Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making

With respect to multi-attribute group decision making (MAGDM) problems in which both the attribute weights and the decision makers (DMs) weights take the form of real numbers, attribute values provided by the DMs take the form of intuitionistic fuzzy numbers, a new group decision making method is developed. Some operational laws, score function and accuracy function of intuitionistic fuzzy numbers are introduced at first. Then a new aggregation operator called induced generalized intuitionistic fuzzy ordered weighted averaging (IG-IFOWA) operator is proposed, which extend the induced generalized ordered weighted averaging (IGOWA) operator introduced by Merigo and Gil-Lafuente [Merigo, J. M., & Gil-Lafuente, A. M. (2009). The induced generalized OWA operator. Information Sciences, 179, 729-741] to accommodate the environment in which the given arguments are intuitionistic fuzzy sets that are characterized by a membership function and a non-membership function. Some desirable properties of the IG-IFOWA operator are studied, such as commutativity, idempotency, monotonicity and boundary. And then, an approach based on the IG-IFOWA and IFWA (intuitionistic fuzzy weighted averaging) operators is developed to solve MAGDM problems with intuitionistic fuzzy information. Finally, a numerical example is used to illustrate the developed approach.     

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.     

Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making

In this paper, some multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights are usually correlative, attribute values take the form of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values, are investigated. Firstly, some operational law, score function and accuracy function of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values are introduced. Then two new aggregation operators: induced intuitionistic fuzzy correlated averaging (I-IFCA) operator and induced intuitionistic fuzzy correlated geometric (I-IFCG) operator are developed and some desirable properties of the I-IFCA and I-IFCG operators are studied, such as commutativity, idempotency and monotonicity. An I-IFCA and IFCA (intuitionistic fuzzy correlated averaging) operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights usually correlative, attribute values take the form of intuitionistic fuzzy values. Then, we extend the developed models and procedures to the interval-valued intuitionistic fuzzy environment. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators

With respect to multiple attribute group decision making (MADM) problems in which attribute values take the form of intuitionistic linguistic numbers, some new group decision making methods are developed. Firstly, some operational laws, expected value, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic power generalized weighted average (ILPGWA) operator and an intuitionistic linguistic power generalized ordered weighted average (ILPGOWA) operator are developed. Furthermore, some desirable properties of the ILPGWA and ILPGOWA operators, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILPGWA and ILPGOWA operators, two approaches to multiple attribute group decision making with intuitionistic linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.     

Some geometric aggregation operators based on intuitionistic fuzzy sets

The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.     

Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making

In this paper, we develop a series of induced generalized aggregation operators for hesitant fuzzy or interval-valued hesitant fuzzy information, including induced generalized hesitant fuzzy ordered weighted averaging (IGHFOWA) operators, induced generalized hesitant fuzzy ordered weighted geometric (IGHFOWG) operators, induced generalized interval-valued hesitant fuzzy ordered weighted averaging (IGIVHFOWA) operators, and induced generalized interval-valued hesitant fuzzy ordered weighted geometric (IGIVHFOWG) operators. Next, we investigate their various properties and some of their special cases. Furthermore, some approaches based on the proposed operators are developed to solve multiple attribute group decision making (MAGDM) problems with hesitant fuzzy or interval-valued hesitant fuzzy information. Finally, some numerical examples are provided to illustrate the developed approaches.     

连续区间直觉乘法集结算子及其在群决策中的应用*

基于连续有序加权几何（C-OWG）算子提出了连续区间直觉乘法有序加权几何（C-IVIMOWG）算子。而后,基于C-IVIMOWG算子提出新的区间直觉乘法数序关系判断准则。为了集结区间直觉乘法数组,提出了加权连续区间直觉乘法有序加权几何（WC-IVIMOWG）算子,研究了其基本性质,并提出了基于WC-IVIMOWG算子与兼容测度的群决策方法。最后,通过实例分析来说明WC-IVIMOWG算子应用于群决策中的有效性和适用性。     

Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making

Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets, we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of generalized intuitionistic fuzzy aggregation operators are developed, including the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The properties of these new generalized aggregation operators are investigated. Moreover, approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach. Finally, we give a systematic comparison between the work of this paper and that of other papers.     

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.     

Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information

With respect to multi-criteria group decision making (MCGDM) problems under trapezoidal intuitionistic fuzzy environment, a new MCGDM method is investigated. The proposed method can effectively avoid the failure caused by the use of inconsistent decision information and provides a decision-making idea for the case of “the truth be held in minority”. It consists of three interrelated modules: weight determining mechanism, group consistency analysis, and ranking and selection procedure. For the first module, distance measures, expected values and arithmetic averaging operator for trapezoidal intuitionistic fuzzy numbers are used to determine the weight values of criteria and decision makers. For the second module, a consistency analysis and correction procedure based on trapezoidal intuitionistic fuzzy weighted averaging operator and OWA operator is developed to reduce the influence of conflicting opinions prior to the ranking process. For the third module, a trapezoidal intuitionistic fuzzy TOPSIS is used for ranking and selection. Then a procedure for the proposed MCGDM method is developed. Finally, a numerical example further illustrates the practicality and efficiency of the proposed method.     

模糊数直觉模糊几何集成算子及其在决策中的应用

模糊数直觉模糊集是直觉模糊集的拓展.针对模糊数直觉模糊信息的集成问题,定义了模糊数直觉模糊数的一些运算法则,基于这些法则给出了一些新的几何集成算子,即模糊数直觉模糊加权几何(FIFWG)算子、模糊数直觉模糊有序加权几何(FIFOWG)算子和模糊数直觉模糊混合几何(FIFHG)算子.在此基础上,提出一种属性权重确知且属性值以模糊数直觉模糊数形式给出的多属性群决策方法.最后通过实例分析结果证明了该方法的有效性.     

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.     

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.     

直觉模糊多属性决策方法综述

直觉模糊多属性决策是当前决策领域的一个研究热点,在实际决策中有着广泛的应用.按照直觉模糊集的发展形式:直觉模糊集、区间直觉模糊集、直觉三角模糊数和直觉梯形模糊数,分别介绍它们在多属性决策与群决策中的研究现状,并对其未来的发展方向进行了探讨与展望.     

A novel induced aggregation method for intuitionistic fuzzy set and its application in multiple attribute group decision making

In this paper, by unifying the induced ordered weighted averaging (IOWA) and the weighted average, a novel induced aggregation method for intuitionistic fuzzy set is investigated. More specifically, a new intuitionistic fuzzy (IF) induced aggregation operator called weighted intuitionistic fuzzy IOWA weighted average (WIFIOWAWA) operator is introduced. A significant advantage of the WIFIOWAWA operator is that it can eliminate the drawback of the existing operators by the dual roles of its order‐inducing variables. In addition, some of its desired properties and families are explored. Furthermore, using the proposed operator, a procedure is developed to solve multiple attribute group decision making problems in the case of IF situation. Finally, an illustrative example is provided to demonstrate the effectiveness and practicality of the developed method.     

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。     

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。     

Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

In this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.     

Some interval-valued q-rung orthopair weighted averaging operators and their applications to multiple-attribute decision making

Q-rung orthopair fuzzy sets (q-ROFSs), initially proposed by Yager, are a new way to reflect uncertain information. The existing intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets are special cases of the q-ROFSs. However, due to insufficiency in available information, it is difficult for decision makers to exactly express the membership and nonmembership degrees by crisp numbers, and interval membership degree and interval nonmembership degree are good choices. In this paper, we propose the concept of interval-valued q-rung orthopair fuzzy set (IVq-ROFS) based on the ideas of q-ROFSs and some operational laws of q-rung orthopair fuzzy numbers (q-ROFNs). Then, some interval-valued q-rung orthopair weighted averaging operators are presented based on the given operational laws of q-ROFNs. Further, based on these operators, we develop a novel approach to solve multiple-attribute decision making (MADM) problems under interval-valued q-rung orthopair fuzzy environment. Finally, a numerical example is provided to illustrate the application of the proposed method, and the sensitivity analysis is further carried out for the parameters.     

广义直觉模糊加权交叉影响平均算子及其在多属性决策中的应用

针对不同直觉模糊集的隶属度与非隶属度可能存在交叉影响, 提出广义直觉模糊加权交叉影响平均(GIFWIA) 算子, 推导出其数学表达式, 研究该算子的性质, 并探讨了基于GIFWIA 算子的多属性决策方法. 通过实例表明了所提出广义算子在决策应用中的有效性, 并分析了不同参数lambda 对决策的影响. 通过灵敏度和相关比较分析, 解释了交叉影响对决策结果的影响, 表明了所提出广义算子的稳定性.