二元语义Bonferroni集成算子及其在多属性群决策中的应用

Bonferroni平均算子的优点是在进行信息集成的过程中能够考虑到输入变量之间的相互影响。本文首先将其推广到语言环境中,提出了二元语义Bonferroni平均(2TLBA)算子、加权2TLBA(W2TLBA)算子和组合W2TLBA(C-W2TLBA)算子的概念,研究它们的相关性质。然后针对决策信息以语言变量给出的多属性群决策问题,提出一种基于W2TLBA算子和C-W2TLBA算子的群决策方法。最后应用实例说明了该方法是切实可行的。     

The OWA-based consensus operator under linguistic representation models using position indexes

When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.     

Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making

This paper deals with multiattribute group decision making (MAGDM) problems with interval-valued 2-tuple linguistic information. First, we introduce some new aggregation operators, such as the interval-valued 2-tuple weighted geometric (IVTWG) operator, the interval-valued 2-tuple ordered weighted geometric (IVTOWG) operator, the generalized interval-valued 2-tuple weighted average (GIVTWA) operator and the generalized interval-valued 2-tuple ordered weighted average (GIVTOWA). Then, we discuss their desired properties and relationships among them. Furthermore, we put forward a new method to determine the weight vector of interval-valued 2-tuple aggregation operator based on the concept of degree of precision. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in dealing with interval-valued 2-tuple linguistic information under multi-granular linguistic contexts.     

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。     

基于准则间关系的多准则语言决策方法

在多准则语言决策问题中,准则间的关系一般有三种:相互独立、相互影响、优先关系.基于这三种关系,结合比例二元组语义信息提出了一种新的多准则语言决策方法.介绍了比例二元组优先加权平均(P2TPWA)算子,并讨论了有关P2TPWA算子的相关性质.另外,将Choquet积分拓展到了比例二元组语言环境,并将P2TPWA算子和比例二元组语言Choquet积分用于实际的决策问题中.     

一种基于犹豫模糊集的多属性关联决策方法

主要讨论属性间具有关联性的条件下犹豫模糊多属性决策问题.首先,基于gλ模糊测度,Shapley值和Choquet积分,定义了两种犹豫模糊信息集成算子:AHFGSCgλ算子和GHFGSCgλ算子.然后,讨论了这些算子的一些性质.最后通过一个实例来说明算子的可行性和有效性.     

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.     

直觉语言Hamacher加权集结算子及其应用

研究带参数的直觉语言Hamacher集结算子。基于Hamacher t-模与s-模定义直觉语言Hamacher运算法则。而后,利用所提Hamacher运算法则提出含参数的直觉语言Hamacher加权平均算子与几何算子,研究其基本性质。进一步地,剖析算子与参数之间的关系,如算子关于参数的单调性、算子关于参数的退化情况等。最后,基于所提出的集结算子构建出多属性决策方法,通过算例分析表明所提决策方法的可行性和实用性。     

不确定语言环境下基于ULHGA算子的群决策方法

研究属性权重和专家权重为确定的实数,属性值为不确定语言变量的多属性群决策问题.提出了一种新的数据信息集成算子不确定语言混合几何集结(ULHGA)算子,并给出不确定语言环境下基于ULWGM算子和ULHGA算子的一种群决策方法.最后进行实例分析,说明该方法的实用性和有效性.     

基于对偶犹豫模糊语言变量的多属性决策方法

首先定义了对偶犹豫模糊语言变量,然后给出其运算规则、得分值函数、精确值函数、比较规则以及对偶犹豫模糊语言变量的加权算术平均算子、有序加权算术平均算子和混合平均算子。针对属性值为对偶犹豫模糊语言变量的多属性决策问题,提出了一种基于对偶犹豫模糊语言变量集结算子的多属性决策方法。最后,结合国家电网公司合作单位选择问题,验证了该方法的有效性和可行性。     

基于直觉模糊二元语义交互式群决策的技术创新项目选择

为适应全球经济一体化的快速发展,企业应选择最优的技术创新项目,从而提升其竞争力。首先定义了直觉模糊二元语义,探讨了将其区间化的方法,建立了直觉模糊二元语义与区间模糊二元语义之间的联系。接着重新定义了直觉模糊二元语义的距离和相似度,给出了群决策的集结算子。通过集结决策者的意见和进行交互式决策,使得群体的决策意见达到满意的一致性水平。最后以技术创新项目选择为例说明了本文提出的方法。     

多粒度区间语言信息的C-OWH算子及其应用

研究了多粒度区间语言信息的集成问题,把连续的有序加权调和(C-OWH)平均算子拓展到多粒度区间语言环境中,提出了连续区间二元语义OWH(ITC-OWH)算子,并在此基础上提出了加权调和的ITC-OWH(WHITC-OWH)算子,有序加权调和的ITC-OWH(OWHITC-OWH)算子以及组合的ITC-OWH(CITC-OWH)算子,探讨了它们的一些性质。最后给出了基于这些算子的多粒度区间语言多属性群决策方法,实例分析结果表明该方法是可行的。     

Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making

In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment.     

犹豫模糊语言Heronian平均算子在多属性决策中的应用

针对输入变量之间的相互影响以及评价值为犹豫模糊语言信息的多属性决策问题,提出一种基于犹豫模糊语言Heronian平均算子的多属性决策方法。由于Heronian平均(HM)算子具有能够反映输入变量之间相互关联的良好特性,在犹豫模糊语言信息环境下,提出了两种新的集成算子,即犹豫模糊语言Heronian平均(HFLHM)算子和犹豫模糊语言几何Heronian平均(HFLGHM)算子,同时研究了它们的一些特性。考虑到输入变量具有不同的重要程度,还定义了犹豫模糊语言加权Heronian平均(HFLWHM)算子和犹豫模糊语言加权几何Heronian平均(HFLWGHM)算子。最后提出了基于HFLWHM算子和HFLWGHM算子的犹豫模糊语言多属性决策方法,并通过实例验证了这些算子的合理性和可行性。     

Generalized triangular fuzzy correlated averaging operator and their application to multiple attribute decision making

We investigate the multiple attribute decision making problems with triangular fuzzy information. Motivated by the ideal of Choquet integral [G. Choquet, Theory of capacities, Ann. Instit. Fourier 5 (1953) 131–295] and generalized OWA operator [R.R. Yager, Generalized OWA aggregation operators, Fuzzy Optim. Dec. Making 3 (2004) 93–107], in this paper, we have developed an generalized triangular fuzzy correlated averaging (GTFCA) operator. The prominent characteristic of the operators is that they cannot only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have applied the GTFCA operator to multiple attribute decision making problems with triangular fuzzy information. Finally an illustrative example has been given to show the developed method.     

Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making

The intuitionistic uncertain fuzzy linguistic variable can easily expressthe fuzzy information, and the power average (PA) operator is a usefultool which provides more versatility in the information aggregation procedure.At the same time, Einstein operations are a kind of various t-normsand t-conorms families which can be used to perform the corresponding intersectionsand unions of intuitionistic fuzzy sets (IFSs). In this paper, wewill combine the PA operator and Einstein operations to intuitionistic uncertainlinguistic environment, and propose some new PA operators. Firstly,the definition and some basic operations of intuitionistic uncertain linguisticnumber (IULN), power aggregation (PA) operator and Einstein operationsare introduced. Then, we propose intuitionistic uncertain linguistic fuzzypowered Einstein averaging (IULFPEA) operator, intuitionistic uncertain linguisticfuzzy powered Einstein weighted (IULFPEWA) operator, intuitionisticuncertain linguistic fuzzy Einstein geometric (IULFPEG) operator and intuitionisticuncertain linguistic fuzzy Einstein weighted geometric (IULFPEWG)operator, and discuss some properties of them in detail. Furthermore, we developthe decision making methods for multi-attribute group decision making(MAGDM) problems with intuitionistic uncertain linguistic information andgive the detail decision steps. At last, an illustrate example is given to showthe process of decision making and the effectiveness of the proposed method.     

An approach to aggregation of ordinal information in multi-criteria multi-person decision making using Choquet integral of Fubini type

An algorithm for the selection among n alternatives based on the evaluation of n (distinct) groups of persons according to the same m criteria is described. The evaluation of each person for each criterion is represented by a proportional ordinal 2-tuple and the overall opinion is aggregated by a pair of quantifier-guided ordered weighted averaging (OWA) aggregation and (floating) anchoring value-based ordered weighted averaging (AV-OWA) aggregation operators. An example is provided to illustrate the algorithm. The decision function of the algorithm is shown to be a Choquet integral of the associated function of two variables (corresponding to the two aggregation processes in the algorithm) which can be accomplished alternatively by a Choquet integral of Fubini type.     

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.     

Extension of VIKOR method for multi-criteria group decision making problem with linguistic information

A new method is proposed to solve multi-criteria group decision making problems in which both the criteria values and criteria weights take the form of linguistic information based on the traditional idea of VIKOR method. Firstly, the linguistic criteria weights given by all decision makers are transformed into trapezoidal fuzzy numbers, and then aggregated and defuzzified to crisp values. Secondly, the individual linguistic decision matrix given by each decision maker (DM) is transformed into 2-tuple linguistic decision matrix, and then aggregated into collective 2-tuple linguistic decision matrix by 2-tuple linguistic arithmetic mean operation. Thirdly, the 2-tuple linguistic values (_Si,_αi),$(S_i\text{,}{\alpha }_i)\text{,}$(_Ri,_αi)$(R_i\text{,}{\alpha }_i)$ and (_Qi,_αi)$(Q_i\text{,}{\alpha }_i)$ are calculated by defining the 2-tuple linguistic positive ideal solution (TL-PIS) and 2-tuple linguistic negative ideal solution (TL-NIS). Furthermore, the compromise solution can be obtained. Finally, a numerical example is used to illustrate the application of the proposed approach, and the method is verified by comparing the evaluation result with that of 2-tuple linguistic TOPSIS (TL-TOPSIS) method.     

Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making

In this study a generated admissible order between interval-valued intuitionistic uncertain linguistic numbers using two continuous functions is introduced. Then, two interval-valued intuitionistic uncertain linguistic operators called the interval-valued intuitionistic uncertain linguistic Choquet averaging (IVIULCA) operator and the interval-valued intuitionistic uncertain linguistic Choquet geometric mean (IVIULCGM) operator are defined, which consider the interactive characteristics among elements in a set. In order to overall reflect the correlations between them, we further define the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet averaging (GS-IVIULCA) operator and the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet geometric mean (GS-IVIULCGM) operator. Moreover, if the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on expert set and attribute set are established, respectively. Finally, a method to multi-attribute group decision making under interval-valued intuitionistic uncertain linguistic environment is developed, and an example is provided to show the specific application of the developed procedure.