Centered OWA Operators

We introduce the idea of centered OWA operators. We define these as OWA operators that give preference to argument values that lie in the middle between the largest and the smallest. An important class of these using Gaussian type weights is investigated in considerable detail. We describe a number of different examples of centered OWA operators.     

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.     

OWA Operators in Regression Problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.      

Social Network Decision Making with Linguistic Trustworthiness–Based Induced OWA Operators

Classic aggregation operators in group decision making such as the ordered weighted averaging (OWA), induced ordered weighted averaging (IOWA), C‐IOWA, P‐IOWA, and I‐IOWA have shown to be successful tools to provide flexibility in the aggregation of preferences. However, these operators do not take advantage of information related to the interaction between experts. Experts involved in a group decision‐making problem may have developed opinions about the reliability of other experts' judgments, either because they have previous history of interaction with each other or because they have knowledge that informs them on the reliability of other colleagues in the group in solving decision‐making problems in the past. In this paper, and within the framework of social network decision making, we present three new social network analysis based IOWA operators that take advantage of the linguistic trustworthiness information gathered from the experts' social network to aggregate the social group preferences. Their use is analysed with simple but illustrative examples.     

A New Family of Induced OWA Operators

A new family of induced ordered weighted averaging (OWA) operators is proposed by invoking the order‐inducing variables at the aggregation step. The objective is to consider the variations in the magnitudes of the order‐inducing variables. The new family of operators include weighted induced OWA, weighted generalized induced OWA, and weighted induced ordered weighted geometric operators. These are further extended to the intuitionistic fuzzy domain. The usefulness of these operators is shown in a supplier selection problem.     

Cluster‐reliability‐induced OWA operators

On the basis of cluster size and cluster cohesion, we propose a generalized cluster‐reliability (CR) measure, which indicates the overall reliability of arguments in a cluster. Taking the reliability of clusters as order‐inducing variables, we introduce a generalized cluster‐reliability‐induced ordered weighted averaging (CRI‐OWA) operator from the viewpoint of combining representative arguments of clusters. Furthermore, we propose a grid‐based cohesion measure for grid‐based clusters. On the basis of this cohesion measure, we obtain the special CR measure and CRI‐OWA operator for the grid‐based clusters. Then we introduced two other special CR measures for graph‐based and prototype‐based clusters, respectively. Taking the CR, computed by these two measures, as order‐inducing variables, we can obtain two other kinds of CRI‐OWA operators for graph‐based and prototype‐based clusters, respectively. © 2012 Wiley Periodicals, Inc.     

Using Stress Functions to Obtain OWA Operators

The ordered weighted averaging operator attempts to provide a user-friendly class of mean type aggregation operators by allowing a user to easily and naturally go from a mental model of a desired type of aggregation to its formal realization. Our objective in this paper is to support this agenda by providing a new methodology to help a user describe the type of aggregation they desire using the idea of a stress function. With this stress function, a user can "stress" which argument values they want to give more weight in the aggregation. An important feature of this stress function is that it is only required to be nonnegative function on the unit interval. This allows a user to completely focus on the issue of where to put the stress in the aggregation without having to consider satisfaction of any other requirements.     

Monotonic argument‐dependent OWA operators

The ordered weighted averaging (OWA) operator introduced by Yager is one of the most popular aggregation technique. In this paper, we develop two kinds of argument‐dependent OWA (DOWA) operators including the pessimistic‐dependent OWA (PE‐DOWA) operator and optimistic‐dependent OWA (OP‐DOWA) operator, that point out that the PE‐DOWA operator is decreasing and the OP‐DOWA operator is increasing, and investigate some properties of our proposed monotonic DOWA operators in detail. Furthermore, we introduce the concept of original function in which a gradient vector generates the weights of the PE‐DOWA and OP‐DOWA operators. Meanwhile, we propose two classes of original functions including summing‐type original function and multiplying‐type original function and investigate the sufficient monotonic conditions for the DOWA operators generated by the original functions. Finally, we discuss the characteristics and properties of our proposed DOWA operators in detail and use a numerical example to illustrate the flexibility of our proposed operators.     

Decision Making in Reinsurance with Induced OWA Operators and Minkowski Distances

The decision to choose a reinsurance program has many complexities because it is difficult to simultaneously achieve high levels in different optimal criteria including maximum gain, minimum variance, and probability of ruin. This article suggests a new method by which, through membership functions, we can measure the distance of each alternative to an optimal result and aggregate it by using different types of aggregations. In this article, particular attention is given to the induced Minkowski ordered weighted averaging distance operator and the induced Minkowski probabilistic ordered weighted averaging distance operator. The main advantage of these operators is that they include a wide range of special cases. Thus, they can adapt efficiently to the specific needs of the calculation processes. By doing so, the reinsurance system can make better decisions by using different scenarios in the uncertain environment considered.     

An Efficient Pruning Method for Decision Alternatives of OWA Operators

In this paper, we present an efficient method for pruning decision alternatives in the case of using ordered weighted averaging (OWA) operators for decision making. The proposed method helps to identify inferior alternatives that are less likely to be selected out of competing alternatives as the OWA aggregation proceeds. It thus enables us to diminish the number of alternatives before applying the OWA operators. The reordering process unique to the OWA aggregation plays an important role in identifying inferior alternatives. The efficacy of the proposed method is demonstrated by simulation analysis in which artificial decision problems of diverse sizes are generated and then examined with four scenarios: pruning alternatives, pruning alternatives with rank-order OWA weights, pruning alternatives with a normalized decision problem, and pruning alternatives with both a normalized decision problem and rank-order OWA weights. The proposed method is easy to use, and the simulation results show that the number of alternatives can be reduced drastically by applying this method.      

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.     

A C‐OWA operator‐based approach to decision making with interval fuzzy preference relation

Yager [IEEE Trans Syst Man Cybern B 2004;34:1952–1963] introduced a continuous interval argument OWA (C‐OWA) operator, which extends the ordered weighted averaging (OWA) operator, introduced by Yager [IEEE Trans Syst Man Cybern B 1988;18:183–190], to the case in which the given argument is a continuous valued interval rather than a finite set of values. In this article, we utilize the C‐OWA operator to derive the priority vector of an interval fuzzy preference relation and then develop a practical approach to solving the decision‐making problem with interval fuzzy preference relation. Finally, a numerical example is provided to demonstrate the practicability and efficiency of the developed approach. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1289–1298, 2006.     

An Extension of Fuzzy L‐R Data Classification with Fuzzy OWA Distance

K‐Nearest neighbor (K‐NN) algorithm is a classification algorithm widely used in machine learning, statistical pattern recognition, data mining, etc. Ordered weighted averaging (OWA) distance based CxK nearest neighbor algorithm is a kind of K‐NN algorithm based on OWA distance. In this study, the aim is two‐fold: i) to perform the algorithm with two different fuzzy metric measures, which are Diamond distance, and weighted dissimilarity measure composed by spread distances and center distances, and ii) to evaluate the effects of different metric measures. K neighbors are searched for each class, and OWA distance is used to aggregate the information. The OWA distance can behave as intercluster distance approaches single, complete, and average linkages by using different weights. The experimental study is performed on well‐known three classification data sets (iris, glass, and wine). N‐fold cross‐validation is used for the evaluation of performances. It is seen that single linkage approach by using two different metric measures has significant different results.     

An Analysis of Some Functions That Generalizes Weighted Means and OWA Operators

In this paper, we analyze several classes of functions proposed in the literature to simultaneously generalize weighted means and ordered weighted averaging (OWA) operators: weighted OWA (WOWA) operators, hybrid weighted averaging (HWA) operators, and ordered weighted averaging‐weighted average (OWAWA) operators. Since, in some cases, the results provided by these operators may be questionable, we introduce functions that also generalize both operators and characterize those satisfying a condition imposed to maintain the relationship among the weights.     

基于三支决策的模糊信息系统OWA算子参数选择

在模糊信息系统中,通过有序加权平均（Ordered weighted averaging,OWA）算子计算对象相似度,可以建立λ截集的相容关系。当λ的值确定后,OWA算子中量词参数(α,β)的选取直接关系到不可区分关系的建立以及信息粒的粗细。因此合理选取参数(α,β)是值得进一步研究的问题。本文采用粗糙集三支决策理论,研究模糊信息系统OWA算子参数选择的相关内容。基于参数的激进、中庸和消极语义,确定OWA算子(α,β)的3种常用取值;进而研究相似度、相容类、双向近似和三支区域在3种参数选择下的性质关系。最后利用实例验证分析了模糊量词参数语义解释的合理性。本文采用三支决策创新视角,得到模糊信息系统OWA算子的深入性质,为相关模糊量词参数提供语义解释与选择依据。     

Type‐Reduction of General Type‐2 Fuzzy Sets: The Type‐1 OWA Approach

For general type‐2 fuzzy sets, the defuzzification process is very complex and the exhaustive direct method of implementing type‐reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type‐2 fuzzy inferencing systems in real‐world applications. The present situation will not be expected to change, unless an efficient and fast method of deffuzzifying general type‐2 fuzzy sets emerges. Type‐1 ordered weighted averaging (OWA) operators have been proposed to aggregate expert uncertain knowledge expressed by type‐1 fuzzy sets in decision making. In particular, the recently developed alpha‐level approach to type‐1 OWA operations has proven to be an effective tool for aggregating uncertain information with uncertain weights in real‐time applications because its complexity is of linear order. In this paper, we prove that the mathematical representation of the type‐reduced set (TRS) of a general type‐2 fuzzy set is equivalent to that of a special case of type‐1 OWA operator. This relationship opens up a new way of performing type reduction of general type‐2 fuzzy sets, allowing the use of the alpha‐level approach to type‐1 OWA operations to compute the TRS of a general type‐2 fuzzy set. As a result, a fast and efficient method of computing the centroid of general type‐2 fuzzy sets is realized. The experimental results presented here illustrate the effectiveness of this method in conducting type reduction of different general type‐2 fuzzy sets.     

基于OWA算子的不同形式偏好信息的群决策方法

研究具有不同形式偏好信息的群决策问题.在描述效用值、序关系值、模糊判断矩阵和AHP判断矩阵等4种形式偏好信息的基础上,首先给出将不同形式的偏好信息转化为模糊判断矩阵形式的计算公式,然后基于OWA算子给出集结各决策者偏好信息和方案优选的方法,最后用一个算例证明了所提出方法的有效性.     

Generating Z‐number based on OWA weights using maximum entropy

In the application of Z‐number, how to generate Z‐number is a significant and open issue. In this paper, we proposed a method of generating Z‐number based on the OWA weights using maximum entropy considering the attitude (preference) of the decision maker. Some numerical examples are used to illustrate the effectiveness of the proposed method. Results show that the attitude (preference) of the decision maker can give an optimal possibility distribution of the reliability for Z‐number using maximum entropy.     

An OWA Operator‐Based Cumulative Belief Degrees Approach for Credit Rating

Credit lenders utilize credit rating approaches to provide a classification system for characterizing credit borrowers. In order to measure the borrowers’ credibility, that is, ability and willingness to repay the debt, there are many financial and non‐financial criteria that should be considered. The basic aim of this study is to propose a multiple‐criteria credit rating approach that integrates different kinds of information and represents the borrowers’ credibility as a distribution among all the credit ratings. The cumulative belief degree approach is proposed for this purpose. Since all the available information is used in the final representation, a distribution‐based credit rating approach is expected to strengthen the lender's inference competency. In order to eliminate subjectivity in the weighting of criteria, an ordered weighted averaging operator is used. Additionally, the credit rating distribution can be transformed into a single credit rating by considering a threshold value. This study proposes a goodness‐of‐fit test to handle the subjectivity and difficulty of setting the threshold value. The applicability of the proposed approach is demonstrated by analyzing the credibility of selected Turkish firms from the stock exchange market of Turkey.