基于勾股模糊语言幂加权平均算子的多属性群体决策方法

针对多属性群决策问题,采用能够方便专家参考语言集信息进行评价并且取值灵活的勾股模糊语言集进行了处理。首先,基于语言集和勾股模糊集的距离测度给出了勾股模糊语言数距离测度的定义与相关性质;然后,以勾股模糊语言数的距离测度作为幂均（PA）算子的距离度量,提出了勾股模糊语言幂加权平均（PFLPWA）算子用以对群决策过程中不同专家评价矩阵进行融合,并同时在融合过程中考虑专家评价的差异性;最后,基于PFLPWA算子构建了勾股模糊语言环境下的群体决策新方法,并通过案例分析检验了PFLPWA算子应用于群决策中的有效性和适用性。     

勾股模糊集的距离测度及其在多属性决策中的应用

首先,讨论3种勾股模糊数排序方法的特点,指出其中两种排序方法的不足;其次,研究勾股模糊集的结构特征,指出勾股模糊数本质上由隶属度、非隶属度、自信度和自信度方向4个特征参数完全刻画;再次,利用上述4个参数分别构造勾股模糊数和勾股模糊集之间的海明距离、欧几里得距离和闵可夫斯基距离,并研究这些距离公式的性质;最后,借助理想点法给出基于勾股模糊集距离的多属性决策方法,并通过实例验证所提方法的合理性.     

动态模糊形式化关系群体决策方法

群体决策问题是决策科学的核心问题之一。基于动态模糊理论,从动态角度研究群体决策问题,提出了一种动态模糊形式化关系决策方法。从个体偏好信息表达、个体偏好数据分析、个体偏好集结、方案选择和意见反馈五个阶段探讨了动态模糊群体决策模型,并通过实例验证了该模型的可行性和合理性。     

基于同构Frank t-模与s-模的勾股模糊 Frank集结算子及其应用

运用单位区间上的自同构构造一种适用于勾股模糊环境下的同构Frank t-模与其对偶s-模,进而定义勾股模糊集的广义运算法则,并探究新法则的相关性质.应用新的运算法则提出勾股模糊Frank加权平均(PFFWA)算子与勾股模糊Frank加权几何(PFFWG)算子,证明算子的相关性质.利用PFFWA与PFFWG算子提出一种解决勾股模糊多属性决策问题的新方法.通过解决航空公司服务质量评估问题,对比分析新方法与现存的决策方法,进而表明新方法的可行性和灵活性, 并验证了新方法具有反馈决策者态度特征的能力.     

基于信息测度的勾股模糊决策模型及其应用

相对于直觉模糊集，勾股模糊集能够更为全面和有效地表达描述复杂问题中的不确定和非一致信息，使其受到了广泛研究。对于属性评价值为勾股模糊数并且属性指标权重信息数据完全未知的多属性决策问题，以提出的勾股模糊信息测度为基础，设计了新的多属性决策模型。该模型运用对数函数设计了一种新的勾股模糊数信息熵计算方法；引入了勾股模糊相似度概念，并结合对数行数提出勾股模糊数相似度的衡量方法，随后挖掘出勾股模糊数的信息熵和相似度之间的内在联系；运用提出的勾股模糊熵和相似度计算方法，构建新的多属性决策模型，并进行应用研究。实验结果表明，提出的模型合理有效，同时拓展了模型的使用范围。     

模糊偏好关系一致性改进算法及其决策应用

模糊偏好关系是处理决策问题的一种有效工具。针对模糊偏好关系,研究了加性一致性模糊偏好关系的若干判定条件,构造了满足加性一致性的特征模糊偏好关系,并提出一致性指数、满意加性一致性等概念。在此基础上,构建了不满足加性一致性模糊偏好关系的改进算法,论证了算法的收敛性,该算法使得改进后的模糊偏好关系具有满意一致性条件,进而使得决策者获得合理可靠的决策结果。最后建立了基于模糊偏好关系加性一致性的决策模型。实例分析说明提出的模糊偏好关系决策模型是可行和有效的。     

勾股模糊H平均决策算法及应用

研究了勾股模糊数信息环境下属性值间存在内在关联性的多属性决策问题。首先定义了基于t-模和t-余模的勾股模糊数运算;将Heronian平均融入到聚合算子的构建过程中;讨论了勾股模糊Heronian平均算法的3个特征性质和经常使用的特例。然后构建了改进的勾股模糊决策模型,该模型在考虑输入属性值之间关联性的同时,提高了决策的使用范围。最后通过多属性决策实例验证了改进的决策模型合理有效。     

勾股模糊H平均算法及其云计算系统选择

研究勾股模糊数信息环境下内在关联度的多属性选择策略问题.首先,定义了实现模糊集模并模或功能的勾股模糊数运算;其次,将模糊H平均用于设计聚合算子,提出了勾股模糊H平均(PFHM)算法,并讨论了勾股模糊H平均算法的3个特征性质及应用实例;然后,构建了新的勾股模糊多属性决策模型,该模型将实际问题属性评价值信息转化为勾股模糊数...     

乘型一致性毕达哥拉斯模糊偏好关系

毕达哥拉斯模糊偏好关系(PFPR)是直觉模糊偏好关系的推广,也是毕达哥拉斯模糊集的重要研究领域.相对于其他模糊偏好关系而言,毕达哥拉斯模糊偏好关系在表达决策者的模糊偏好时更加灵活有力.在乘型一致性区间模糊偏好关系和乘型一致性直觉模糊偏好关系研究成果的启发下,定义毕达哥拉斯模糊偏好关系的乘型一致性,并提出利用毕达哥拉斯模...     

考虑直觉模糊偏好关系的双边稳定匹配及应用

针对现有双边匹配决策要求主体给出另一方全体偏好序信息的条件过于苛刻的问题, 提出一种新的匹配方法. 一方主体先两两比较另一方全体成员, 给出直觉模糊集形式的评价值并由全体成员评价值组成直觉模糊偏好关系; 然后, 通过改进的最小对数二乘法对其进行转化, 间接得到主体满意度; 进一步以双方主体满意度最大为目标, 同时考虑稳定匹配约束条件, 建立单目标优化模型并求解获得匹配方案; 最后, 通过算例分析表明了所提出方法的可操作性和有效性.

     

Compatibility of interval fuzzy preference relations with the COWA operator and its application to group decision making

We develop a new compatibility for the interval fuzzy preference relations based on the continuous ordered weighted averaging (COWA) operator and use it to determine the weights of experts in group decision making (GDM). We define some concepts of the compatibility degree and the compatibility index for the two interval fuzzy preference relations based on the COWA operator. We study some desirable properties of the compatibility index and investigate the relationship between the each expert’s interval fuzzy preference relation and the synthetic interval fuzzy preference relation. The prominent characteristic of the compatibility index based on the COWA operator is that it can deal with the compatibility of all the arguments by using a controlled parameter considering the attitude of decision maker rather than the compatibility of the simply two points in intervals. To determine the experts’ weights in the GDM with the interval fuzzy preference relations, we propose an optimal model based on the criterion of minimizing the compatibility index. In the end, we give a numerical example to develop the new approach to GDM with interval fuzzy preference relations.     

基于三角Pythagorean模糊集的多准则决策方法

Pythagorean模糊集在直觉模糊集的基础上扩大了适用范围,三角模糊数在决策过程中可以保留决策者较多的不确定信息.鉴于此,首先提出三角Pythagorean模糊集的定义及其欧氏距离表示;然后定义三角Pythagorean模糊加权平均(TPFWA)算子、广义三角Pythagorean模糊加权平均(GTPFWA)算子、三角Pythagorean模糊加权几何(TPFWG)算子和广义三角Pythagorean模糊加权几何(GTPFWG)算子,并对算子所满足的幂等性、有界性和单调性予以证明;最后通过一个医药代表选择的多准则决策问题和灵敏度分析验证所提出算子的合理性和有效性.     

Multi-criteria group decision making with incomplete hesitant fuzzy preference relations

In order to simulate the hesitancy and uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of hesitant fuzzy preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. This paper defines the concept of additive consistent hesitant fuzzy preference relations. The characterizations of additive consistent hesitant fuzzy preference relations are studied in detail. Owing to the limitations of the experts’ professional knowledge and experience, the provided preferences in a hesitant fuzzy preference relation are usually incomplete. Consequently, this paper introduces the concepts of incomplete hesitant fuzzy preference relation, acceptable incomplete hesitant fuzzy preference relation, and additive consistent incomplete hesitant fuzzy preference relation. Then, two estimation procedures are developed to estimate the missing information in an expert's incomplete hesitant fuzzy preference relation. The first procedure is used to construct an additive consistent hesitant fuzzy preference relation from the lowest possible number, (n − 1), of pairwise comparisons. The second one is designed for the estimation of missing elements of the acceptable incomplete hesitant fuzzy preference relations with more known judgments. Moreover, an algorithm is given to solve the multi-criteria group decision making problem with incomplete hesitant fuzzy preference relations. Finally, a numerical example is provided to illustrate the solution processes of the developed algorithm and to verify its effectiveness and practicality.     

Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making

Linguistic intuitionistic fuzzy sets can be regarded as a qualitative form of intuitionistic fuzzy sets. This type of fuzzy sets uses a linguistic membership degree and a linguistic non-membership degree to represent the qualitative preferred and non-preferred judgments of decision makers. Preference relation is a useful and efficient tool for decision making that only requires the decision makers to compare two objects at one time. Taking the advantages of linguistic intuitionistic fuzzy sets and preference relations, this paper introduces linguistic intuitionistic fuzzy preference relations (LIFPRs) and studies their application to decision making. To ensure the ranking of objects reasonably, an additive consistency concept is introduced, and several of its desirable properties are discussed. To cope with inconsistent and incomplete LIFPRs, programming model-based methods to derive additively consistent LIFPRs and determine missing values are constructed, respectively. Subsequently, an approach to multi-criteria decision making with LIFPRs is offered, and the application of the new approach is illustrated by using a decision-making problem about evaluating mobile phones.     

Intuitionistic preference relations and their application in group decision making

Intuitionistic fuzzy set, characterized by a membership function and a non-membership function, was introduced by Atanassov [Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96]. In this paper, we define the concepts of intuitionistic preference relation, consistent intuitionistic preference relation, incomplete intuitionistic preference relation and acceptable intuitionistic preference relation, and study their various properties. We develop an approach to group decision making based on intuitionistic preference relations and an approach to group decision making based on incomplete intuitionistic preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionistic fuzzy weighted arithmetic averaging operator are used to aggregate intuitionistic preference information, and the score function and accuracy function are applied to the ranking and selection of alternatives. Finally, a practical example is provided to illustrate the developed approaches.     

Linguistic labels for expressing fuzzy preference relations infuzzy group decision making

This paper proposes improvements to pairwise group decision making based on fuzzy preference relations in three ways. First, it extends the fuzzy preference relation representation using linguistic labels. Decision makers may express their preference relations in linguistic labels which are more practically implementable for solving group decision making problems. Second, it modifies the computational procedures by using fuzzy sets representation and computation, and by avoiding the use of strict threshold values. This allows natural representation, preserves the preference accuracy, and produces more intuitively meaningful solutions. Finally, it considers fuzzy criteria of the alternatives explicitly. Solutions are first derived based on each criterion, and then by using neat ordered weighted average (OWA) operator the final solutions which accommodate all criteria are determined. The proposed method is verified for solving fuzzy group decision making problems, i.e., advertising media selection cases.     

Analysis of self-confidence indices-based additive consistency for fuzzy preference relations with self-confidence and its application in group decision making

Preference relations have been widely used in group decision-making (GDM) problems. Recently, a new kind of preference relations called fuzzy preference relations with self-confidence (FPRs-SC) has been introduced, which allow experts to express multiple self-confidence levels when providing their preferences. This paper focuses on the analysis of additive consistency for FPRs-SC and its application in GDM problems. To do that, some operational laws for FPRs-SC are proposed. Subsequently, an additive consistency index that considers both the fuzzy preference values and self-confidence is presented to measure the consistency level of an FPR-SC. Moreover, an iterative algorithm that adjusts both the fuzzy preference values and self-confidence levels is proposed to repair the inconsistency of FPRs-SC. When an acceptable additive consistency level for FPRs-SC is achieved, the collective FPR-SC can be computed. We aggregate the individual FPRs-SC using a self-confidence indices-based induced ordered weighted averaging operator. The inherent rule for aggregation is to give more importance to the most self-confident experts. In addition, a self-confidence score function for FPRs-SC is designed to obtain the best alternative in GDM with FPRs-SC. Finally, the feasibility and validity of the research are demonstrated with an illustrative example and some comparative analyses.     

Pythagorean linguistic preference relations and their applications to group decision making using group recommendations based on consistency matrices and feedback mechanism

In this paper, we introduce a new type of fuzzy set, called Pythagorean linguistic sets (PLSs), to address the preferred and nonpreferred degrees of linguistic variables. Moreover, it allows decision makers to offer effectively handle uncertain information more flexible than intuitionistic linguistic sets (ILSs) when one compares two alternatives in the process of decision making. Some of the fundamental operational laws, score, accuracy, and aggregation operators are defined, and their properties are investigated. Preference relation (PR) is a useful and efficient tool for decision making that only requires the decision makers to compare two alternatives at one time. Taking the advantages of PLSs and PRs, this paper also introduces Pythagorean linguistic preference relations (PLPRs) and studies their application. We propose an approach for group decision making using group recommendations based on consistency matrices and feedback mechanism. First, the proposed method constructs the collective consistency matrix, the weight collective PRs, and the group collective PRs. Then, it constructs a consensus relation for each expert and determines the group consensus degree (GCD) for all experts. If the GCD is smaller than a predefined threshold value, then a feedback mechanism is activated to update the PLPRs. Finally, after the GCD is greater than or equal to the predefined threshold value, we calculate the arithmetic mathematical average values of the updated group collective PR to select the most appropriate alternative.     

A new approach to fuzzy group decision making with trapezoidal fuzzy preference relations by using compatibility measure

This paper aims to develop a new approach to deal with fuzzy group decision making (GDM) with additive trapezoidal fuzzy preference relations (ATFPRs) by using compatibility measure. We firstly present some concepts of compatibility index and expected preference relation (PR) for ATFPR and then propose a compatibility improving algorithm to help each individual PR achieve acceptable compatibility . Moreover, a least deviation model is provided to obtain the priority vector. Besides, based on the criterion of minimizing the compatibility index, we put forward an optimal model to determine the weights of experts in GDM. Finally, the GDM process with compatibility of ATFPRs is presented, and an illustrative example is utilized to verify the developed approach . The main features of our approach are that: (1) It guarantees that each individual ATFPR is acceptably compatible by using compatibility improving algorithm. (2) It ensures that experts’ weights in group aggregation are determined objectively by optimal model.