Ordered Weighted Averaging Operators 1988–2014: A Citation‐Based Literature Survey

This study surveys the ordered weighted averaging (OWA) operator literature using a citation network analysis. The main goals are the historical reconstruction of scientific development of the OWA field, the identification of the dominant direction of knowledge accumulation that emerged since the publication of the first OWA paper, and to discover the most active lines of research. The results suggest, as expected, that Yager's paper 1 (IEEE Trans. Systems Man Cybernet, 18(1), 183–190, 1988) is the most influential paper and the starting point of all other research using OWA. Starting from his contribution, other lines of research developed and we describe them.     

On the properties of equidifferent RIM quantifier with generating function

Comparing the large number of research papers on the ordered weighted averaging (OWA) operator, the researches on relative quantifier are relatively rare so far. In the present paper, based on the quantifier guided aggregation method with OWA operator which was proposed by Yager [“Quantifier guided aggregation using OWA operators”, Int. J. Intell. Syst., 11, pp. 49–73, 1996], a generating function representation method for regular increasing monotone (RIM) quantifiers is proposed. We extend the the properties of OWA operator to the RIM quantifier which is represented with a monotone function instead of the OWA weighting vector. A class of parameterized equidifferent RIM quantifier which has minimum variance generating function is proposed and its properties are also analyzed. The equidifferent RIM quantifier is consistent with its orness level for any aggregated elements, which can be used to represent the decision maker's preference.     

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.     

Comment on “Some hybrid weighted averaging operators and their application to decision making”

The weighted averaging (WA) operator and the ordered weighted averaging (OWA) operator are the basic aggregation operators. Recently, a new hybrid weighted arithmetical averaging (HWAA) operator is proposed by Lin and Jiang to provide a unified framework between the WA and OWA operators. In this paper, I have some comments on their results. The major one concerns the monotonicity of the HWAA operator.     

Generalized prioritized aggregation operators

This paper deals with multicriteria decision‐making problems in which the criteria are partitioned into q categories, and a prioritization relationship exists over categories. We aggregate the criteria in the same priority category by a weighted OWA (ordered weighted averaging) operator and introduce two averaging operators, a generalized prioritized averaging operator and a generalized prioritized OWA operator. In the case with one criterion in each priority category, the two operators reduce to the prioritized averaging operator and the prioritized OWA operator as proposed by Yager. © 2012 Wiley Periodicals, Inc.     

Induced and uncertain heavy OWA operators

In this paper, we analyse in detail the ordered weighted averaging (OWA) operator and some of the extensions developed about it. We specially focus on the heavy aggregation operators. We suggest some new extensions about the OWA operator such as the induced heavy OWA (IHOWA) operator, the uncertain heavy OWA (UHOWA) operator and the uncertain induced heavy OWA (UIHOWA) operator. For these three new extensions, we consider some of their main properties and a wide range of special cases found in the weighting vector such as the heavy weighted average (HWA) and the uncertain heavy weighted average (UHWA). We further generalize these models by using generalized and quasi-arithmetic means obtaining the generalized heavy weighted average (GHWA), the induced generalized HOWA (IGHOWA) and the uncertain IGHOWA (UIGHOWA) operator. Finally, we develop an application of the new approach in a decision-making problem.     

Linear aggregation with weighted ranking

This paper considers the ordered weighted averaging (OWA) operator for the calculation of the averaged value of a finite number set. The specific feature of such an aggregation is the feasibility of the averaging strategy based on a ranking strategy rather than the particular values of the averaged quantities. The notion of a transposed operator for the OWA operator is introduced. The behavior of the OWA operator in the case of linear transformations of the aggregated values is studied. Theorems stating the linearity and additivity of the OWA operator for linear argument transformations are proved.     

On Obtaining Piled OWA Operators

In this study, we propose the concept of piled ordered weighted averaging (OWA) operators, which generalize the centered OWA operators and also connect the step OWA operators with the Hurwicz OWA operators with given the orness degree. We propose a controllable algorithm to generate the family of piled OWA operators depending on their predefined three parameters: orness degree, step‐like or Hurwicz‐like degree, and the numbers of “supporting” vectors. By these preferences, we can generate infinite more piled OWA operators with miscellaneous forms, and each of them is similar to the well‐known binomial OWA operator, which is very useful but only has one form corresponding to one given orness degree.     

Characterization of the ordered weighted averaging operators

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators. The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and presents the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with the same unit, independent zeroes and ordered values. These two classes correspond to the weighted ordered averaging operator (OWA) introduced by Yager in 1988. It is also shown that the OWA aggregator can be expressed as a Choquet integral     

基于词表示模型的领域文献数据可视分析方法

随着科学技术的发展,科研文献数量越来越大,如何从海量文献信息中找出特定领域的研究主题、有影响力的学者和高水平论文是一个巨大的挑战。为此提出一种基于词表示模型的领域文献数据可视分析方法,首先利用词嵌入模型word2vec向量化推荐领域相关的关键词,根据这些词向量之间的近似度筛选出领域相关的论文;然后应用BERTopic模型从领域论文摘要中提取主题;基于PageRank算法计算论文影响力,应用综合考虑作者署名顺序、发表论文数量和论文影响力的作者影响力评价方法 Author-Rank计算作者的影响力;最后使用多视图协同和交互的可视化方法帮助研究人员从领域的主题词频、主题演变、文献影响力和引用关系、作者影响力等多个角度对特定领域进行快速理解和分析。将该方法应用于食品安全领域的文献数据分析,应用结果和用户测试说明了其有效性。     

Generalized compensative weighted averaging aggregation operators

The compensative weighted averaging (CWA) operator is generalized to develop a class of powerful generalized compensative weighted averaging (GCWA) operators with a very fine range of compensatory effects. The conventional means are shown to be the special cases of the proposed GCWA operator. A few extensions are investigated by combining GCWA operator with ordered weighted averaging (OWA) and induced OWA (IOWA) operators. An exponential class of aggregation operators such as exponential CWA, exponential OWA and exponential IOWA operators are developed. The usefulness of GCWA operators is shown through several examples and a case-study.     

Two new models for determining OWA operator weights

The determination of ordered weighted averaging (OWA) operator weights is a very crucial issue of applying the OWA operator for decision making. This paper proposes two new models for determining the OWA operator weights. The weights determined by the new models do not follow a regular distribution and therefore make more sense than those obtained by other methods.     

A method for fuzzy group decision making based on induced aggregation operators and Euclidean distance

In this paper, we present the fuzzy‐induced Euclidean ordered weighted averaging distance (FIEOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Euclidean distance and uncertain information represented by fuzzy numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision maker by using order‐inducing variables in the aggregation of the Euclidean distance. Moreover, it is able to deal with uncertain environments where the information is very imprecise and can be assessed with fuzzy numbers. We study some of its main properties and particular cases such as the fuzzy maximum distance, fuzzy minimum distance, fuzzy‐normalized Euclidean distance (FNED), fuzzy‐weighted Euclidean distance (FWED), and fuzzy Euclidean ordered weighted averaging distance (FEOWAD) operator. Finally, we present an application of the operator to a group decision‐making problem concerning the selection of strategies.     

Knowledge mapping of supply chain risk research based on CiteSpace

Supply chain risk is a relatively new research field, and research results have been published in journals, and in master and doctoral articles. In this article, we first performed a quantitative analysis of existing literature on supply chain risk indexed in Web of Science (WOS). Then, we analyzed the author, institution, keywords, research hotspot, and cocited literature of existing publications in the research field of supply chain risk by using CiteSpace. The aim of this study is to investigate the trend, geographical distribution, author distribution, research field, keywords, keyword clustering, and other features of scientific articles on supply chain risk published in global journals, using the most advanced bibliometric analysis tools. The results of this study can be used to determine the most influential research institutions and authors in the research field of supply chain risk, as well as the research hotspots in different periods, and different research directions in this field.     

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.     

The ordered weighted geometric averaging operators

The ordered weighted averaging (OWA) operator was introduced by Yager. 1 The fundamental aspect of the OWA operator is a reordering step in which the input arguments are rearranged in descending order. In this article, we propose two new classes of aggregation operators called ordered weighted geometric averaging (OWGA) operators and study some desired properties of these operators. Some methods for obtaining the associated weighting parameters are discussed, and the relationship between the OWA and DOWGA operators is also investigated. © 2002 Wiley Periodicals, Inc.     

An OWA operator with fuzzy ranks

The ordered weighted averaging (OWA) operator of Yager was introduced to provide a method for aggregating several inputs which lies between the max and min operators. The fundamental aspect of the OWA operator is a reordering step in which the input arguments are rearranged according to their integer ranks. In this paper, we generalize the OWA operator to include the case of real-number or fuzzy ranks. © 1998 John Wiley & Sons, Inc.13: 69–81, 1998     

Pythagorean Fuzzy Multiattribute Group Decision Making with Probabilistic Information and OWA Approach

The aim of this paper is to develop a Pythagorean fuzzy multiattribute group decision making (MAGDM) method based on probabilistic information and the ordered weighted averaging (OWA) approach. The Pythagorean fuzzy probabilistic ordered weighted averaging (PFPOWA) operator is presented. It is a new aggregation operator that considers the probabilities and the OWA in the same formulation. Therefore, it is able to take into account the degree of importance that each concept has in the particular problem considered. Some main properties and different particular cases of the PFPOWA operators are studied. Moreover, a method based on the proposed operator for multiattribute group decision making is put forward. Finally, an example showing analysis of a supplier selection is given to verify the effectiveness and practicability of the proposed method.     

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator, including the main characteristics of both the generalized OWA and the induced OWA operator. This operator uses generalized means and order-inducing variables in the reordering process. It provides a very general formulation that includes as special cases a wide range of aggregation operators, including all the particular cases of the IOWA and the GOWA operator, the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator via quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we present a numerical example to illustrate the new approach in a financial decision-making problem.     

The uncertain induced quasi‐arithmetic OWA operator

We present the uncertain induced quasi‐arithmetic OWA (Quasi‐UIOWA) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the quasi‐arithmetic OWA (Quasi‐OWA) and the uncertain OWA (UOWA) operator. Thus, this generalization uses quasi‐arithmetic means, order inducing variables in the reordering process and uncertain information represented by interval numbers. A key feature of the Quasi‐UIOWA operator is that it generalizes a wide range of aggregation operators such as the uncertain quasi‐arithmetic mean, the uncertain weighted quasi‐arithmetic mean, the UOWA, the uncertain weighted generalized mean, the uncertain induced generalized OWA (UIGOWA), the Quasi‐UOWA, the uncertain IOWA, the uncertain induced ordered weighted geometric (UIOWG), and the uncertain induced ordered weighted quadratic averaging (UIOWQA) operator. We study some of the main properties of this approach including how to obtain a wide range of particular cases. We further generalize the Quasi‐UIOWA operator by using discrete Choquet integrals. We end the article with an application of the new approach in a decision making problem about investment selection. © 2010 Wiley Periodicals, Inc.