基于二元语义TAC积分算子的语言型多属性群决策方法

针对属性之间存在模糊关联的语言型多属性群决策问题,给出了二元语义TAC(Two-Additive Choquet)积分算子的定义,分析和证明了算子的有关性质,并提出了相应的决策方法。该方法首先将各专家提供的语言短语形式的属性权重信息、属性关联信息与属性评价信息转化为二元语义形式,然后利用二元语义TAC积分算子将转化后的属性相关信息集结为各专家的方案评价值,并进一步集结专家意见获得方案的综合评价值,从而确定其排序。最后,通过实例分析和方法比较说明了所给方法的有效性和优点。研究结果表明,该方法具有属性关联刻画细致、计算过程简单且无信息损失、决策结果可解释性强等优点,为求解属性之间存在模糊关联的语言型多属性群决策问题提供了一种新的途径。     

A genetic design of linguistic terms for fuzzy rule based classifiers

The determination of fuzzy information granules including the estimation of their membership functions play a significant role in fuzzy system design as well as in the design of fuzzy rule based classifiers (FRBCSs). However, although linguistic terms are fundamental elements in the process of elucidating expert’s knowledge, the problem of linguistic term design along with their fuzzy-set-based semantics has not been fully addressed, since term-sets of attributes have not been interpreted as a formalized structure. Thus, the essential relationship between linguistic terms, as syntax, and the constructed fuzzy sets, as their quantitative semantics, or in other words, the problem of the natural semantics of terms behind the linguistic literal has not been addressed. In this paper, we introduce the problem of the design of optimal linguistic terms and propose a method of the design of FRBCSs which may incorporate with the design of linguistic terms to ensure that the presence of linguistic literals are supported not only by data but also by their natural semantics. It is shown that this problem plays a primordial role in enhancing the performance and the interpretability of the designed FRBCSs and helps striking a better balance between the generality and the specificity of the desired fuzzy rule bases for fuzzy classification problems. A series of experiments concerning 17 Machine Learning datasets is reported.     

Group decision making based on novel fuzzy modified TOPSIS method

The aim of this paper is to present a novel fuzzy modified technique of order preference by a similarity to ideal solution (TOPSIS) method by a group of experts, which can select the best alternative by considering both conflicting quantitative and qualitative evaluation criteria in real-life applications. The proposed method satisfies the condition of being the closest to the fuzzy positive ideal solution and also being the farthest from the fuzzy negative ideal solution with multi-judges and multi-criteria. The performance rating values of alternatives versus conflicting criteria as well as the weights of criteria are described by linguistic variables and are transformed into triangular fuzzy numbers. Then a new collective index is introduced to discriminate among alternatives in the evaluation process with respect to subjective judgment and objective information. This paper shows that the proposed fuzzy modified TOPSIS method is a suitable decision making tool for the manufacturing decisions with two examples for the robot selection and rapid prototyping process selection.     

基于直觉梯形模糊偏好相似度的多属性决策方法

在解决模糊多属性决策问题中,相似度是一种有效的方法.针对已有的相似度的不足,构造了一种新的两个矢量之间的相似度,证明其满足相似度的性质,并把它应用解决直觉梯形模糊偏好多属性决策问题.方法用语言值的直觉梯形模糊数来表示决策方案的信息,通过计算每个决策方案的期望矢量,与正理想方案和负理想方案的期望矢量的相对相似度,并由相对相似度大小来排列决策方案.最后用一案例来讨论方法的可行性,数值结果表明方法计算简单,实用性强.     

A new multiple attribute group decision making method in intuitionistic fuzzy setting

The multiple attribute group decision making (MAGDM) problem with intuitionistic fuzzy information investigated in this paper is very useful for solving complicated decision problems under uncertain circumstances. Since experts have their own characteristics, they are familiar with some of the attributes, but not others, the weights of the decision makers to different attributes should be different. We derive the weights of the decision makers by aggregating the individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. The expert has a big weight if his evaluation value is close to the mean value and has a small weight if his evaluation value is far from the mean value. For the incomplete attribute weight information, we establish some optimization models to determine the attribute weights. Furthermore, we develop several algorithms for ranking alternatives under different situations, and then extend the developed models and algorithms to the MAGDM problem with interval-valued intuitionistic fuzzy information. Numerical results finally illustrate the practicality and efficiency of our new algorithms.     

含语言评价信息的一种模糊多属性群决策方法

对于多属性群决策问题的处理,有时需要采用先决策、后综合的处理方法,而含有语言评价信息的多属性群决策问题,定性目标一般用语言评价信息描述,由决策人给出定性目标和权系数的语言变量评价,用梯形模糊数表示,对定量目标进行无量纲化处理;将决策人对于单一目标的评价指标聚合成多个目标的评价模糊数,采用Bass-Kw akernaak模糊数排序方法对方案进行排序;群体的评价通过Borda函数来集结方案集的群体排序.     

构建不确定语言型多属性决策的投影模型

研究不确定语言型多属性决策评价结果与决策者对方案的偏好信息之间存在偏差的问题.通过建立与区间型语言标度对应的术语指标矩阵,及方案综合属性值与决策者主观偏好值之间的投影模型,确定属性的权重,然后运用加权法得到方案的综合属性值,利用已有的可能度矩阵排序公式得到决策方案的排序.构建了一种基于方案综合属性质与决策者主观偏好值之间的投影模型,通过算例对该方法的实用性和有效性进行了证明.     

模糊多属性群体决策模糊距离折中比值法及应用

为解决复杂条件下的模糊多属性群体决策问题,利用模糊距离的概念,提出了模糊距离折中比值法(FCRM)。在FCRM中,属性权重和定性属性评估值由语言变量和三角模糊数描述,并用模糊距离度量模糊数之间的距离。FCRM的决策原则是所选择的最优解在尽可能地贴近正理想解的同时尽可能地远离负理想解,同时充分考虑多个决策者的主观态度。文中详细阐述了FCRM的决策过程,通过实例将其应用于军事航线优选问题并与其他相关方法进行了比较分析,证实了该方法的有效性。     

一种基于残缺语言判断矩阵的群决策方法

本文针对具有残缺语言判断矩阵形式方案偏好信息的群决策问题,提出了一种决策分析方法.首先,阐述了二元语义的概念,并提出了一种扩展的二元语义有序加权平均(ETOWA)算子;然后,采用ETOWA算子集结具有残缺语言判断矩阵形式的方案偏好信息,可计算出每个方案优于其他方案的总体偏好程度,进而可得到所有方案的排序结果.最后,通过给出一个算例说明了本文提出方法的可行性和实用性.     

考虑决策者心理行为的直觉语言多属性决策方法

针对应用直觉语言集来表达决策信息的语言多属性决策问题,在考虑决策者有限理性的心理行为基础上,提出一种决策方法。该方法通过比较每个属性下方案之间的得分函数和精确函数, 构建方案的收益-损失分析矩阵。在考虑决策者参照依赖和损失规避心理行为基础上,计算每个方案相对于其它方案在每个属性下的收益-损失值优先度;在此基础上,计算备选方案的综合优先度, 并根据其大小对方案进行排序择优。最后通过一个算例验证所提出方法的有效性和合理性。     

Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting

Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method.     

A Direct Approach to Group Decision Making with Uncertain Additive Linguistic Preference Relations

In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of uncertain additive linguistic preference relations. We define the concept of uncertain additive linguistic preference relation, and introduce a formula based on possibility measure for comparing two uncertain linguistic preference values. We introduce some aggregation operators such as the uncertain linguistic averaging (ULA) operator and uncertain linguistic weighted averaging (ULWA) operator, etc. Based on the ULA and ULWA operators, we develop a direct approach to group decision making with uncertain additive linguistic preference relations without loss of information. Finally, an illustrative numerical example is given to verify the developed approach.     

基于概率测度的不确定语言多属性决策方法及应用

针对具有不确定语言信息的多属性决策问题,给出了一种基于语言概率测度的决策分析方法。阐述了不确定语言变量的概念,提出了一种用于处理不确定语言变量的语言概率有序加权平均（linguistic probabilistic ordered weighted averaging,LPOWA）算子。采用LPOWA算子将不确定语言转化为二元语义,再通过ETOWA算子得到每个方案的综合评价值,进而可得到所有方案的排序结果。利用LPOWA算子和ETOWA算子,对辽宁省风险投资企业进行评估和优选。理论分析和计算结果表明：该方法简洁可行,便于应用。     

An integrated model-based interactive approach to FMAGDM with incomplete preference information

Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking, strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations, inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate the developed approach.     

An interactive procedure for linguistic multiple attribute decision making with incomplete weight information

In this paper, we consider the multiple attribute decision making (MADM) problems, in which the information about attribute weights is partly known and the attribute values are expressed in linguistic labels. We first define the concepts of linguistic positive ideal point, linguistic negative ideal point, and satisfactory degree of alternative. Based on these concepts, we then establish some linear programming models, through which the decision maker interacts with the analyst. Furthermore, we establish a practical interactive procedure for solving the MADM problems considered in this paper. The interactive process can be realized by giving and revising the satisfactory degrees of alternatives till an optimum satisfactory solution is achieved. Finally, a practical example is given to illustrate the developed procedure.     

Approach to group decision making based on determining the weights of experts by using projection method

The aim of this paper is to present a new approach for determining weights of experts in the group decision making problems. Group decision making has become a very active research field over the last decade. Especially, the investigation to determine weights of experts for group decision making has attracted great interests from researchers recently and some approaches have been developed. In this paper, the weights of experts are determined in the group decision environment via projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, the weight of expert is determined by the projection of individual decision on the ideal decision. By using the weights of experts, all individual decisions are aggregate into a collective decision. Then an ideal solution of alternatives of the collective decision, expressed by a vector, is determined. Further, the preference order of alternatives are ranked in accordance with the projections of alternatives on the ideal solution. Comparisons with an extended TOPSIS method are also made. Finally, an example is provided to illustrate the developed approach.     

一种基于三参数区间灰色语言变量的多属性群决策方法

针对属性值为三参数区间灰色语言变量的不确定型多属性决策问题进行了研究,本文将语言变量和三参数区间数融合, 提出了三参数区间灰色语言变量的概念, 定义了三参数区间灰色语言变量的运算规则和可能度公式,在此基础上建立了基于投影模型的三参数区间灰色语言变量的多属性群决策方法。最后,通过对移动银行服务质量评估案例验证本模型的有效性。     

PROMETHEE-MD-2T method for project selection

Project selection is a real problem of multicriteria group decision making (MCGDM) where each decision maker expresses his/her preferences depending on the nature of the alternatives and on his/her own knowledge over them. Thus, information, as much quantitative as qualitative, coexists. The traditional methods of MCGDM developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information, and this is due to the capability to integrate this first type of information inside their procedure. In this article, two new multicriteria 2-tuple group decision methods called “Preference Ranking Organisation Method for Enrichment Evaluation Multi Decision maker 2-Tuple-I and II” (PROMETHEE-MD-2T-I and II) are presented. They are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context. This has been performed by integrating a 2-tuple linguistic representation model dealing with non-homogeneous and imprecise information data made up by valued intervals, numerical and linguistic values into the aggregation operators of Promethee methods. Although they have been developed for project selection problems, these proposed methods can be applied to all kinds of decision-making problems with heterogeneous and multigranular information.