基于区间粗糙算子的粗糙随机多准则决策方法

定义了区间粗糙随机变量、区间粗糙数的运算法则以及期望值和区间粗糙集结算子（WIRDAA）.针对准则权重信息不完全,准则值为区间粗糙随机变量的粗糙随机多准则决策问题,提出一种基于WIRDAA算子的决策方法.该方法首先计算出变量的期望值矩阵,利用距离最小化建立模型求解出准则权重;然后利用WIRDAA算子求出各方案的综合评价值,通过比较得到方案集的排序;最后通过实例表明了所提出方法的有效性和可行性.     

诱导连续区间有序加权平均算子及其在区间数群决策中的应用

基于诱导有序加权平均(IOWA)算子和连续区间有序加权平均(C-OWA)算子,提出一种诱导连续区间有序加权平均(IC-OWA)算子,并讨论了该算子的优良性质.针对区间数互补判断矩阵提出了连续偏好矩阵的概念,定义了基于专家评判水平偏差的诱导连续区间有序加权平均(DIC-OWA)算子,并给出一种基于该算子的区间数群决策方法.最后通过算例说明了该方法的可行性.     

不确定多传感器目标识别的区间相离度法

针对目标特征值和测量值均以区间数表达的多传感器目标识别问题,提出了一种不确定性融合方法．该方法定义区间相离度,通过对特征值的区间聚类和诱导有序加权平均算子集结得到属性的权重,利用综合相离度给出目标识别方法．能够克服属性权重选取的主观性,提高了目标识别结果的可信度．仿真实例验证了所提出方法的有效性和实用性．     

Generalized aggregation operators for intuitionistic fuzzy sets

The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93–107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval‐valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval‐valued intuitionistic fuzzy weighted averaging operator, generalized interval‐valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval‐valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval‐valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval‐valued intuitionistic fuzzy information. © 2009 Wiley Periodicals, Inc.     

群决策中两类三端点区间数判断矩阵的集结方法

研究群决策过程中三端点区间数互反判断矩阵和三端点区间数互补判断矩阵的集结. 采用OWA(Ordered weighted averaging) 方法将决策者的偏好信息集结为两个三端点区间数判断矩阵. 基于三端点区间数判断矩阵的完全一致性概念, 建立三端点区间数判断矩阵的权重求解模型. 根据群决策背景下专家群最大一致的目标, 建立求解专家群体偏好权重的模型. 在第二阶段建立群偏好权重分布范围估计模型, 最后通过可能度方法以排定各方案的最终优劣顺序.     

Logarithmic aggregation operators and distance measures

The Hamming distance is a well‐known measure that is designed to provide insights into the similarity between two strings of information. In this study, we use the Hamming distance, the optimal deviation model, and the generalized ordered weighted logarithmic averaging (GOWLA) operator to develop the ordered weighted logarithmic averaging distance (OWLAD) operator and the generalized ordered weighted logarithmic averaging distance (GOWLAD) operator. The main advantage of these operators is the possibility of modeling a wider range of complex representations of problems under the assumption of an ideal possibility. We study the main properties, alternative formulations, and families of the proposed operators. We analyze multiple classical measures to characterize the weighting vector and propose alternatives to deal with the logarithmic properties of the operators. Furthermore, we present generalizations of the operators, which are obtained by studying their weighting vectors and the lambda parameter. Finally, an illustrative example regarding innovation project management measurement is proposed, in which a multi‐expert analysis and several of the newly introduced operators are utilized.     

Multicriteria decision making under uncertainty: An advanced ordered weighted averaging operator for planning electric power systems

In this study, an advanced ordered weighted averaging (AOWA) operator is proposed for tackling multicriteria decision making (MCDM) problems under uncertainties. The AOWA incorporates techniques of interval theory and a center of gravity (COG) method within a traditional ordered weighted averaging (OWA) operator. It can deal with the uncertain inputs under optimistic and pessimistic conditions without knowing their distribution information and linguistic important degrees of all inputs in MCDM systems. The results obtained help decision makers select the optimal alternative according to their optimism degrees. A case study of planning electric power problems is provided for demonstrating the applicability of the proposed method. The results indicate that reasonable solutions have been generated for both discrete intervals and linguistic inputs. For all criteria under consideration, corrective alternatives can be undertaken sensitively under various optimism degrees and thus can help resolve the conflicts in electric power systems under uncertainties.     

二元语义信息下的动态激励群体评价方法及应用

针对目前关于动态群体评价问题的研究相对较少,且主要是基于点值信息评价的不足,提出一种新的二元语义信息下的动态激励群体评价方法,将动态激励评价及语言评价信息引入到群体评价中。首先探讨了能够较好地集结群体语言评价信息的二元语义一致算子;然后在各阶段的动态评价中引入激励区间,并运用时间诱导的二元语义时序激励加权平均算子集结得到受“奖惩”的动态群体综合评价值,从而进行最终评价。最后,通过算例给出了所提方法的步骤,并进行了结果分析,证明了该方法的可行性和有效性。     

New exponential operational laws and their aggregation operators for interval‐valued Pythagorean fuzzy multicriteria decision‐making

In this article, we define two new exponential operational laws about the interval‐valued Pythagorean fuzzy set (IVPFS) and their corresponding aggregation operators. However, the exponential parameters (weights) of all the existing operational laws of IVPFSs are crisp values in IVPFS decision‐making problems. As a supplement, this paper first introduces new exponential operational laws of IVPFS, where bases are crisp values or interval numbers and exponents are interval‐valued Pythagorean fuzzy numbers. The prominent characteristic of these proposed operations is studied. Based on these laws, we develop some new weighted aggregation operators, namely the interval‐valued Pythagorean fuzzy weighted exponential averaging operator and the dual interval‐valued Pythagorean fuzzy weighted exponential averaging. Finally, a decision‐making approach is presented based on these operators and illustrated with some numerical examples to validate the developed approach.     

Study on the ranking problems in multiple attribute decision making based on interval‐valued intuitionistic fuzzy numbers

This paper puts forward a new ranking method for multiple attribute decision‐making problems based on interval‐valued intuitionistic fuzzy set (IIFS) theory. First, the composed ordered weighted arithmetic averaging operator and composed ordered weighted geometric averaging operator are extended to the IIFSs in which they are, respectively, named interval‐valued intuitionistic fuzzy composed ordered weighted arithmetic averaging (IIFCOWA) operator and interval‐valued intuitionistic composed ordered weighted geometric averaging (IIFCOWG) operator. Afterwards, to compare interval‐valued intuitionistic fuzzy numbers, we define the concepts of the maximum, the minimum, and ranking function. Some properties associated with the concepts are investigated. Using the IIFCOWA or IIFCOWG operator, we establish the detailed steps of ranking alternatives (or attributes) in multiple attribute decision making. Finally, an illustrative example is provided to show that the proposed ranking method is feasible in multiple attribute decision making.     

Dependent uncertain ordered weighted aggregation operators

Xu and Da [Z.S. Xu, Q.L. Da, The uncertain OWA operator, International Journal of Intelligent Systems, 17 (2002) 569–575] introduced the uncertain ordered weighted averaging (UOWA) operator to aggregate the input arguments taking the form of intervals rather than exact numbers. In this paper, we develop some dependent uncertain ordered weighted aggregation operators, including dependent uncertain ordered weighted averaging (DUOWA) operators and dependent uncertain ordered weighted geometric (DUOWG) operators, in which the associated weights only depend on the aggregated interval arguments and can relieve the influence of unfair interval arguments on the aggregated results by assigning low weights to those “false” and “biased” ones.     

Evaluating multifactor risks under conceptual uncertainty

A tool is proposed to evaluate multifactor risks during the operation of an innovation system of technological forecast. A modified BOCR method of analytic hierarchy process (AHP) is developed. It allows: integrating the situation and force majeur risk evaluation into an overall structure of decision making with the help of AHP along with evaluating benefits, costs, and opportunities for each alternative; processing expert judgments in the form of fuzzy preference relations; taking into account a time parameter, when decision factors and alternatives may be corrected or fundamentally changed during some period. Indices of the risk of subjective judgment (information risk) evaluation are developed for given point, interval, and fuzzy expert judgments and probability distribution of expert judgments. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 72–82, March–April 2009.     

Generalized power aggregation operators and their applications in group decision making

In this paper, we investigate a generalized power average (GPA) operator and its weighted form, which are on the basis of the power average (PA) operator and the generalized mean, and develop a generalized power ordered weighted average (GPOWA) operator based on the power ordered weighted average (POWA) operator. Then, we extend these operators to uncertain environments and present an uncertain generalized power average (UGPA) operator and its weighted form, and an uncertain generalized power ordered weighted average (UGPOWA) operator to aggregate the input arguments taking the form of interval of numerical values. We also extend the GPA operator and the GPOWA operator to intuitionistic fuzzy environment, and obtain the generalized intuitionistic fuzzy power averaging (GIFPA) operator and the generalized intuitionistic fuzzy power ordered weighted averaging (GIFPOWA) operator. Moreover, some properties of these operators are studied. We also present new approaches on the basis of the proposed operators in an example of strategic decision making.     

Compatibility of interval fuzzy preference relations with the COWA operator and its application to group decision making

We develop a new compatibility for the interval fuzzy preference relations based on the continuous ordered weighted averaging (COWA) operator and use it to determine the weights of experts in group decision making (GDM). We define some concepts of the compatibility degree and the compatibility index for the two interval fuzzy preference relations based on the COWA operator. We study some desirable properties of the compatibility index and investigate the relationship between the each expert’s interval fuzzy preference relation and the synthetic interval fuzzy preference relation. The prominent characteristic of the compatibility index based on the COWA operator is that it can deal with the compatibility of all the arguments by using a controlled parameter considering the attitude of decision maker rather than the compatibility of the simply two points in intervals. To determine the experts’ weights in the GDM with the interval fuzzy preference relations, we propose an optimal model based on the criterion of minimizing the compatibility index. In the end, we give a numerical example to develop the new approach to GDM with interval fuzzy preference relations.     

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.     

Quantile-induced vector-based heavy OWA operator and the application in dynamic decision making

To the incentive problems in dynamic decision making, we propose a new type of aggregation operator denoted the quantile-induced vector-based heavy ordered weighted averaging (QI-VHOWA) operator. The main characteristic of the operator is that the arguments are aggregated using the form of vector. Additionally, the decision maker's incentive expectation is integrated into the aggregation process by various segmented incentive coefficients. We calculate the quantile measures of the argument vectors based on the technique for order of preference by similarity to ideal solution method. We determine the QI-VHOWA weighting vector by considering the location position of an alternative's performance as well as the development trend. The primary properties of the operator are discussed, including commutativity, boundness, and monotonicity under certain conditions. Finally, a numerical example regarding the evaluation of employees' performances in multiple periods is provided. The results are compared with that of the vector-based OWA and vector-based weighted arithmetic averaging operators. It is found that the incentive effectiveness of the QI-VHOWA is the most significant. The use of the QI-VHOWA operator is helpful to guide the long-term development of an alternative.     

基于新型距离测度的概率犹豫模糊多属性群决策方法

研究属性权重已知、专家权重未知条件下的概率犹豫模糊多属性群决策问题.首先,针对传统概率犹豫模糊距离测度的不足,提出改进的新型距离测度,并对其有效性和合理性进行数学证明;其次,在属性权重向量已知的前提下,通过加权算术平均的方式实现单个专家视角下的概率犹豫模糊信息初次集结,并基于分差最大化准则构建专家权重向量求解模型,采用...     

Multiple attribute group decision-making method with single-valued neutrosophic interval number information

To describe decision makers’ judgments for an evaluated object more comprehensively in the decision-making process, this paper firstly defines the concept of a single-valued neutrosophic interval number (SVNIN), which is composed of both its interval number (interval judgment) and its single-valued neutrosophic number (SVNN) (confident degree). Then we present the basic operational laws of SVNINs and the score function of SVNIN based on the attitude index and confident level of decision makers to compare SVNINs. Next, we propose a single-valued neutrosophic interval number weighted arithmetic averaging (SVNINWAA) operator and a single-valued neutrosophic interval number weighted geometric averaging (SVNINWGA) operator to aggregate SVNIN information. Further, a multiple attribute group decision-making (MDGDM) method using the proposed SVNINWAA or SVNINWGA operator is established under an SVNIN environment. Finally, an illustrative example regarding the selection problem of global suppliers is presented to show the application and effectiveness of the developed method.     

Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information

This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality.     

Maximum expert consensus models with linear cost function and aggregation operators

In group decision making problems, consensus is a very important issue for the aggregation of individual opinions. Based on the concept of maximum expert consensus model (MECM), this paper incorporates aggregation operators into the MECM, and proposes a novel framework of MECM. When the aggregation operator is set to be the weighted averaging operator or the ordered weighed averaging (OWA) operator, this paper equivalently transforms the MECM into mixed 0–1 linear programming problems. Additionally, this paper also shows that the minimum cost consensus model under the OWA operator with any weights can be similarly transformed into a mixed 0–1 linear programming problem. Numerical examples and a comparison analysis are used to demonstrate the validity of the proposed model.