基于一种新得分函数和累积前景理论的毕达哥拉斯模糊TOPSIS法

针对属性权重未知、评价信息为毕达哥拉斯模糊数的多属性决策问题,对毕达哥拉斯模糊集的得分函数进行深入分析,为解决现有得分函数中存在的不足,提出一种新得分函数,通过证明其相关定理,分析新得分函数的性质.将新得分函数运用到毕达哥拉斯模糊多属性决策问题中,以帮助决策者更好地处理模糊的决策信息.此外,针对现有大多数毕达哥拉斯模糊...     

基于累积前景理论和Choquet积分的直觉梯形模糊多属性决策

针对属性值为直觉梯形模糊数且属性存在关联性的风险决策问题, 提出一种基于累积前景理论和Choquet积分的直觉梯形模糊多属性决策方法。根据直觉梯形模糊数距离公式定义了直觉梯形模糊信息的前景价值函数, 通过价值函数和决策权重函数计算方案单属性前景值, 并运用Choquet积分融合属性间存在关联性的前景价值信息获得方案综合前景值, 根据综合前景值的大小实现方案的排序和优选。风险投资实例分析说明了该方法的可行性。     

基于累积前景理论的可变下标犹豫模糊语言多准则投资组合优化

将累积前景理论的价值函数引入投资组合决策,从行为金融学的角度对传统整数犹豫模糊语言术语集下标进行改进,改进后的可变下标犹豫模糊语言术语集不仅可以反映投资人对金融产品的不确定程度,还能描述投资人给出评价本身时对收益或损失的心理感知.在单投资者多准则评价视角下,利用可变下标的犹豫模糊语言多准则投资组合评价系统对不同股票进行量化评价,针对激进型、稳健型和保守型3类投资者分别提出收益最大化、风险最小化犹豫模糊语言投资组合模型,通过对等价非线性模型求解得到投资组合的最优解.最后,利用数值仿真验证所提出模型和方法的有效性.     

An interindividual iterative consensus model for fuzzy preference relations

Consensus reaching models are widely used to derive a representative solution in group decision-making problems. Current models present limitations regarding the achievement of the agreement and keeping enough consistency for achieving valid solutions. Therefore, this paper proposed a new consensus model based on the deviation degree of two fuzzy preference relations (FPRs), in which a novel consistency index (CI) is defined to measure whether an FPR is of acceptable consistency. Additionally, an interindividual similarity index (ISI) is devised to measure the consensus degree of two FPRs. In the proposed consensus reaching process, ISI is also used to guide the two most incompatible decision-makers (DMs) to modify their judgments. The proposed iterative consensus reaching algorithm is convergent, CI preservation. After that, a stationary vector method is adopted to determine DMs’ weights for the aggregation process based on DMs’ opinion transition probabilities. Finally, an illustrative example and comparative analysis is given to demonstrate the effectiveness of the proposed model.     

Partial preference structure with fuzzy relations for MCDM problems

A fuzzy outranking relation to solve a multiple criteria decision-making (MCDM) problem involving a discrete set of incomparable decision alternatives is investigated. The relation is exploited to rank the alternatives in various classes in a preferential order for their sequential implementation using fuzzy graph theory. A numerical example is solved to highlight the procedure.     

Incomplete interval fuzzy preference relations and their applications

This paper investigates incomplete interval fuzzy preference relations. A characterization, which is proposed by Herrera-Viedma et al. (2004), of the additive consistency property of the fuzzy preference relations is extended to a more general case. This property is further generalized to interval fuzzy preference relations (IFPRs) based on additive transitivity. Subsequently, we examine how to characterize IFPR. Using these new characterizations, we propose a method to construct an additive consistent IFPR from a set of n − 1 preference data and an estimation algorithm for acceptable incomplete IFPRs with more known elements. Numerical examples are provided to illustrate the effectiveness and practicality of the solution process.     

Consistency test and weight generation for additive interval fuzzy preference relations

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b).     

Methods for fuzzy complementary preference relations based on multiplicative consistency

To improve the consistency of a preference relation is a hot topic in decision making. Wang and Chen (2008) gave a simple method to construct the complete fuzzy complementary preference relation from only n − 1 pairwise comparisons. However, some values may not be in the defined scope and need to be transformed, and thus some original information may be lost in the transformation process. In this paper, we propose a new method to avoid this issue based on the multiplicative consistency of the fuzzy complementary preference relation and apply it to fuzzy Analytic Hierarchy Process (AHP). An example is further given to illustrate our method.     

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.

     

An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was recently introduced to efficiently deal with situations in which the membership and non-membership are represented as linguistic terms. In this paper, we study the issues of additive consistency and the derivation of the intuitionistic fuzzy weight vector of an IFLPR. First, the new concepts of order consistency, additive consistency and weak transitivity for IFLPRs are introduced, and followed by a discussion of the characterisation about additive consistent IFLPRs. Then, a parameterised transformation approach is investigated to convert the normalised intuitionistic fuzzy weight vector into additive consistent IFLPRs. After that, a linear optimisation model is established to derive the normalised intuitionistic fuzzy weights for IFLPRs, and a consistency index is defined to measure the deviation degree between an IFLPR and its additive consistent IFLPR. Furthermore, we develop an automatic iterative decision-making method to improve the IFLPRs with unacceptable additive consistency until the adjusted IFLPRs are acceptable additive consistent, and it helps the decision-maker to obtain the reasonable and reliable decision-making results. Finally, an illustrative example is provided to demonstrate the validity and applicability of the proposed method.     

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.     

Pythagorean fuzzy combined compromise solution method integrating the cumulative prospect theory and combined weights for cold chain logistics distribution center selection

The evaluation and selection of cold chain logistics distribution centers are of vital importance for third-party logistics companies which want to build green cold chain logistics networks. To select distribution centers, the conflicts among multiple criteria should be considered. The combined compromise solutions (CoCoSo) method can help enterprises make a structural decision; however, in the original CoCoSo method, the evaluation information was expressed by crisp numbers. Nevertheless, in many cases, because of the imprecision and incompleteness of information, it may be more flexible for evaluators to provide imprecise and fuzzy values rather than crisp numbers. In addition, the judgment values are often expressed based on decision-makers' psychological expectations. The evaluation criteria of alternatives have relevance to some extent, which would influence the evaluation results. Based on these concerns, this study presents a modified CoCoSo method in the Pythagorean fuzzy environment in which evaluators can express psychological expectations on alternatives. To achieve this goal, the cumulative prospect theory is introduced to obtain the Pythagorean fuzzy prospect weights. Then, an objective weight determination method of criteria under the Pythagorean fuzzy environment is proposed to eliminate the influence of homogeneity of criteria. Based on the Pythagorean fuzzy prospect weights and the combined weights, the original CoCoSo method is extended to the Pythagorean fuzzy environment. A case of selection logistics distribution center is investigated to demonstrate the practicality of the proposed method. The advantages of the proposed method are verified by comparative analysis.     

Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations

A novel intuitionistic fuzzy set (IFS) score function and an intuitionistic fuzzy preference relation (IFPR) quantifier guided non-dominance based prioritisation method are introduced. Based on Yager’s continuous OWA (COWA) operator, the interval-valued intuitionistic fuzzy COWA (IVIF-COWA) operator is defined, and a new attitudinal expected score function for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The novelty of this attitudinal expected score function is that it allows the comparison of IVIFNs by taking into account of the decision makers’ attitudinal character. Moreover, we show that the new attitudinal expected score function extends: (i) the IFS score function introduced in this paper, which is mathematically equivalent to Chen and Tan’s score function (Chen and Tan, 1994); and (ii) Xu and Chen’s score function for IVIFNs (Xu and Chen, 2007). Using the proposed score functions, a method is developed to construct FPRs from a given IFPR and IVIFPR, respectively. When the hesitancy degree function is null, we prove that the score FPRs coincide with their respective IFPR and IVIFPR. Finally, a ranking sensitivity analysis of the attitudinal expected score function with respect to the attitudinal parameter is provided.     

Group decision making based on incomplete multiplicative and fuzzy preference relations

The main aim of this paper is to investigate the group decision making on incomplete multiplicative and fuzzy preference relations without the requirement of satisfying reciprocity property. This paper introduces a new characterization of the multiplicative consistency condition, based on which a method to estimate unknown preference values in an incomplete multiplicative preference relation is proposed. Apart from the multiplicative consistency property among three known preference values, the method proposed also takes the multiplicative consistency property among more than three values into account. In addition, two models for group decision making with incomplete multiplicative preference relations and incomplete fuzzy preference relations are presented, respectively. Some properties of the collective preference relation are further discussed. Numerical examples are provided to make a discussion and comparison with other similar methods.     

勾股模糊偏好关系及其在群体决策中的应用

以区间模糊偏好关系(IVFPR)和直觉模糊偏好关系(IFPR)的理论框架为依据,将勾股模糊数(PFN)引入偏好关系中,定义勾股模糊偏好关系(PFPR)和加性一致性PFPR.然后,提出标准化勾股模糊权重向量(PFWV)的概念,并给出构造加性一致性PFPR的转换公式.为获取任意给定的PFPR的权重向量,建立以给定的PFPR与构造的加性一致性PFPR偏差最小为目标的优化模型.针对多个勾股模糊偏好关系的集结,利用能够有效处理极端值并满足关于序关系单调的勾股模糊加权二次(PFWQ)算子作为集结工具.进一步,联合PFWQ算子和目标优化模型提出一种群体决策方法.最后,通过案例分析表明所提出方法的实用性和可行性.     

基于证据理论和前景理论的犹豫-直觉模糊语言多准则决策方法

在犹豫模糊语言和直觉模糊语言的基础上,提出一种新的犹豫-直觉模糊语言集,并定义得分函数、精确函数和Hamming距离公式.针对准则值为犹豫-直觉模糊语言的不确定多准则决策问题,构建基于证据理论和前景理论的拓展型VIKOR方法.该决策方法利用证据理论处理自然状态发生的概率未知的不确定状况,应用前景理论刻画人在做决策时的有限理性行为,使决策结果更能反映实际情况.最后,通过算例表明了所提出方法的有效性和可行性.     

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.

     

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。     

基于模糊偏序关系评估决策的智能信息融合

针对信息融合系统应综合考虑获取信息所要求的资源、计算复杂度和时间所需要的最小成本的问题,提出了基于模糊偏序关系评估决策的智能信息融合系统,利用模糊偏序关系的排序方法,来对传感器进行评估决策和智能选择,并与证据理论相组合,应用于目标识别,仿真结果表明了该方法的有效性。