Distance measures with heavy aggregation operators

The use of distance measures and heavy aggregations in the ordered weighted averaging (OWA) operator is studied. We present the heavy ordered weighted averaging distance (HOWAD) operator. It is a new aggregation operator that provides a parameterized family of aggregation operators between the minimum distance and the total distance operator. Thus, it permits to analyze an aggregation from its usual average (normalized distance) to the sum of all distances available in the aggregation process. We analyze some of its main properties and particular cases such as the normalized Hamming distance, the weighted Hamming distance and the OWA distance (OWAD) operator. This approach is generalized by using quasi-arithmetic means obtaining the quasi-arithmetic HOWAD (Quasi-HOWAD) operator and with norms obtaining the heavy OWA norm (HOWAN). Further extensions to this approach are presented by using moving averages forming the moving HOWAD (HOWMAD) and the moving Quasi-HOWAN (Quasi-HOWMAN) operator. The applicability of the new approach is studied in a decision making model regarding the selection of national policies. We focus on the selection of monetary policies. The key advantage of this approach is that we can consider several sources of information that are independent between them.     

Generalized triangular fuzzy correlated averaging operator and their application to multiple attribute decision making

We investigate the multiple attribute decision making problems with triangular fuzzy information. Motivated by the ideal of Choquet integral [G. Choquet, Theory of capacities, Ann. Instit. Fourier 5 (1953) 131–295] and generalized OWA operator [R.R. Yager, Generalized OWA aggregation operators, Fuzzy Optim. Dec. Making 3 (2004) 93–107], in this paper, we have developed an generalized triangular fuzzy correlated averaging (GTFCA) operator. The prominent characteristic of the operators is that they cannot only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have applied the GTFCA operator to multiple attribute decision making problems with triangular fuzzy information. Finally an illustrative example has been given to show the developed method.     

The uncertain probabilistic OWA distance operator and its application in group decision making

In this paper, we present the uncertain probabilistic ordered weighted averaging distance (UPOWAD) operator. Its main advantage is that it uses distance measures in a unified framework between the probability and the OWA operator that considers the degree of importance of each concept in the aggregation. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases such as the uncertain probabilistic distance (UPD) and the uncertain OWA distance (UOWAD) operator. We end the paper by presenting an application to a group decision making problem regarding the selection of robots.     

A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers

With respect to the multiple attribute group decision making problems in which the attribute values take the form of generalized interval-valued trapezoidal fuzzy numbers (GITFN), this paper proposed a decision making method based on weighted geometric aggregation operators. First, some operational rules, the distance and comparison between two GITFNs are introduced. Second, the generalized interval-valued trapezoidal fuzzy numbers weighted geometric aggregation (GITFNWGA) operator, the generalized interval-valued trapezoidal fuzzy numbers ordered weighted geometric aggregation (GITFNOWGA) operator, and the generalized interval-valued trapezoidal fuzzy numbers hybrid geometric aggregation (GITFNHGA) operator are proposed, and their various properties are investigated. At the same time, the group decision methods based on these operators are also presented. Finally, an illustrate example is given to show the decision-making steps and the effectiveness of this method.     

Group decision making with simplified neutrosophic ordered weighted distance operator

Simplified neutrosophic set is a convenient tool proposed for dealing with complex problems; it is effective in providing more data for decision‐making process. In this study, we develop a simplified neutrosophic ordered weighted distance operator which combines the neutrosophic distance measures and the ordered weighted average distance in the same formulation. It is a new handy aggregation operator that considers the situations where the input data are represented in simplified neutrosophic numbers, and it also contains diverse distance aggregation operators. Parameterized families of simplified neutrosophic ordered weighted distance operator are handled. Moreover, we establish a new neutrosophic group decision‐making method based on the simplified neutrosophic ordered weighted distance operator, which has 2 extended approaches for determining the weights of decision makers and decision attributes in decision‐making process, respectively. Finally, an illustrative example demonstrates the application of the proposed method. The effectiveness and advantages of the proposed method are shown by the comparative analysis with existing relative methods.     

Generalized OWA Aggregation Operators

We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.     

Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators

Expertons and uncertain aggregation operators are tools for dealing with imprecise information that can be assessed with interval numbers. This paper introduces the uncertain generalized probabilistic weighted averaging (UGPWA) operator. It is an aggregation operator that unifies the probability and the weighted average in the same formulation considering the degree of importance that each concept has in the aggregation. Moreover, it is able to assess uncertain environments that cannot be assessed with exact numbers but it is possible to use interval numbers. Thus, we can analyze imprecise information considering the minimum and the maximum result that may occur. Further extensions to this approach are presented including the quasi-arithmetic uncertain probabilistic weighted averaging operator and the uncertain generalized probabilistic weighted moving average. We analyze the applicability of this new approach in a group decision making problem by using the theory of expertons in strategic management.     

The orness measures for two compound quasi-arithmetic mean aggregation operators

The paper first summarizes the orness measures and their common characteristics of some averaging operators: the quasi-arithmetic mean, the ordered weighted averaging (OWA) operator, the regular increasing monotone (RIM) quantifier and the weighted function average operator, respectively. Then it focuses on the aggregation properties and operator determination methods for two kinds of quasi-arithmetic mean-based compound aggregation operators: the quasi-OWA (ordered weighted averaging) operator and the Bajraktarevi? mean. The former is the combination of the quasi-arithmetic mean and the OWA operator, while the latter is the combination of the quasi-arithmetic mean and the weighted function average operator. Two quasi-OWA operator forms are given, where the OWA operator is assigned directly or generated from a RIM (regular increasing monotone) quantifier indirectly. The orness indexes to reflect the or-like level of the quasi-OWA operator and Bajraktarevi? mean are proposed. With generating function techniques, the properties of the quasi-OWA operator and Bajraktarevi? mean are discussed to show the rationality of these orness definitions. Based on these properties, two families of parameterized quasi-OWA operator and Bajraktarevi? mean with exponential and power function generators are proposed and compared. It shows that the method of this paper can also be applied to other function-based aggregation operators.     

Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making

This paper deals with multiattribute group decision making (MAGDM) problems with interval-valued 2-tuple linguistic information. First, we introduce some new aggregation operators, such as the interval-valued 2-tuple weighted geometric (IVTWG) operator, the interval-valued 2-tuple ordered weighted geometric (IVTOWG) operator, the generalized interval-valued 2-tuple weighted average (GIVTWA) operator and the generalized interval-valued 2-tuple ordered weighted average (GIVTOWA). Then, we discuss their desired properties and relationships among them. Furthermore, we put forward a new method to determine the weight vector of interval-valued 2-tuple aggregation operator based on the concept of degree of precision. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in dealing with interval-valued 2-tuple linguistic information under multi-granular linguistic contexts.     

一种模糊有序加权(FOWA)算子及其应用

针对多个三角模糊数的集结问题，提出一种新的模糊有序加权(FOWA)算子。该算子是对传统OWA算子的扩展，它使三角模糊数可根据其所在排序位置进行集结。分析FOWA算子所具有的性质，给出在群决策中模糊信息集结的一个应用算例。     

Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices

This paper explores the application of ordered weighted averaging (OWA) operators to develop water quality index, which incorporates an attitudinal dimension in the aggregation process. The major thrust behind selecting the OWA operator for aggregation of multi-criteria is its capability to encompass a range of operators bounded between minimum and maximum. A new approach for generating OWA weight distributions using probability density functions (PDFs) is proposed in this paper. The basic parameters (mean and standard deviation) of the probability density functions can be determined using the number of criteria (e.g., water quality indicators) in the aggregation process.     

Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers

The aim of this work is to present some cases of aggregation operators with intuitionistic trapezoidal fuzzy numbers and study their desirable properties. First, some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Next, based on these operational laws, we develop some geometric aggregation operators for aggregating intuitionistic trapezoidal fuzzy numbers. In particular, we present the intuitionistic trapezoidal fuzzy weighted geometric (ITFWG) operator, the intuitionistic trapezoidal fuzzy ordered weighted geometric (ITFOWG) operator, the induced intuitionistic trapezoidal fuzzy ordered weighted geometric (I-ITFOWG) operator and the intuitionistic trapezoidal fuzzy hybrid geometric (ITFHG) operator. It is worth noting that the aggregated value by using these operators is also an intuitionistic trapezoidal fuzzy value. Then, an approach to multiple attribute group decision making (MAGDM) problems with intuitionistic trapezoidal fuzzy information is developed based on the ITFWG and the ITFHG operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

基于双边犹豫模糊非均衡语言优先集成算子的应急响应预案评估方法

在应用多属性决策理论求解应急响应预案评估问题时,问题结构的复杂性往往使决策者评价信息存在高度不确定性且属性相对重要性仅能以优先级关系来表征。为此,本文首先提出了双边犹豫模糊非均衡语言集这种新型信息形式以使决策者能够灵活有效的表征复杂评价信息,并定义了运算法则、熵和距离测度;其次,基于熵测度开发了双边犹豫模糊非均衡语言优先加权集成算子,并构建了能够考虑属性优先关系的多属性决策方法;进一步针对属性相对重要性不能由定性分析获得的情况,设计了客观权重确定方法,并构建了另一种更具实际灵活性的VIKOR决策方法;最后,实例研究表明了方法的有效性与优势。     

On characterizing features of OWA aggregation operators

We introduce the ordered weighted averaging (OWA) operator and emphasize how the choice of the weights, the weighting vector, allows us to implement different types of aggregation. We describe two important characterizing features associated with OWA weights. The first of these is the attitudinal character and the second is measure of dispersion. We discuss some methods for generating the weights and the role that these characterizing features can play in the determination of the OWA weights. We note that while in many cases these two features can help provide a clear distinction between different types of OWA operators there are some important cases in which these two characterizing features do not distinguish between OWA aggregations. In an attempt to address this we introduce a third characterizing feature associated with an OWA aggregation called the focus. We look at the calculation of this feature in a number of different situations.     

Soft computing-based aggregation methods for human resource management

We are interested in the personnel selection problem. We have developed a flexible decision support system to help managers in their decision-making functions. This DSS simulates experts’ evaluations using ordered weighted average (OWA) aggregation operators, which assign different weights to different selection criteria. Moreover, we show an aggregation model based on efficiency analysis to put the candidates into an order.     

Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making

In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment.     

Generalized weighted exponential proportional aggregation operators and their applications to group decision making

We present a new aggregation operator called the generalized ordered weighted exponential proportional averaging (GOWEPA) operator, which is based on an optimal model. We study some properties and different families of the GOWEPA operator. We also generalize the GOWEPA operator. The key advantage of the GOWEPA operator is that it is an aggregation operator with theoretic basis on aggregation. Moreover, we propose an orness measure of the GOWEPA operator and indicate some properties of this orness measure. Furthermore, we introduce the least exponential squares method (LESM) to determine the GOWEPA operator weights based on its orness measure. In the end, we develop an application of the new approach in a case of group decision making in investment selection.     

广义梯形模糊数密度加权算子及其应用

针对多属性决策问题,本文面向广义梯形模糊数的决策信息,提出了广义梯形模糊数密度加权算子(TF-DWA算子)的信息集结方法。首先介绍了广义梯形模糊数密度加权算子及其合成算子,并分析了其性质特点。然后,基于信息分布的疏密程度讨论了广义梯形模糊数的分组问题,通过质心排序指标值进行聚类。在此基础上,基于熵值法求解密度加权向量。最后,通过一个应用算例对本文提出的算子进行简要说明。     

一种基于犹豫模糊集的多属性关联决策方法

主要讨论属性间具有关联性的条件下犹豫模糊多属性决策问题.首先,基于gλ模糊测度,Shapley值和Choquet积分,定义了两种犹豫模糊信息集成算子:AHFGSCgλ算子和GHFGSCgλ算子.然后,讨论了这些算子的一些性质.最后通过一个实例来说明算子的可行性和有效性.     

基于泛性模糊数的VIKOR方法研究

建立了一种泛性模糊数可比较的度量,对决策信息通常为泛性模糊数的决策问题进行加工和扩展,提出了基于泛性模糊数不确定信息的VIKOR决策方法,实现了属性为泛性模糊数的多属性群决策及信息融合的目的.