基于ε-修正的直觉模糊信息集成方法及其在决策中的应用

已有的一些直觉模糊集成算子在处理一些特殊直觉模糊数时会出现反直觉现象。首先介绍了两个直觉模糊集成算子和直觉模糊数的比较方法。接着,举例说明了这些集成算子在某些情况下出现的反直觉现象。然后提出了基于ε-修正的直觉模糊集成算子,并讨论了ε取值对此算子结果的影响。之后建立了一种基于ε-修正的直觉模糊集成算子的决策方法。最后通过一个实例比较了原集成算子和本文提出的修正集成算子的集成结果,验证基于ε-修正的直觉模糊集成算子可以修正这些反直觉现象,这也拓宽了原集成算子的使用范围。     

Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making

Yager (Fuzzy Sets, Syst 2003;137:59–69) extended the idea of order‐induced aggregation to the Choquet aggregation and defined induced Choquet ordered averaging operator. In this paper, an induced intuitionistic fuzzy Choquet (IFC) integral operator is proposed for the multiple criteria decision making. Some of its properties are investigated. Furthermore, an induced generalized IFC integral operator is introduced. It is worth mentioning that most of the existing intuitionistic fuzzy aggregation operators are special cases of this induced aggregation operator. A decision procedure based on the proposed induced aggregation operator is developed for solving the multicriteria decision‐making problem in which all the decision information is represented by intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure. © 2011 Wiley Periodicals, Inc.     

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.     

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.     

Multiattribute decision making based on interval-valued intuitionistic fuzzy values

In this paper, we present a new multiattribute decision making method based on the proposed interval-valued intuitionistic fuzzy weighted average operator and the proposed fuzzy ranking method for intuitionistic fuzzy values. First, we briefly review the concepts of interval-valued intuitionistic fuzzy sets and the Karnik–Mendel algorithms. Then, we propose the intuitionistic fuzzy weighted average operator and interval-valued intuitionistic fuzzy weighted average operator, based on the traditional weighted average method and the Karnik–Mendel algorithms. Then, we propose a fuzzy ranking method for intuitionistic fuzzy values based on likelihood-based comparison relations between intervals. Finally, we present a new multiattribute decision making method based on the proposed interval-valued intuitionistic fuzzy weighted average operator and the proposed fuzzy ranking method for intuitionistic fuzzy values. The proposed method provides us with a useful way for multiattribute decision making based on interval-valued intuitionistic fuzzy values.     

Intuitionistic Fuzzy Hybrid Weighted Aggregation Operators

Intuitionistic fuzzy sets (IFSs) have attracted more and more scholars’ attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper proposes a family of intuitionistic fuzzy hybrid weighted aggregation operators, such as the intuitionistic fuzzy hybrid weighted averaging operator, the intuitionistic fuzzy hybrid weighted geometric operator, the generalized intuitionistic fuzzy hybrid weighted averaging operator, and the generalized intuitionistic fuzzy hybrid weighted geometric operator. All these newly developed operators not only can weight both the arguments and their ordered positions simultaneously but also have some desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed intuitionistic fuzzy hybrid weighted aggregation operators, a simple schema for decision making with intuitionistic fuzzy information is developed. An example concerning the human resource management is given to illustrate the validity and applicability of the proposed method and also the hybrid weighted aggregation operators.     

Prioritized Information Fusion Method for Triangular Intuitionistic Fuzzy Set and its Application to Teaching Quality Evaluation

In this article, we examine the issue of triangular intuitionistic fuzzy information fusion. We first propose some new triangular intuitionistic fuzzy aggregation operators based on the prioritized average operator, such as the triangular intuitionistic fuzzy prioritized weighted average and the triangular intuitionistic fuzzy prioritized weighted geometric operators. We study some desired properties of the proposed operators, such as idempotency, noncompensatory, and boundary. We then develop an approach to deal with group decision‐making problems under triangular intuitionistic fuzzy environments. Finally, a practical example about teaching quality evalution is provided to illustrate the group decision‐making process.     

Multicriteria decision making based on intuitionistic fuzzy prioritized arithmetic mean

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a nonmembership function, and a hesitancy function, is a generalization of a fuzzy set. Various aggregation operators are defined for AIFSs to deal with multicriteria decision‐making problems in which there exists a prioritization of criteria. However, these existing intuitionistic fuzzy prioritized aggregation operators are not monotone with respect to the total order on Atanassov’s intuitionistic fuzzy values (AIFVs), which is undesirable. We propose an intuitionistic fuzzy prioritized arithmetic mean based on the ?ukasiewicz triangular norm, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a consumer selects a car to illustrate the validity and applicability of the proposed method aggregation operator.     

Intuitionistic fuzzy geometric Heronian mean aggregation operators

In this paper, the multi-criteria decision making problem with the assumption that the criteria are correlative is studied under intuitionistic fuzzy environment. Some new aggregation operators for intuitionistic fuzzy information are proposed, including the intuitionistic fuzzy geometric Heronian mean (IFGHM) operator and the intuitionistic fuzzy geometric weighed Heronian mean (IFGWHM) operator. We investigate the properties of the proposed operators, such as idempotency, monotonicity, permutation and boundary. Moreover, an approach is proposed for multi-criteria decision making based on IFGWHM operator. An example about talent introduction is given to illustrate the proposed method.     

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.     

Intuitionistic fuzzy geometric aggregation operators based on einstein operations

Intuitionistic fuzzy information aggregation plays an important part in Atanassov's intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new geometric aggregation operators, such as the intuitionistic fuzzy Einstein weighted geometric operator and the intuitionistic fuzzy Einstein ordered weighted geometric operator, which extend the weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators. In addition, we compare the proposed operators with the existing intuitionistic fuzzy geometric operators and get the corresponding relations. Finally, we apply the intuitionistic fuzzy Einstein weighted geometric operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. © 2011 Wiley Periodicals, Inc.     

Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and efficiency of our accuracy function are provided by giving related examples. A fuzzy multicriteria decision making method is established to select the best alternative in multicriteria decision making process which is taken as interval-valued intuitionistic fuzzy set of criterion values for alternatives. While aggregating the interval-valued intuitionistic fuzzy information corresponding to each alternative, we utilize the interval-valued intuitionistic fuzzy weighted aggregation operators. Then the accuracy degree of the aggregated interval-valued intuitionistic fuzzy information is computed via the new proposed accuracy function. Thus, we can rank all the alternatives according to the accuracy function and choose the optimal one(s). Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach.     

区间直觉模糊信息的集成方法及其在决策中的应用

对区间直觉模糊信息的集成方法进行了研究.定义了区间直觉模糊数的一些运算法则,并基于这些运算法则,给出区间直觉模糊数的加权算术和加权几何集成算子.定义了区间直觉模糊数的得分函数和精确函数,进而给出了区间直觉模糊数的一种简单的排序方法.最后提供了一种基于区间直觉模糊信息的决策途径,并进行了实例分析.     

基于集成算子的改进IITFN多属性群决策方法

对区间直觉梯形模糊数决策方法进行研究。定义了区间直觉梯形模糊数期望值、得分函数和精确函数,进而给出了区间直觉梯形模糊数的一种新的排序方法。另一方面,给出了有序加权平均算子和混合集成算子。建立了基于区间直觉梯形模糊数的多属性群决策方法,给出了相应的群决策方法。实例分析验证了所提出方法的有效性。     

Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making

For the real decision making problems, most criteria have inter-dependent or interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. Thus, to approximate the human subjective decision making process, it would be more suitable to apply fuzzy measures, where it is not necessary to assume additivity and independence among decision making criteria. In this paper, an intuitionistic fuzzy Choquet integral is proposed for multiple criteria decision making, where interactions phenomena among the decision making criteria are considered. First, we introduced two operational laws on intuitionistic fuzzy values. Then, based on these operational laws, intuitionistic fuzzy Choquet integral operator is proposed. Moreover, some of its properties are investigated. It is shown that the intuitionistic fuzzy Choquet integral operator can be represented by some special t-norms and t-conorms, and it is also a generalization of the intuitionistic fuzzy OWA operator and intuitionistic fuzzy weighted averaging operator. Further, the procedure and algorithm of multi-criteria decision making based on intuitionistic fuzzy Choquet integral operator is given under uncertain environment. Finally, a practical example is provided to illustrate the developed approaches.     

Generalized Atanassov’s intuitionistic fuzzy power geometric operators and their application to multiple attribute group decision making

In this paper, we extend the power geometric (PG) operator and the power ordered weighted geometric (POWG) operator [Z.S. Xu, R.R. Yager, Power-geometric operators and their use in group decision making, IEEE Transactions on Fuzzy Systems 18 (2010) 94–105] to Atanassov’s intuitionistic fuzzy environments, i.e., we develop a series of generalized Atanassov’s intuitionistic fuzzy power geometric operators to aggregate input arguments that are Atanassov’s intuitionistic fuzzy numbers (IFNs). Then, we study some desired properties of these aggregation operators and investigate the relationships among these operators. Furthermore, we apply these aggregation operators to develop some methods for multiple attribute group decision making with Atanassov’s intuitionistic fuzzy information. Finally, two practical examples are provided to illustrate the proposed methods.     

Prioritized intuitionistic fuzzy aggregation operators

In some multi-attribute decision making problems, distorted conclusions will be generated due to the lack of considering various relationships among the attributes of decision making. In this paper, we investigate the prioritization relationship of attributes in multi-attribute decision making with intuitionistic fuzzy information (i.e., partial or all decision information, like attribute values and weights, etc., is represented by intuitionistic fuzzy values (IFVs)). Firstly, we develop a new method for comparing two IFVs, based on which the basic intuitionistic fuzzy operations satisfy monotonicities. In addition, we devise a method to derive the weights with intuitionistic fuzzy forms, which can indicate the importance degrees of the corresponding attributes. Then we develop a prioritized intuitionistic fuzzy aggregation operator, which is motivated by the idea of the prioritized aggregation operators [R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263–274]. Furthermore, we propose an intuitionistic fuzzy basic unit monotonic (IF-BUM) function to transform the derived intuitionistic fuzzy weights into the normalized weights belonging to the unit interval. Finally, we develop a prioritized intuitionistic fuzzy ordered weighted averaging operator on the basis of the IF-BUM function and the transformed weights.     

Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process

In this article, a new linguistic Pythagorean fuzzy set (LPFS) is presented by combining the concepts of a Pythagorean fuzzy set and linguistic fuzzy set. LPFS is a better way to deal with the uncertain and imprecise information in decision making, which is characterized by linguistic membership and nonmembership degrees. Some of the basic operational laws, score, and accuracy functions are defined to compare the two or more linguistic Pythagorean fuzzy numbers and their properties are investigated in detail. Based on the norm operations, some series of the linguistic Pythagorean weighted averaging and geometric aggregation operators, named as linguistic Pythagorean fuzzy weighted average and geometric, ordered weighted average and geometric with linguistic Pythagorean fuzzy information are proposed. Furthermore, a multiattribute decision‐making method is established based on these operators. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.     

Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making

In general, for multi-criteria group decision making problem, there exist inter-dependent or interactive phenomena among criteria or preference of experts, so that it is not suitable for us to aggregate them by conventional aggregation operators based on additive measures. In this paper, based on fuzzy measures a generalized intuitionistic fuzzy geometric aggregation operator is investigated for multiple criteria group decision making. First, some operational laws on intuitionistic fuzzy values are introduced. Then, a generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator is proposed. Moreover, some of its properties are given in detail. It is shown that GIFOGA operator can be represented by special t-norms and t-conorms and is a generalization of intuitionistic fuzzy ordered weighted geometric averaging operator. Further, an approach to multiple criteria group decision making with intuitionistic fuzzy information is developed where what criteria and preference of experts often have inter-dependent or interactive phenomena among criteria or preference of experts is taken into account. Finally, a practical example is provided to illustrate the developed approaches.     

Induced generalized intuitionistic fuzzy operators

We study the induced generalized aggregation operators under intuitionistic fuzzy environments. Choquet integral and Dempster–Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuitionistic fuzzy Dempster–Shafer operators. Then we investigate their various properties and some of their special cases. Additionally, we apply the developed operators to financial decision making under intuitionistic fuzzy environments. Some extensions in interval-valued intuitionistic fuzzy situations are also pointed out.