

Note on ranking fuzzy triangular numbers

This paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision-making situations. Three new methods are proposed, and a notion of preference between alternatives is suggested. A comparison with other methods is provided in the concluding table. © 1998 John Wiley & Sons, Inc.     

区间值模糊随机多准则决策方法

针对不完全信息的区间值模糊随机多准则决策问题,提出了两种求解方法。第一种方法利用离差最大化构建区间参数线性规划,通过区间数运算法则和定位规划求得最优准则权重向量、状态集结值区间决策矩阵与期望值区间决策矩阵,根据决策者风险偏好水平得到各方案的期望集结值从而确定排序。第二种方法将区间值模糊数决策矩阵转化为直觉模糊数决策矩阵,利用不完全的准则权重,通过规划模型求解,获取各方案在各自然状态下的加权记分函数值与加权精确函数值的区间,利用不完全的状态概率,得到各方案的记分函数期望值与精确函数期望值的区间,根据决策者风险偏好水平,求得各方案的记分函数与精确函数的期望集结值,进而确定方案的排序结果。算例分析验证了两种方法的有效性和可行性。     

Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets

In this paper, we present a new method to handle fuzzy multiple attributes group decision-making problems based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision-making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision-making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes.     

考虑决策者情绪更新机制的多阶段应急决策方法

针对决策者情绪影响下参照点的动态调整可能导致不同决策结果的情形,提出一种考虑决策者情绪更新机制的多阶段应急决策方法.首先,描述突发事件下的多阶段应急决策问题,并以直觉模糊数的形式刻画相关决策信息;其次,给出决策者情绪影响下动态参照点的设置方法,并运用累积前景理论计算突发事件各个演化阶段的情景价值,据此建立决策者的情绪更新机制;然后,计算各个演化阶段的情景权重,并结合备选方案的期望价值、投入成本及启动时间价值,计算方案在各个演化阶段的前景价值;进一步,通过给出各个演化阶段权重的计算方法,计算备选方案的综合前景价值,并据此给出备选方案的优劣次序;最后,通过算例分析及与其他方法的对比验证所提出方法的有效性.     

一种对方案有偏好的Vague集多属性决策方法

研究了方案属性值和偏好值均为Vague值的多属性决策问题。针对相关文献中,将由Vague值表示的方案属性值与偏好值转化为直觉模糊数,并根据直觉模糊数表示的方案属性值与偏好值之间的偏差建立规划模型并求解属性权重这一过程,分析了建立的规划模型的不合理性。提出通过最小化直觉模糊数表示的方案综合值与偏好值的偏差,建立并求解一个规划模型计算属性权重的改进方法。通过将Vague值转化为模糊值,利用模糊值矩阵的线性序构造模糊优先矩阵,并对其进行分割,从而实现方案的排序择优。通过一个实例说明了该方法的可行性。     

一种结合主客观信息的多属性决策方法

研究了具有模糊偏好信息的模糊多属性决策问题．提出一种结合主观偏好信息与客观信息的综合特征向量方法．主观偏好信息由决策方案的模糊偏好互补矩阵和属性权重的两两比较互反矩阵组成，客观信息由客观决策矩阵组成．给出了求解模糊多属性决策问题的最小二乘偏差估计方法．通过建立二次规划模型决定属性权重向量，并对方案进行排序．最后，给出了使用该方法的数值例子．     

MAGDM Linear-Programming Models With Distinct Uncertain Preference Structures

Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.