基于证据理论的偏好型直觉模糊群决策方法

针对直觉模糊多属性群决策问题,研究属性和专家权重的确定以及信息的集结方法.利用直觉模糊熵确定属性客观权重,并根据偏好信息确定合理的属性综合权重;在属性层面区分专家权重,将直觉模糊评价值作为Mass函数,构建证据冲突度模型确定专家权重,并利用犹豫度加以修正,避免综合支持度低而对方案排序影响大的专家权重过分削弱;采用证据理论集结决策信息,根据得分值进行方案排序.最后通过算例分析,验证了所提出方法的合理性和有效性.     

一种基于直觉模糊集相似度的多属性决策方法

直觉模糊集（ＩＦＳ）是对模糊集理论的一种扩充,能更好地处理模糊概念．首先给出一种新的直觉模糊集相似度;然后提出基于直觉模糊集相似度的多属性决策方法;最后通过线性目标规划模型和直觉模糊集相似度,得到属性的最优权重和相应的方案排序．数值实例表明,该方法是有效而可行的．     

一种新的区间直觉模糊集决策方法: 区间证据组合的角度

基于证据理论,提出一种新的区间直觉模糊集决策模型.首先采用区间直觉模糊集表示属性值,将区间直觉模糊数转换为区间BPA;然后利用基于区间数的组合规则进行融合;最后将融合后的区间BPA转换为经典BPA用于决策,可直接方便地实现多属性数据的融合.该模型的优点在于:简单直观,能更有效地反映原始信息的不确定度;通用性好,可以推广到其他区间直觉模糊集的应用领域.算例结果表明了所提出模型的有效性.     

基于区间直觉模糊集的模糊多目标群决策

为提高数据决策的准确性,结合区间直觉模糊集理论,对模糊多目标群决策算法进行优化。并针对部分权重信息并不一定完整的情况,利用迭代计算的方式向最优决策逐步逼近。实例显示,该算法具有时间复杂度低、便于计算机实现等特点,并说明了算法的有效性和准确性。     

基于直觉模糊集的时域证据组合方法研究

证据理论已广泛应用于时空信息融合领域,由于时域信息融合表现出明显的序贯性和动态性,为实现基于证据理论的时域信息融合,有效处理时域冲突信息,结合证据可靠性评估和证据折扣的思想,在直觉模糊框架内提出了一种基于复合可靠度的时域证据组合方法.首先定义一种基于可靠度的直觉模糊数排序方法,在此基础上提出一种基于直觉模糊多属性决策的证据可靠性评估方法;然后,基于此方法对时域信息序列中相邻时间节点的证据可靠性进行评估,得到时域证据的相对可靠性因子;最后,结合由时域证据可靠度衰减模型得到的实时可靠性因子,得到时域证据的复合可靠性因子,再基于证据折扣运算和Dempster证据组合规则提出一种基于复合可靠度的时域证据组合方法.数值算例和仿真表明,该方法具有较强的时间敏感性,充分体现了时域信息融合的动态性特点,可以较好地处理时域证据中的冲突信息,基于该方法构建的融合识别系统具有较强的抗干扰能力.     

基于组合模型的直觉模糊集多属性决策方法

针对直觉模糊集是对模糊集理论的一种扩充,能够更好地处理模糊概念,研究了基于直觉模糊集的多属性决策问题.提出了直觉指数加权平均最大化和最小化组合模型,通过线性规划模型得到了属性的最优权重和相应的方案排序.数值例子表明,该方法是可行而有效的.     

基于区间直觉模糊集的多准则决策方法

研究基于区间直觉模糊集的多准则决策方法.首先定义了区间直觉模糊点算子,并讨论了其性质;然后对区间直觉模糊集定义了一系列得分函数,并给出两种基于区间直觉模糊集的多准则决策方法.将该方法应用于区间直觉模糊集多准则决策问题,所得结果推广了有关直觉模糊集的相关结果.     

基于后悔理论和证据理论的犹豫模糊决策方法

针对属性值为犹豫模糊信息、属性权重和自然状态发生概率完全未知的多属性群决策问题,考虑决策者心理行为,提出一种基于后悔理论和证据理论的多属性群决策方法。首先,运用证据理论计算各自然状态发生的概率;然后,基于区间模糊矩阵、t-分布估计以及得分函数矩阵确定属性信息的效用值,进而依据后悔理论得到每个自然状态下的感知效用矩阵;通过加权算术平均得到综合感知效用矩阵,并依据方案综合感知效用的大小确定方案优劣排序;最后,将所提方法运用于对投资公司的选择实例中。实验结果表明,虽然所提方法与现有方法得到的决策结果相同,但是所提方法在决策过程中只需考虑较少数量的参数。对比分析实验表明,所提方法得到的决策结果合理、可靠,且能反映实际决策情况。     

Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology

In this paper, we propose a new fuzzy multiattribute group decision making method based on intuitionistic fuzzy sets and the evidential reasoning methodology. First, the proposed method uses the evidential reasoning methodology to aggregate each decision maker’s decision matrix and the weights of the attributes to get the aggregated decision matrix of each decision maker. Then, it uses the obtained aggregated decision matrices of the experts, the weights of the experts and the evidential reasoning methodology to get the aggregated intuitionistic fuzzy value of each alternative. Finally, it calculates the transformed value of the obtained intuitionistic fuzzy value of each alternative. The smaller the transformed value, the better the preference order of the alternative. The proposed method can overcome the drawbacks of the existing methods for fuzzy multiattribute group decision making in intuitionistic fuzzy environments.     

Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making

The main feature of Pythagorean fuzzy sets is that it is characterized by five parameters, namely membership degree, nonmembership degree, hesitancy degree, strength of commitment about membership, and direction of commitment. In this paper, we first investigate four existing comparison methods for ranking Pythagorean fuzzy sets and point out by examples that the method proposed by Yager, which considers the influence fully of the five parameters, is more efficient than the other ones. Later, we propose a variety of distance measures for Pythagorean fuzzy sets and Pythagorean fuzzy numbers, which take into account the five parameters of Pythagorean fuzzy sets. Based on the proposed distance measures, we present some similarity measures of Pythagorean fuzzy sets. Furthermore, a multiple criteria Pythagorean fuzzy group decision‐making approach is proposed. Finally, a numerical example is provided to illustrate the validity and applicability of the presented group decision‐making method.     

直觉模糊多属性决策的新方法

针对属性值以直觉模糊数形式给出的多属性决策中确定属性权重的问题,提出了一种直觉模糊数熵权的确定方法,依照传统权熵的确定方法的思路,通过一个公式求得直觉模糊熵;然后求得属性的信息熵;根据传统熵权确定公式得到属性权重,进而利用得分函数对方案进行排序;最后通过算例说明该方法的有效性和实用性。     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.     

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.     

A consensus‐ and harmony‐based feedback mechanism for multiple attribute group decision making with correlated intuitionistic fuzzy sets

In this study, an interactive consensus model is proposed for correlated multiple attribute group decision making (MAGDM) problems with intuitionistic triangular fuzzy numbers (ITFNs). The harmony degree (HD) is investigated to determine the degree of maintaining experts' original information while the consensus level is defined as the proximity degree (PD) between an expert and other experts on three levels: evaluation elements of alternatives, alternatives, and decision matrices. Combining HD and PD, a three‐dimensional feedback mechanism is proposed to identify discordant experts, alternatives, and corresponding preference values that contribute less to consensus, and provides advice to reach a higher consensus level. Additionally, visual representation of experts' consensus position within the group is provided. Furthermore, a graphical simulation of future consensus and harmony status, if the recommended values were to be implemented, is also provided. Therefore, our proposed feedback mechanism guarantees that it increases the consensus level of the set of experts while maintaining, as much as possible, experts' original information. Then, the PD‐induced intuitionistic triangular fuzzy correlated averaging (PD‐IITFCA) operator is investigated to aggregate the interactive individual opinions between experts. Finally, the intuitionistic triangular fuzzy correlated averaging (ITFCA) operator is developed to aggregate the evaluation elements of alternatives under correlative attributes. Based on the score and accurate functions of ITFNs, an order relation is proposed to obtain the final solution of alternatives.     

Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information

With respect to multi-criteria group decision making (MCGDM) problems under trapezoidal intuitionistic fuzzy environment, a new MCGDM method is investigated. The proposed method can effectively avoid the failure caused by the use of inconsistent decision information and provides a decision-making idea for the case of “the truth be held in minority”. It consists of three interrelated modules: weight determining mechanism, group consistency analysis, and ranking and selection procedure. For the first module, distance measures, expected values and arithmetic averaging operator for trapezoidal intuitionistic fuzzy numbers are used to determine the weight values of criteria and decision makers. For the second module, a consistency analysis and correction procedure based on trapezoidal intuitionistic fuzzy weighted averaging operator and OWA operator is developed to reduce the influence of conflicting opinions prior to the ranking process. For the third module, a trapezoidal intuitionistic fuzzy TOPSIS is used for ranking and selection. Then a procedure for the proposed MCGDM method is developed. Finally, a numerical example further illustrates the practicality and efficiency of the proposed method.     

基于IFN 输入的复杂系统关联MCGDM方法

考虑现有直觉模糊熵公理化定义存在的不足,提出改进直觉模糊熵的公理化定义及其计算公式;同时,定义广义幂均算子,验证其相关性质,给出确定幂方参数的方法,并将其推广至广义直觉模糊幂均算子;在以直觉模糊数(IFN)为信息输入的复杂系统框架内,针对决策者及准则之间均存在交互关联关系且权重信息完全未知的多准则群决策(MCGDM)问题,提出基于直觉模糊熵与广义直觉模糊幂均算子的关联MCGDM方法。案例分析表明,所提出的方法是可行且有效的。