Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with 2-tuple linguistic information. Firstly, motivated by the ideas of Choquet integral and Shapley index, we propose three 2-tuple linguistic aggregation operators called Shapley 2-tuple linguistic Choquet averaging operator, Shapley 2-tuple linguistic Choquet geometric operator and generalized Shapley 2-tuple linguistic Choquet averaging operator. Then we discuss some properties of these operators, such as idempotency, monotonicity, boundary and commutativity. Secondly, if the information about the weights of decision makers (DMs) and attributes is incompletely known, we build two models to determine the optimal fuzzy measures on DM set and attribute set, respectively. Furthermore, we develop a new method for multiple attribute group decision making under 2-tuple linguistic environment based on the proposed operators. Finally, we apply the developed MAGDM method to select the most desirable emergency alternative and the validity of the developed method is verified by comparing the evaluation results with those obtained from the existing 2-tuple correlated aggregation operators.     

Some q-rung orthopair fuzzy 2-tuple linguistic Muirhead mean aggregation operators and their applications to multiple-attribute group decision making

Multiple-attribute group decision making (MAGDM) under linguistic environment is an important part of modern decision sciences, and information aggregation operator plays an import role in solving MAGDM problems. In this paper, an approach for solving MAGDM problem with q-rung orthopair fuzzy 2-tuple linguistic information is developed. First, the q-rung orthopair fuzzy 2-tuple linguistic weighted averaging (q-ROFTLWA) operator and the q-rung orthopair fuzzy 2-tuple linguistic weighted geometric (q-ROFTLWG) operator are presented. Furthermore, the q-rung orthopair fuzzy 2-tuple linguistic Muirhead mean (q-ROFTLMM) operator and the q-rung orthopair fuzzy 2-tuple linguistic dual Muirhead mean (q-ROFTLDMM) operator are proposed on the basis of Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator. Then, an approach is developed to deal with MAGDM problem under q-rung orthopair fuzzy 2-tuple linguistic environment based on the proposed operators. Finally, a numerical example for selecting desirable emergency alternative(s) in the process of designing emergency preplan is given to illustrate the application of the developed method and demonstrate its effectiveness.     

Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making

With respect to multiple attribute group decision making problems with linguistic information, some new decision analysis methods are proposed. Firstly, we develop three new aggregation operators: generalized 2-tuple weighted average (G-2TWA) operator, generalized 2-tuple ordered weighted average (G-2TOWA) operator and induced generalized 2-tuple ordered weighted average (IG-2TOWA) operator. Then, a method based on the IG-2TOWA and G-2TWA operators for multiple attribute group decision making is presented. In this approach, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.     

New aggregation operators based on the Choquet integral and 2-tuple linguistic information

Considered in this paper is the group decision making problem with inter-dependent or interactive attributes, where evaluation values of decision makers are in linguistic arguments. By using the Choquet integral, some new aggregation operators are introduced, including the 2-tuple correlated averaging operator, the 2-tuple correlated geometric operator and the generalized 2-tuple correlated averaging operator. The proposed operators can better reflect the correlations among the elements. After investigating properties of these operators, a new multiple attribute decision making method based on the new operators is proposed. Finally, a numerical example is provided to illustrate the feasibility and efficiency of the proposed method.     

Partitioned Bonferroni mean based on two-dimensional uncertain linguistic variables for multiattribute group decision making

The two-dimensional uncertain linguistic variables (2DULVs) add a self-evaluation on the reliability of the assessment results given by decision makers (DMs), so they can better describe some uncertain information, and the partition Bonferroni mean (PBM) operator has the advantages, which assumes that all aggregated arguments are partitioned into several subparts, and members in the same subpart are interrelated and members in different subparts are no interrelationships. However, the traditional PBM can only deal with the crisp numbers and cannot aggregate the 2DULVs. In this paper, we extend the PBM operator to deal with the 2DULVs and propose some PBM operators for 2DULVs. First, we introduce the concepts, properties, operational laws, and comparison methods of 2DULVs, and then we propose the PBM operator for 2DULVs (2DULPBM), the weighted PBM operator for 2DULVs (2DULWPBM), the partitioned geometric Boferroni mean (PGBM) operator for 2DULVs (2DULPGBM), and weighted PGBM operator for 2DULVs (2DULWPGBM). Further, we develop a method to solve multiattribute group decision-making (MAGDM) problems with the 2DULVs. Finally, we give an example to verify that the method based on the proposed operators is effective and influential.     

Hesitant 2-tuple linguistic Bonferroni operators and their utilization in group decision making

Hesitant 2-tuple linguistic variable realizes a graded information approach to characterize the uncertainty of human cognition. This study is concerned with the development of new aggregation operators and aims to design a new group decision making approach to address the information fusion involving the interrelationship between aggregated terms and the prioritization relationship among decision makers under hesitant 2-tuple linguistic situation. Firstly, hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator and prioritized weighted hesitant 2-tuple linguistic Bonferroni mean (PWH2TLBM) operator are established. Subsequently, some pertinent properties and special forms of the developed operators are studied in detail. To employ the proposed operators to solve group decision making problems, a novel TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method based on possibility degree is developed under the situation of hesitant 2-tuple linguistic information. The designed decision making method not only inherits the merits of the traditional TODIM approach, but also characterizes the interrelationship of criteria. The detailed process of solving problems is exemplified to highlight the practicality and feasibility of the designed method. Furthermore, comparative analysis with other methods is carried out to further offer insights on the designed decision method.     

语言比例二元组Bonferroni平均算子的群决策方法

针对语言比例二元组信息集成的问题,提出了语言比例二元组Bonferroni平均算子的群决策方法。基于基本单位区间单调（BUM）函数的定义,提出了三角模糊数的中心有序加权平均算子的概念。由于三角模糊数的中心有序加权平均算子和语言术语的数值表示（NR）之间存在交互关联,提出了用三角模糊数的中心有序加权平均算子代替语言术语的数值表示的方法,并将此方法得到的NR和语言术语的NR进行了对比分析。引入了语言比例二元组Bonferroni平均算子,介绍了语言比例二元组Bonferroni平均算子的群决策方法,并用一个实例来说明其可行性。     

2TLCGPOWA算子及其在多属性群决策中的应用

基于集对分析理论中二元联系数的不确定性,将联系变量引入到区间二元语义环境中,定义了二元语义联系变量,给出了二元语义联系变量的运算法则,并提出了几种新的算术集结算子。针对决策矩阵元素为区间二元语义变量和属性权重完全未知的不确定多属性群决策问题,提出了一种基于2TLCGPOWA算子的不确定多属性群决策方法。最后通过对某大学教师的任职和晋升考核来说明该方法的可行性和有效性。     

Two-tuple linguistic utility aggregation operator and its applications to group decision-making

This paper aims to develop an aggregation operator for two-tuple linguistic information based on utility function, which characterizes the influence of decision makers' psychological factors on the linguistic aggregation process. First, we propose a new two-tuple linguistic ordered utility aggregation (TOU) operator, and then, we investigate its properties that are suitable for any utility function. Subsequently, we derive a specific form of the TOU operator, which is called the two-tuple linguistic generalized ordered weighted utility averaging-hyperbolic absolute risk aversion (TOHU) operator, under the hyperbolic absolute risk aversion utility function. Then, we further investigate its families including a wide range of aggregation operators. To determine the weights of the TOHU operator, which take the form of two-tuple linguistic, we establish an optimization weighting model by combining the information of input arguments and subjective considerations of decision makers. Furthermore, we propose a two-tuple linguistic aggregation method to deal with the multiple attribute group decision-making (MAGDM) problem based on the TOHU operator. Finally, we provide an example to demonstrate the application of the TOHU operator to MAGDM.     

Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making

The power average (PA) operator and Maclaurin symmetric mean (MSM) operator are two important tools to handle the multiple attribute group decision‐making (MAGDM) problems, and the combination of two operators can eliminate the influence of unreasonable information from biased decision makers (DMs) and can capture the interrelationship among any number of arguments. The Pythagorean fuzzy linguistic set (PFLS) is parallel to the intuitionistic linguistic set (ILS), which is more powerful to convey the uncertainty and ambiguity of the DMs than ILS. In this paper, we propose some power MSM aggregation operators for Pythagorean fuzzy linguistic information, such as Pythagorean fuzzy linguistic power MSM operator and Pythagorean fuzzy linguistic power weighted MSM (PFLPWMSM) operator. At the same time, we further discuss the properties and special cases of these operators. Then, we propose a new method to solve the MAGDM problems with Pythagorean fuzzy linguistic information based on the PFLPWMSM operator. Finally, some illustrative examples are utilized to show the effectiveness of the proposed method.     

Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making

In this paper, some uncertain linguistic aggregation operators called uncertain linguistic weighted harmonic mean (ULWHM) operator, uncertain linguistic ordered weighted harmonic mean operator and uncertain linguistic hybrid harmonic mean (ULHHM) operator are proposed. An approach to multiple attribute group decision making (MAGDM) with uncertain linguistic information is developed based on the ULWHM and the ULHHM operators. Finally, a practical application of the developed approach to MAGDM problem with uncertain linguistic information is given.     

Some generalized interval-valued hesitant uncertain linguistic aggregation operators and their applications to multiple attribute group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the assessment values of attributes take the form of interval-valued hesitant uncertain linguistic elements, a novel MAGDM method is proposed in this paper. Firstly, the concept, operational laws and score function of interval-valued hesitant uncertain linguistic elements (IVHULEs) are introduced. Then, based on the operational laws of IVHULEs, some generalized aggregation operators are proposed for aggregating the interval-valued hesitant uncertain linguistic information, including the generalized interval-valued hesitant uncertain linguistic weighted aggregation operators, the generalized interval-valued hesitant uncertain linguistic ordered weighted aggregation operators and the generalized interval-valued hesitant uncertain linguistic hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed. Based on the proposed operators, an approach to multiple attribute group decision making with unknown weight information is developed under interval-valued hesitant uncertain linguistic environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.     

区间直觉二元语言集成算子及其群决策方法

基于下标以零为中心对称的语言评估标度,将区间不确定二元语言集与区间直觉模糊集结合,提出区间直觉二元语言集及变量的概念;讨论区间直觉二元语言变量的运算及可能度;提出区间直觉二元语言加权算术平均算子、区间直觉二元语言有序加权平均算子,并在此基础上,通过可能度矩阵对区间直觉二元语言变量进行排序提出区间直觉二元语言混合加权平均算子;最后基于这些算子构建了一种新的直觉模糊多属性群决策方法,并将其运用于供应商选择过程中。     

区间二元语义Bonferroni集成算子及其决策应用

区间二元语义值是一种常用的不确定环境下决策信息表达形式。考虑到决策信息的交叉影响作用,定义了区间二元语义值的Bonferroni平均算子以及相应的加权形式,在此基础上,给出了组合形式的区间二元语义值的加权Bonferroni平均算子的概念,并研究了算子的幂等性、单调性等数学性质,给出了基于C-I2TLWBA算子区间二元语义值的集成模型和决策应用。实例表明了该模型具有较好的有效性。     

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。     

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.     

Some 2-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision-making

In this paper, we expand the generalised Heronian mean (GHM) operator, generalised weighted Heronian mean (GWHM), geometric Heronian mean (GHM) operator, and weighted geometric Heronian mean (WGHM) operator with 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) to propose generalised 2-tuple linguistic Pythagorean fuzzy Heronian mean (G2TLPFHM) operator, generalised 2-tuple linguistic Pythagorean fuzzy weighted Heronian mean (G2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy geometric Heronian mean (2TLPFGHM) operator, 2-tuple linguistic Pythagorean fuzzy weighted geometric Heronian mean (2TLPFWGHM) operator. Then, the MADM methods are proposed with these operators. In the end, we utilise an applicable example for green supplier selection to prove the proposed methods.     

An integrated fuzzy MCDM approach for supplier evaluation and selection

A fuzzy multi-criteria group decision making approach that makes use of quality function deployment (QFD), fusion of fuzzy information and 2-tuple linguistic representation model is developed for supplier selection. The proposed methodology seeks to establish the relevant supplier assessment criteria while also considering the impacts of inner dependence among them. Two interrelated house of quality matrices are constructed, and fusion of fuzzy information and 2-tuple linguistic representation model are employed to compute the weights of supplier selection criteria and subsequently the ratings of suppliers. The proposed method is apt to manage non-homogeneous information in a decision setting with multiple information sources. The decision framework presented in this paper employs ordered weighted averaging (OWA) operator, and the aggregation process is based on combining information by means of fuzzy sets on a basic linguistic term set. The proposed framework is illustrated through a case study conducted in a private hospital in Istanbul.     

Some 2-tuple linguistic neutrosophic number Muirhead mean operators and their applications to multiple attribute decision making

In this paper, we expand the Muirhead mean (MM) operator and dual MM (DMM) operator with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose the 2-tuple linguistic neutrosophic numbers MM (2TLNNMM) operator, 2-tuple linguistic neutrosophic numbers weighted MM (2TLNNWMM) operator, 2-tuple linguistic neutrosophic numbers DMM (2TLNNDMM) operator and 2-tuple linguistic neutrosophic numbers weighted DMM (2TLNNWDMM) operator. Then, the MADM methods are proposed with these two operators. Finally, an example for green supplier selection is used to show the proposed methods.     

A new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator and its application for enterprise location

Recently some new models based on Pythagorean fuzzy sets (PFSs) have been proposed to deal with the uncertainty in multiple attribute group decision making (MAGDM) problems. In this paper, considering linguistic variables and entropic, we propose a new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator to solve MAGDM problems. Next, we study some main properties by utilizing some operational laws of the trapezoidal Pythagorean fuzzy linguistic variables. Finally, a numerical example concerning the enterprise location is given to illustrate the practicality and effectiveness of the proposed operator.