Quantile-induced uncertain heavy ordered weighted averaging operator and the application in incentive evaluation problems

To uncertain evaluation problems, we integrate incentive management into the aggregation process and propose an aggregation operator called quantile-induced uncertain heavy ordered weighted averaging (QI-UHOWA) operator, which is an extension of the quantile-induced heavy ordered weighted averaging (QI-HOWA) operator. We provide an approach for determining the quantile order-inducing variables by using the technique for order preference by similarity to ideal solution method and the Hamming distance. In this case, the quantile values are measurements of relative developments of alternatives. Furthermore, we analyze the main properties of the operator including commutativity, boundedness, and monotonicity with uniform development space. The QI-UHOWA weighting vector is calculated using the maximum entropy measure with a given level of incentive attitude. We further expand the weighting method to the case of hierarchical stimulation. Moreover, the QI-UHOWA operator is generalized using the quasi-arithmetic mean. Finally, a numerical example regarding the selection of the optimal candidate(s) is given. The aggregation results are compared with those of the UOWA and QI-UOWA operator to illustrate the validity of the QI-UHOWA operator.     

Elliptical distribution-based weight-determining method for ordered weighted averaging operators

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the regular increasing monotone quantifier. Motivated by the idea of normal distribution-based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.     

Induced cluster-based OWA operators with reliability measures and the application in group decision-making

Considering the distributed structural characteristics of arguments to be aggregated, we propose a new type of aggregation operator, called induced cluster-based ordered weighted averaging (OWA; abbreviated as cluster-IOWA) operator, in this article. The main characteristic of the cluster-IOWA operator is that the arguments are aggregated by local clusters, and the order-inducing variable is used for representing a particular characteristic with respect to a local cluster. The cluster-OWA operator is commutativity, idempotence, and boundedness. We then discuss two important issues with respect to the cluster-IOWA operator. The order-inducing variables are determined by considering the overall reliability of the local cluster. Based on this, the position weighting vector of the local clusters is designed by taking into account both the reliability measures and the decision maker's preference. Finally, a numerical example, regarding the performance evaluation of middle managers carried out by a group of participants, is developed to illustrate the application and validity of the cluster-IOWA operator.     

Prioritized aggregation operators based on the priority degrees in multicriteria decision-making

We consider the multicriteria decision-making (MCDM) problems where there exists a prioritization relationship over the criteria. We introduce the concept of the priority degree. Then we give three kinds of prioritized aggregation operators based on the priority degrees: the prioritized averaging operator with the priority degrees, the prioritized scoring operator with the priority degrees, and the prioritized ordered weighted averaging operator with the priority degrees. Some desired properties of these prioritized aggregation operators are also investigated. The priority degree plays an important role in the prioritized MCDM problems. We also investigate how to select a proper priority degree according to the giving decision information. By using an illustrative example, we show that the prioritized aggregation operators based on the priority degrees provide the decision-makers more choices and they are more flexible in the process of decision-making.     

基于OWA算子的模糊n-cell数排序方法

针对基于模糊n-cell数的多属性排序问题,提出了一种基于有序加权平均算子（OWA算子）的模糊n-cell数排序方法。该方法首先根据样本数据对评估对象的属性构造模糊n-cell数,其次根据均值将属性按照从大到小排列,然后选取合适的权重向量,应用OWA算子进行信息聚合得到综合模糊n-cell数,接着根据各分量均值得到排序结果。最后,将该方法运用到实例中,并与传统的均值方法进行了比较。结果表明该方法不仅灵活有效,可根据具体情况选择不同的OWA权重来消除部分不合理的情况,使结果更有说服力,还弥补了传统均值方法的不足。     

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.     

A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making

As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.     

An interactive method for fuzzy multiple attribute group decision making

In this paper, we develop an interactive method for multiple attribute group decision making under fuzzy environment. The method can be used in situations where the information about attribute weights is partly known, the weights of decision makers are expressed in exact numerical values or triangular fuzzy numbers, and the attribute values are triangular fuzzy numbers. The method transforms fuzzy decision matrices into their expected decision matrices, constructs the corresponding normalized expected decision matrices by two simple formulas, and then aggregates these normalized expected decision matrices into a complex decision matrix. Moreover, the decision makers are asked to provide their preferences gradually in the course of interactions. By solving linear programming models, the method diminishes the given alternative set gradually, and finally finds the most preferred alternative. By using the method, the decision makers can provide and modify their preference information gradually in the process of decision making so as to make the decision result more reasonable. The method can not only reflect the importance of the given arguments and the ordered positions of the arguments, but also relieve the influence of unfair arguments on the decision result. Finally, a practical problem is used to illustrate the developed method.     

Linguistic-induced ordered weighted averaging operator for multiple attribute group decision-making

To solve the problems of making decision with uncertain and imprecise information, Zadeh proposed the concept of Z-number as an ordered pair, the first component of which is a restriction of variable, and the second one is a measure of reliability of the first component. But the decision-makers’ confidence in decision-making was neglected. In this paper, firstly, we present a new method to evaluate and rank -numbers based on the operations of trapezoidal Type 2 fuzzy numbers and generalized trapezoidal fuzzy numbers. Then, linguistic-induced ordered weighted averaging operator and linguistic combined weighted averaging aggregation operator are developed to solve multiple attribute group decision-making problems. And we analyze the main properties of them by utilizing some operational laws of fuzzy linguistic variables. Finally, a numerical example is provided to illustrate the rationality of the proposed method.     

Discriminative aggregation operators for multi criteria decision making

A general aggregation formalism for multi criteria decision making (MCDM) applications is presented. Using this formalism, we derive the existing aggregation operators, and also develop some new ones. The proposed general formalism is further extended to develop discriminative class of aggregation operators for aiding MCDM. The proposed discriminative aggregation operators are based on the consideration of the variability in the various evaluations of a criterion. Four families of discriminative aggregation operators are developed using the extended formalism. These operators and applied in a managerial real world case-study.     

动态信任预测的认知模型

开放系统中的信任关系本质上是最复杂的社会关系之一,涉及到假设、期望、行为和环境等多种因子,很难准确地定量表示和预测.结合人类社会的认知行为,提出了一种符合人类心理认知习惯的动态信任预测模型:(1) 构建了自适应的基于历史证据窗口的总体可信性决策方法,不但克服了已有模型常用的确定权重的主观判断方法,而且可以解决直接证据不足时的可信性预测问题;(2) 使用已有的DTT(direct trust tree)机制进行全局反馈信任信息的搜索与聚合,以降低网络带宽消耗,增强系统在大规模分布式系统中的可扩展性;(3) 引入诱导有序加权平均(induced ordered weighted averaging,简称IOWA)算子的概念,建立了基于IOWA算子的直接信任预测模型,可以用来解决传统预测模型动态适应能力不足的问题.实验结果表明,与已有模型相比,该模型具有更稳健的动态适应性,在模型的预测准确性方面也有显著的改善.     

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。     

A ranking method for multiple attribute decision-making problems based on the possibility degrees of trapezoidal intuitionistic fuzzy numbers

To solve multiple attribute decision-making problems with attribute values or decision values characterized by trapezoidal intuitionistic fuzzy numbers (TIFNs), we define a trapezoidal intuitionistic fuzzy induced ordered weighted arithmetic averaging (TIFIOWA) operator, which is an extension of the induced ordered weighted arithmetic averaging operator. We derive and prove some related properties and conclusions of the TIFIOWA operator. To compare the TIFNs, we define possibility degrees of the TIFNs. Based on the possibility degrees of the TIFNs and the TIFIOWA operator, we construct a new method to determine the order of alternatives in multiple attribute decision making and to choose the best alternative. Finally, a numerical example shows that the developed method is feasible and effective.     

Analysis of self-confidence indices-based additive consistency for fuzzy preference relations with self-confidence and its application in group decision making

Preference relations have been widely used in group decision-making (GDM) problems. Recently, a new kind of preference relations called fuzzy preference relations with self-confidence (FPRs-SC) has been introduced, which allow experts to express multiple self-confidence levels when providing their preferences. This paper focuses on the analysis of additive consistency for FPRs-SC and its application in GDM problems. To do that, some operational laws for FPRs-SC are proposed. Subsequently, an additive consistency index that considers both the fuzzy preference values and self-confidence is presented to measure the consistency level of an FPR-SC. Moreover, an iterative algorithm that adjusts both the fuzzy preference values and self-confidence levels is proposed to repair the inconsistency of FPRs-SC. When an acceptable additive consistency level for FPRs-SC is achieved, the collective FPR-SC can be computed. We aggregate the individual FPRs-SC using a self-confidence indices-based induced ordered weighted averaging operator. The inherent rule for aggregation is to give more importance to the most self-confident experts. In addition, a self-confidence score function for FPRs-SC is designed to obtain the best alternative in GDM with FPRs-SC. Finally, the feasibility and validity of the research are demonstrated with an illustrative example and some comparative analyses.     

Using robust optimization to play against an imperfect opponent

 Traditional game theory is based on the assumption that the opponent is a perfect reasoner and all payoff information is available. Based on this assumption, game theory recommends to estimate the quality of each possible strategy by its worst possible consequences. In real-life, opponents are often not perfect and payoff information is often not exact. If the only disadvantage of some action is that an unusually clever opponent can find a complicated way to counter it, then this action may be a perfect recommendation for a play against a normal (not unusually clever) opponent. In other words, to estimate the quality of each move, instead of a normal minimum of possible consequences, we must consider the robust minimum that takes into consideration the fact that some of the consequences will never occur to the normal opponent. We show that in a reasonable statistical setting, this idea leads to the class of OWA operators. It turns out that playing against an imperfect opponent is not only a more realistic strategy, it is also often a simpler one: e.g., for the simplest game for which playing against a perfect opponent is computationally intractable (NP-hard), playing against an imperfect opponent is computationally feasible.     

基于WOWA-FAHP的网络安全态势评估

从入侵响应决策与安全管理的实际需求出发,提出了基于WOWA合成的模糊层次分析法(WOWA-FAHP)和基于WOWA-FAHP的网络安全态势评估模型.WOWA-FAHP方法在继承模糊层次分析法优点的基础上兼顾属性间的客观、主观关联性,能够适应各种决策偏好.基于WOWA-FAHP的评估模型把动态评估与静态评估相结合,充分利用系统安全风险评估、入侵警报融合关联、异常监测与安全审计所提供的多种信息,综合考虑警报类、异常类、脆弱性、后果性等多方面的评价指标,并依据不同安全策略,通过WOWA-FAHP方法处理诸如评价要素间的复杂关系.网络应用服务系统安全态势评估实例证明了方法与模型的有效性.     

Behavioral ordered weighted averaging operator and the application in multiattribute decision making

This paper introduces a new type of behavioral ordered weighted averaging (BOWA) operator, to incorporate decision maker’s gains and losses behavior tendency into the information aggregation process. The main characteristic of this BOWA operator is that it considers behavioral weights and ordered weights in the same formulation. We further provide a calculation method of the behavioral weights, in which various psychological preferences of different attribute types of the decision maker can be expressed intuitively. In addition, we discuss some particular cases of BOWA operator and its main properties. Finally, a numerical example is used to illustrate the use of the proposed method.     

大数据分割式极限学习机算法

在海量数据输入背景下，为提升极限学习机算法的学习速度，降低计算机内存消耗，提出一种分割式极限学习机算法。将海量数据分割成[K]等份，分别训练极限学习机并获得单一外权，基于算术平均算子得到分割式极限学习机的综合外权；为避免异常数据对极限学习机输出结果的影响，采用有序加权平均算子融合单一极限学习机的输出信息，使分割式极限学习机的输出结果更为稳定。数值对比仿真显示：分割式极限学习机比传统极限学习机的学习速度、拟合精度和内存消耗都高，验证了该方法的有效性和可行性。     

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.     

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.