A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

Fuzzy Entropic Ordered Weighted Averaging Operator and Its Application in Group Decision Making

In the paper, we develop a new method for multiple attribute group decision making) for fuzzy numbers. The fuzzy entropic weighted averaging (FEOWA) operator is an extension of the entropic ordered weighted averaging operator, which unifies the fuzzy entropy and the ordered weighted averaging operator in the same formulation. Then, some of its main properties by utilizing some operational laws of fuzzy numbers are studied. We also present the generalized entropic ordered weighted averaging operator and the fuzzy generalized entropic ordered weighted averaging operator. Moreover, a method based on the FEOWA operator for decision making is presented. Finally, a numerical example illustrates the applicability and effectiveness of the proposed method.     

Interval‐Valued Intuitionistic Fuzzy Multiattribute Group Decision Making Based on Cross Entropy Measure and Choquet Integral

In this paper, a new operator called the arithmetic interval‐valued intuitionistic fuzzy Choquet aggregation (AIVIFCA) operator is defined. Since interactions between elements might exist in all their combinations, the generalized Shapley AIVIFCA (GSAIVIFCA) operator is introduced. Further, to simplify the complexity of solving a fuzzy measure, the 2‐additive generalized Shapley AIVIFCA (2AGSAIVIFCA) operator is presented. Moreover, a decision procedure to interval‐valued intuitionistic fuzzy multiattribute group decision making is developed. When the weight vectors on attribute set and expert set are not exactly known, the models for obtaining the optimal fuzzy measures are established by using the defined cross entropy measure and the Shapley function. Finally, a numerical example is provided to illustrate the developed procedure.     

A Novel Method for Multiattribute Decision Making with Interval‐Valued Pythagorean Fuzzy Linguistic Information

Pythagorean fuzzy set (PFS), proposed by Yager (2013), is a generalization of the notion of Atanassov's intuitionistic fuzzy set, which has received more and more attention. In this paper, first, we define the weighted Minkowski distance with interval‐valued PFSs. Second, inspired by the idea of the Pythagorean fuzzy linguistic variables, we define a new fuzzy variable called interval‐valued Pythagorean fuzzy linguistic variable set (IVPFLVS), and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Third, some aggregation operators are presented for aggregating the interval‐valued Pythagorean fuzzy linguistic information such as the interval‐valued Pythagorean fuzzy linguistic weighted averaging (IVPFLWA), interval‐valued Pythagorean fuzzy linguistic ordered weighted averaging (IVPFLOWA) , interval‐valued Pythagorean fuzzy linguistic hybrid averaging, and generalized interval‐valued Pythagorean fuzzy linguistic ordered weighted average operators. Fourth, some desirable properties of the IVPFLWA and IVPFLOWA operators, such as monotonicity, commutativity, and idempotency, are discussed. Finally, based on the IVPFLWA or interval‐valued Pythagorean fuzzy linguistic geometric weighted operator, a practical example is provided to illustrate the application of the proposed approach and demonstrate its practicality and effectiveness.     

Group Decision Making Under Interval‐Valued Multiplicative Intuitionistic Fuzzy Environment Based on Archimedean t‐Conorm and t‐Norm

The main focus of this paper is to investigate group decision‐making (GDM) method under interval‐valued multiplicative intuitionistic fuzzy environment based on Archimedean t‐conorm and t‐norm. First of all, some operations laws are proposed for interval‐valued multiplicative intuitionistic fuzzy elements, which is an extension of multiplicative intuitionistic fuzzy operations developed earlier by other scholars. The effectiveness of these proposed operations is illustrated with some numerical examples. Then, a series of aggregation operators are proposed and the desirable properties are also studied. This paper reveals that some existing multiplicative intuitionistic fuzzy and interval‐valued multiplicative intuitionistic fuzzy aggregation operators are the special cases of the operators proposed in this paper. Finally, a GDM method based on proposed operators under interval‐valued multiplicative intuitionistic fuzzy environment is proposed, and a real case about annual evaluation for personnel of Zhejiang University of Finance and Economics is presented to illustrate the effectiveness of the proposed method.     

A New Intuitionistic Fuzzy Linguistic Hybrid Aggregation Operator and Its Application for Linguistic Group Decision Making

The linguistic aggregation operator is an important decision‐making model that is proving effective for dealing with the input data that takes the form of uncertain information. In this paper, considering the principal component of the intuitionistic fuzzy linguistic variables, we develop a new intuitionistic fuzzy linguistic hybrid aggregation (NIFLHA) operator to solve group decision‐making problems under the situation with intuitionistic fuzzy linguistic information. Then, we study some of its main properties by utilizing some operational laws of intuitionistic fuzzy linguistic variables and the different families of the NIFLHA operator. Moreover, the multiperson NIFLHA (MP‐NIFLHA) operator is introduced to evaluate the opinions of experts. Finally, an illustrative example about a multiperson decision‐making problem is developed to reveal the applicability and the availability of the raised operator.     

A Novel Intuitionistic Fuzzy Induced Ordered Weighted Euclidean Distance Operator and Its Application for Group Decision Making

In the paper, we develop the novel intuitionistic fuzzy induced ordered weighted Euclidean distance (NIFIOWED) operator based on the generalized intuitionistic fuzzy distance for multiple attribute group decision making problems. The NIFIOWED operator's attribute values take the form of Atanassov's intuitionistic fuzzy numbers(A‐IFNs), and the principal component x of A‐IFN is taken into account first. The prime properties of the NIFIOWED operator are investigated. Finally, a new method and a numerical example are provided to reveal the availability and practicability of the NIFIOWED operator.     

An Interval‐Valued Pythagorean Fuzzy Outranking Method with a Closeness‐Based Assignment Model for Multiple Criteria Decision Making

The concept of interval‐valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real‐world applications. This paper focuses on multiple criteria decision analysis involving IVPF information and proposes a new outranking decision‐making method that uses a closeness‐based assignment model. In contrast to the existing assignment‐based methodology, the uniqueness of this paper is the consideration of uncertain information represented by IVPF values, the determination of criterion‐wise precedence rankings based on a closeness‐based approach, and the development of a new measure for scalar representation. First, to underlie anchored judgments in subjective decision‐making processes, this paper presents a compromising concept of the closeness index with the positive‐ideal and negative‐ideal IVPF values to identify criterion‐wise precedence ranks among alternatives. Next, this paper defines the concept of matrices of precedence frequency and contribution to provide a basis for the proposed assignment model. To overcome the difficulty of lacking nontrivial scalar representations, a useful measure is also developed to appropriately describe IVPF values. Based on a closeness‐based assignment approach, a novel outranking decision‐making method is proposed to transform the extended criterion‐wise ranks into the ultimate priority orders of the alternatives. The proposed method is first implemented in a practical problem of selecting a bridge construction method to demonstrate its feasibility and applicability. Moreover, its practicality and effectiveness are verified through a comparative analysis with relevant assignment‐based approaches. Further comparative analyses with newly developed IVPF decision‐making methods are conducted for both a risk evaluation problem and an investment problem to examine the advantages of the proposed method and extend the current technique by considering distinct preference information for adapting to the particularities in practice.     

基于相对信息熵和语言加权算子的网络舆情突发事件模糊多指标应急决策方法

在仔细分析网络舆情突发事件的成因与应急决策特性的基础上,从舆情状态、突发事件本身和民众关注3方面构建 网络舆情突发事件的属性指标。考虑到网络舆情突发事件指标的语言不确定性和多样性,以及应急专家对舆情事件危机评价的语言判断矩阵差异性,本文提出一个基于相对信息熵和语言加权算子的网络舆情突发事件模糊多指标群决策模型。首先根据应急指标重要性的判断矩阵,计算出每个专家对各指标权重的评价;然后基于相对熵的多属性组合赋权方法来获取应急专家的权重,计算得出各舆情事件指标的综合权重;再根据各应急专家对网络舆情事件的语言指 标评价值,利用语言加权算术平均算子,集结得到各网络舆情突发事件的综合决策评价值,进而对各舆情事件危机程度快速排序。最后,通过一个实例来证明本文方法的实用性。     

Fuzzy Linguistic Induced Euclidean OWA Distance Operator and its Application in Group Linguistic Decision Making

In this paper, we develop a new method for group linguistic decision making, in which the attribute values take the form of fuzzy linguistic information, namely the fuzzy linguistic induced Euclidean ordered weighted averaging distance (FLIEOWAD) operator. This operator is an extension of the IOWA operator that utilizes induce OWA operator, Euclidean distance measures, and uncertain information represented as fuzzy linguistic variables. Then, some of its main properties by utilizing some operational laws of fuzzy linguistic variables are studied. Thus, a method based on the FLIEOWAD operator for decision making is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.     

基于改进直觉模糊熵和信息集成算子的多准则群决策方法

针对直觉模糊环境下准则权重和决策者权重完全未知的群决策问题,提出了一种基于改进直觉模糊熵和信息集成算子的多准则群决策方法.首先,借助直觉模糊数、语言变量法和定量指标值转化公式,将决策者的初始评价准则值规范化;其次,引入改进的直觉模糊熵度量方法确定准则权重和决策者权重;进一步对直觉模糊决策矩阵用直觉模糊加权平均算子和直觉模糊有序加权平均算子进行信息集成,利用新的得分函数对备选方案排序择优.从理论上论证了该方法的可行性,结合算例验证了该方法的有效性.     

Fuzzy Linguistic Induced Generalized OWA Operator and Its Application in Fuzzy Linguistic Decision Making

With respect to multiple attribute group decision making problems, in which the attribute values take the form of fuzzy linguistic scale variables, some decision analysis approaches are proposed. In this paper, we introduce the fuzzy linguistic induce generalized ordered weighted averaging operator and study some of its main properties by utilizing some operational laws of fuzzy linguistic scale variables. We end the paper with a numerical example of the new approach in a fuzzy linguistic decision making.     

Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with interval‐valued Pythagorean fuzzy sets (IVPFSs). First, the concept, operational laws, score function, and accuracy function of IVPFSs are defined. Then, based on the operational laws, two interval‐valued Pythagorean fuzzy aggregation operators are developed for aggregating the interval‐valued Pythagorean fuzzy information, such as interval‐valued Pythagorean fuzzy weighted average (IVPFWA) operator and interval‐valued Pythagorean fuzzy weighted geometric (IVPFWG) operator. A series of inequalities of aggregation operators are studied. Later, we develop some interval‐valued Pythagorean fuzzy point operators. Moreover, combining the interval‐valued Pythagorean fuzzy point operators with IVPFWA operator, we present some interval‐valued Pythagorean fuzzy point weighted averaging (IVPFPWA) operators, which can adjust the degree of the aggregated arguments with some parameters. Then, we propose an interval‐valued Pythagorean fuzzy ELECTRE method to solve uncertainty MAGDM problem. Finally, an illustrative example for evaluating the software developments is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

On Two‐Player Interval‐Valued Fuzzy Bayesian Games

Game theory is an important basis to simulate several situations where multiple agents interact strategically for decision making and support. In many applications, such as auctions, frequently used for resource management involving two or more agents competing for the resources, the interacting agents only know their own characteristics and must make decisions while having to estimate the characteristics of the others. When probabilities are assigned for the different types of the interacting agents, this kind of strategic interaction constitutes a Bayesian game. In cases in which it is very difficult to characterize the private information of each agent, the payoffs can be given by approximate (not probabilistic) values, but the concept of Bayesian Nash equilibrium cannot be applied in this context. Fuzzy set theory is an excellent basis for studying this type of game, where the payoffs are represented by fuzzy numbers. When it is the case that there is also uncertainty about such fuzzy numbers, the use of interval fuzzy numbers appears as a good modeling alternative. This paper introduces an approach for interval‐based fuzzy Bayesian games, based on interval‐valued fuzzy probabilities for modeling the types of agents involved in the interaction. We present two different case studies, namely the (Interval) Fuzzy Bayesian Hiring Game and (Interval) Fuzzy Bayesian Prisoner's Dilemma with Moral Standards, comparing the results obtained with the crisp, fuzzy and interval fuzzy approaches, highlighting a particular case in which the interval fuzzy approach presents a solution although the two other do not.     

基于广义直觉语言算子的多属性群决策方法

针对属性权重未知,属性值为直觉语言数的多属性决策问题,提出了一种基于直觉语言熵和广义直觉语言算子的群决策方法.定义了直觉语言熵,并利用直觉语言熵确定属性权重,提出了三种直觉语言算子:广义直觉语言加权几何平均(GILWGA)算子、广义直觉语言有序加权几何(GILOWG)算子及广义直觉语言混合几何(GILHG)算子.利用GILWGA和GILHG算子集结信息,采用基于直觉语言数的得分函数及精确函数进行方案排序与择优,最后通过一个算例说明了该方法的有效性和合理性.     

Aggregation Operators of Interval‐Valued 2‐Tuple Linguistic Information

The group decision‐making problem with linguistic information evaluation values of decision makers are used based on 2‐tuple interval‐valued. Operational laws on interval value 2‐tuple are introduced. On the basis of these laws, new aggregation operators are introduced by using the Choquet integral. A multiple attribute decision‐making method based on these aggregation operators is proposed. An example is given to illustrate the efficiency, practicality, and feasibility of our method.     

Correlation for Dual Hesitant Fuzzy Sets and Dual Interval‐Valued Hesitant Fuzzy Sets

Ever since fuzzy set has been introduced, several extensions have been established, such as interval‐valued fuzzy sets, Atanassov's intuitionistic fuzzy sets, interval‐valued Atanassov's intuitionistic fuzzy sets, fuzzy multisets, hesitant fuzzy sets, interval‐valued hesitant fuzzy sets, and dual hesitant fuzzy sets. In this contribution, we propose dual interval‐valued hesitant fuzzy sets, which encompass fuzzy sets and its aforementioned extensions as special cases. Because of the importance of correlation measure in data analysis, we propose an approach for deriving the correlation coefficient of dual hesitant fuzzy sets, and then extend the approach to the dual interval‐valued hesitant fuzzy set theory. We also put forward some formulas to create new correlation coefficients for fuzzy sets and its extensions in a general way. In addition, we give a practical example to illustrate the application of correlation coefficient for dual hesitant fuzzy sets in medical diagnosis.     

Cluster Analysis Based on T‐transitive Interval‐Valued Fuzzy Relations

In this paper, we consider cluster analysis based on T‐transitive interval‐valued fuzzy relations. A fuzzy relation with its partitional tree for obtaining an agglomerative hierarchical clustering has been studied and applied. In general, these fuzzy‐relation‐based clustering approaches are based on real‐valued memberships of fuzzy relations. Since interval‐valued memberships may be better than real‐valued memberships to represent higher order imprecision and vagueness for human perception, in this paper we first extend fuzzy relations to interval‐valued fuzzy relations and then construct a clustering algorithm based on the proposed T‐transitive interval‐valued fuzzy relations. We use two examples to demonstrate the efficiency and usefulness of the proposed method. In practical application, we apply the proposed clustering method to performance evaluations for academic departments of higher education by using actual engineering school data in Taiwan.     

Generalized Bonferroni Mean Operator for Fuzzy Number Intuitionistic Fuzzy Sets and its Application to Multiattribute Decision Making

The Bonferroni mean (BM) was originally introduced by Bonferroni in 1950. A prominent characteristic of BM is its capability to capture the interrelationship between input arguments. This makes BM useful in various application fields, such as decision making, information retrieval, pattern recognition, and data mining. In this paper, we examine the issue of fuzzy number intuitionistic fuzzy information fusion. We first propose a new generalized Bonferroni mean operator called generalized fuzzy number intuitionistic fuzzy weighted Bonferroni mean (GFNIFWBM) operator for aggregating fuzzy number intuitionistic fuzzy information. The properties of the new aggregation operator are studied and their special cases are examined. Furthermore, based on the GFNIFWBM operator, an approach to deal with multiattribute decision‐making problems under fuzzy number intuitionistic fuzzy environment is developed. Finally, a practical example is provided to illustrate the multiattribute decision‐making process.     

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation (IFPR) is a suitable technique to express fuzzy preference information by decision makers (DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR, by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly, a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.