Ordered Weighted Averaging Operator Research Articles

On OWA Linear Operators for Decision Making

ABSTRACTWhen we deal with problems of decision making where we need to give an order of alternatives and the rewards (number of points earned in a race) are not associated with the criteria, but with positions, it makes sense to deal with ordered weighted averaging (OWA) operators. Within the class of OWA operators we can consider those that are based on a linear function. This paper is related to a study of the properties that verify the linear functions set. Taking these properties into account we shall see how the final classification for drivers in Formula One changes when the number of points earned in a race is given by means of a linear function as opposed to the current assignments.

Heavy Moving Averages and Their Application in Econometric Forecasting

ABSTRACTThis paper presents the heavy ordered weighted moving average (HOWMA) operator. It is an aggregation operator that uses the main characteristics of two well-known techniques: the heavy ordered weighted averaging (OWA) and the moving averages. Therefore, this operator provides a parameterized family of aggregation operators from the minimum to the total operator and includes the OWA operator as a special case. It uses a heavy weighting vector in the moving average formulation and it represents the information available and the knowledge of the decision maker about the future scenarios of the phenomenon, according to his attitudinal character. Some of the main properties of this operator are studied, including a wide range of families of HOWMA operators such as the heavy moving average and heavy weighted moving average operators. The HOWMA operator is also extended using generalized and quasi-arithmetic means. An example concerning the foreign exchange rate between US dollars and Mexican pesos is also presented.

Some Characterizations of Lattice OWA Operators

Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.

Robustifying OWA Operators for Aggregating Data With Outliers

We propose a version of ordered weighted averaging (OWA) operators, which are robust against inputs with outliers. Outliers may heavily bias the outputs of the standard OWA. The penalty-based method proposed here comprises both outlier detection and reallocation of weights of the OWA. At the first stage, the outliers are identified based on a robust criterion that can accommodate up to half the inputs being outliers, but at the same time not removing the inputs unnecessarily. Three numerical algorithms for calculating the optimal value of this criterion are proposed. At the second stage, the OWA weights are recalculated for a subset of clean data while preserving the overall character of the weighting vector. The method is numerically tested on simulated data and exemplified on aggregating a large number of online ratings where the outliers represent biased, missing, or erroneous evaluations.

Exploiting Data Reliability and Fuzzy Clustering for Journal Ranking

Journal impact indicators are widely accepted as possible measurements of academic journal quality. However, much debate has recently surrounded their use, and alternative journal impact evaluation techniques are desirable. Aggregation of multiple indicators offers a promising method to produce a more robust ranking result, avoiding the possible bias caused by the use of a single impact indicator. In this paper, fuzzy aggregation and fuzzy clustering, especially the ordered weighted averaging (OWA) operators are exploited to aggregate the quality scores of academic journals that are obtained from different impact indicators. Also, a novel method for linguistic term-based fuzzy cluster grouping is proposed to rank academic journals. The paper allows for the construction of distinctive fuzzy clusters of academic journals on the basis of their performance with respect to different journal impact indicators, which may be subsequently combined via the use of the OWA operators. Journals are ranked in relation to their memberships in the resulting combined fuzzy clusters. In particular, the nearest-neighbor guided aggregation operators are adopted to characterize the reliability of the indicators, and the fuzzy clustering mechanism is utilized to enhance the interpretability of the underlying ranking procedure. The ranking results of academic journals from six subjects are systematically compared with the outlet ranking used by the Excellence in Research for Australia, demonstrating the significant potential of the proposed approach.

A New Approach to Solve the Constrained OWA Aggregation Problem

Constrained ordered weighted averaging (OWA) aggregation attempts to optimize the OWA aggregation problem with multiple constraints. It is inherently nonlinear, and Yager presented a novel method to transform the nonlinear problem to a mixed integer linear problem. Later, a simple algorithm for exact computation of optimal solutions to a single constrained OWA aggregation problem was presented. In this paper, we deal with the same problem, but in completely different ways in a sense that it is linearized by utilizing the reordering property of the OWA operators. We attempt to solve the linear programming problem via the extreme points in lieu of using a linear programming package for the purpose of deriving an explicit formula for the optimal solution. Furthermore, we consider its dual problem that leads to an equivalent optimal solution. Finally, the proposed method is extended to the OWA optimization problem with multiple constraints including the attitudinal character as well as a range of incomplete arguments.

Orness For Idempotent Aggregation Functions

Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.

Cloud Generalized Power Ordered Weighted Average Operator and Its Application to Linguistic Group Decision-Making

In this paper, we develop a new linguistic aggregation operator based on the cloud model for solving linguistic group decision-making problem. First, an improved generating cloud method is proposed so as to transform linguistic variables into clouds, which modifies the limitation of the classical generating cloud method. We then address some new cloud algorithms, such as cloud possibility degree and cloud support degree which can be respectively used to compare clouds and determine the weights. Combining the cloud support degree with power aggregation operator, we develop a new cloud aggregation operator dubbed the cloud generalized power ordered weighted average (CGPOWA) operator. We study the properties of the CGPOWA operator and investigate its family including a wide range of aggregation operators such as the CGPA operator, CPOWA operator, CPOWGA operator, CPWQA operator, CWAA and CWGA operator. Furthermore, a new approach for linguistic group decision-making is presented on the basis of the improved generating cloud method and CGPOWA operator. Finally, an illustrative example is provided to examine the effectiveness and validity of the proposed approach.

Sensitivity analysis of the ordered weighted averaging operator via linear models

The efficient computation of the weights in an ordered weighted averaging (OWA) operator plays an important role in the successful design and application of the OWA operator. In some applications, an OWA weight vector with positive and distinct components for any desired orness level is preferable. This paper proposes two complementary linear OWA (CLOWA) models for determining the weights and a compact form of the optimal weights in the general case (i.e., for any level of orness and n). The proposed models produce a unique OWA weight vector with distinct and positive components for any orness level α∈(0,1). In addition to a combined goodness measure, the sensitivity analysis on the outputs of theOWA operator with respect to the optimism degree of the decision maker (DM) is important. This study obtains the combined goodness measure and sensitivity analysis models for two linear methods: the minimax disparity (MD) and new proposed models. Then, to assign reliable ranks to the alternatives in the presence of two conflicting objectives—maximizing the combined goodness measure and minimizing its sensitivity to the optimism degree of the DM—the composite measure of goodness is extended. The proposed methods are applied in a water resource management problem.

Landfill site selection using combination of fuzzy logic and multi-attribute decision-making approach

During the last decades, growth of urbanization and industrialization led to an increase in solid waste generation. Landfilling is the most prevalent ultimate disposal method for the municipal solid wastes in developing countries. The rapid municipal solid waste generation in Markazi province (central part of Iran) causes the need for precision in finding a suitable landfill site selection. In the present study, 12 factors (environmental and socioeconomic factors) have been applied to select the landfill site in Markazi province, Iran. The different methods including the analytic network process (ANP) combined with fuzzy linguistic quantifier, ordered weighted average (OWA), and weighted linear combination (WLC) approach in geographic information system was applied to find an appropriate landfill site. The OWA operator function permits the evaluation of the wide spectrum of consequences (with different scenario) obtained from different management strategies. Results revealed that integration of fuzzy logic, ANP, and OWA provides flexible and better ideas compared to the Boolean logic and WLC to select a suitable landfill site.

An approach to obtain the generalized mixed linear stress function for known owa weights with artificial bee colony algorithm

Abstract
 OWA (Ordered Weighted Averaging) is a flexible aggregation operator which is come up with Yager to create a decision function in multi-criteria decision making. It is possible to determine how optimistic or pessimistic the decision maker's opinion with the value obtained from the weights of this operator. The determination of OWA weights cannot provide characterization by itself. If it is desired to aggregate various sized objects in terms of generalization and reusability of OWA weights, a more general form is needed. In this study, we propose the parameterized piecewise linear stress function and the approach to characterize OWA weights. The stress function is expressed by parameters which are obtained by artificial bee colony algorithm. Also the weights are approximately found by using parameters.
 Keywords – OWA operator, aggregation, artificial bee colony algorithm.

From quantitative to qualitative orness for lattice OWA operators

This paper deals with OWA (ordered weighted average) operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. A qualitative orness measure for any OWA operator is suggested, based on its proximity to the OR operator that yields the maximum of the given data. In the particular case of a finite distributive lattice, considering the t-norm given by the meet and the t-conorm given by the join, this qualitative measure agrees with the value that some discrete Sugeno integral takes on the vector consisting of all the members of the lattice. Some applications of the qualitative orness of OWA operators to decision-making problems are shown. In addition, OWA operators defined on a finite product lattice are also applied in image processing. We analyze the effect of several OWA operators with respect to their orness.

Mean-Variance Portfolio Selection With the Ordered Weighted Average

Portfolio selection is the theory that studies the process of selecting the optimal proportion of different assets. The first approach was introduced by Harry Markowitz and was based on a mean-variance framework. This paper introduces the ordered weighted average (OWA) in the mean-variance model. The main idea is to replace the classical mean and variance by the OWA operator. By doing so, the new model is able to study different degrees of optimism and pessimism in the analysis being able to develop an approach that considers the decision makers attitude in the selection process. This paper also suggests a new framework for dealing with the attitudinal character of the decision maker based on the numerical values of the available arguments. The main advantage of this method is the ability to adapt to many situations offering a more complete representation of the available data from the most pessimistic situation to the most optimistic one. An illustrative with fictitious data and a real example are studied.

Exploring the Ordered Weighted Averaging Operator Knowledge Domain: A Bibliometric Analysis

Ordered weighted averaging (OWA) operator has been received increasingly widespread interest since its appearance in 1988. Recently, a topic search with the keywords “ordered weighted averaging operator” or “OWA operator” on Web of Science (WOS) found 1231 documents. As the publications about OWA operator increase rapidly, thus a scientometric analysis of this research field and discovery of its knowledge domain becomes very important and necessary. This paper studies the publications about OWA operator between 1988 and 2015, and it is based on 1213 bibliographic records obtained by using topic search from WOS. The disciplinary distribution, most cited papers, influential journals, as well as influential authors are analyzed through citation and cocitation analysis. The emerging trends in OWA operator research are explored by keywords and references burst detection analysis. The research methods and results in this paper are meaningful for researchers associated with OWA operator field to understand the knowledge domain and establish their own future research direction.

Positional Voting Rules Generated by Aggregation Functions and the Role of Duplication

In this paper, we consider a typical voting situation where a group of agents show their preferences over a set of alternatives. Under our approach, such preferences are codified into individual positional values, which can be aggregated in several ways through particular functions, yielding positional voting rules and providing a social result in each case. We show that scoring rules belong to such class of positional voting rules. But if we focus our interest on OWA (ordered weighted averaging) operators as aggregation functions, other well-known voting systems naturally appear. In particular, we determine those ones verifying duplication (i.e., clone irrelevance) and present a proposal of an overall social result provided by them.

BONFERRONI DISTANCES WITH HYBRID WEIGHTED DISTANCE AND IMMEDIATE WEIGHTED DISTANCE

The aim of the paper is to develop new aggregation operators using Bonferroni means, ordered weighted averaging (OWA) operators and some measures of distance. We introduce the Bonferroni Hybrid-weighted distance (BON-HWD), and Bonferroni distances with OWA operators and weighted averages (BON-IWOWAD). The main advantages of using these operators are that they allow the consideration of different aggregations contexts to be considered and multiple-comparison between each argument and distance measures in the same formulation. We develop a mathematical application to show the versatility of new models. Finally, this new group of family distances can be used in a wide range of management and economic fields.

Hybrid Models for the OWA Optimization

When dealing with multicriteria problems, the aggregation of multiple outcomes plays an essential role in finding a solution, as it reflects the decision-maker's preferencerelation. The Ordered Weighted Averaging (OWA) operator provides a exible preference model that generalizes many objective functions. It also ensures the impartiality and allow to obtain equitable solutions, which is vital when the criteria represent evaluations of independent individuals. These features make the OWA operator very useful in many fields, one of which is location analysis. However, in general the OWA aggregation makes the problem nonlinear and hinder its computational complexity. Therefore, problems with the OWA operator need to be devised in an efficient way. The paper introduces new general formulations for OWA optimization and proposes for them some simple valid inequalities to improve efficiency. A hybrid structure of proposed models makes the number of binary variables problem type dependent and may reduce it signicantly. Computational results show that for certain problem types, some of which are very useful in practical applications, the hybrid models perform much better than previous general models from literature.

The Metric Space of Ordered Weighted Average Operators with Distance Based on Accumulated Entries

Ordered weighted average (OWA) operators with their weighting vectors are very important in many applications. We show that directly taking Minkowski distances (including Manhattan distance and Euclidean distance) as the distances for any two OWA operator is not reasonable. In this study, we propose the standard distance measures for any two OWA operators and then propose a standard metric space for the set of all n-dimension OWA operators. We analyze and discuss some properties of the introduced OWA metric and further propose a metric space of Choquet integrals represented by the underlying fuzzy measures. Some applications in decision making of OWA distances are also presented in this study.

Distance measures, weighted averages, OWA operators and Bonferroni means

The ordered weighted average (OWA) is an aggregation operator that provides a parameterized family of operators between the minimum and the maximum. This paper presents the OWA weighted average distance operator. The main advantage of this new approach is that it unifies the weighted Hamming distance and the OWA distance in the same formulation and considering the degree of importance that each concept has in the analysis. This operator includes a wide range of particular cases from the minimum to the maximum distance. Some further generalizations are also developed with generalized and quasi-arithmetic means. The use of Bonferroni means under this framework is also studied. The paper ends with an application of the new approach in a group decision making problem with Dempster-Shafer belief structure regarding the selection of strategies.

How well does the OWA operator represent real preferences?

We present the results of an empirical study, in which we analyze the ability of the Ordered Weighted Average (OWA) operator to model actual preferences in a multi-attribute ranking task. We compare the OWA to a competing model (Simple Additive Weighting SAW), and we also study whether its characteristic feature, the ability to represent different attitudes toward compensation among attributes, is reflected in the preferences provided by subjects. We find that in general, the OWA model fits slightly less well to empirical data. Subjects whose preferences are better explained by the SAW model are also more consistent in their choice behavior. Our results furthermore indicate that preferences of most subjects are not fully compensatory. Thus the ability of the OWA operator to represent different attitudes toward compensation can be a useful feature in modeling actual preferences. The structure of the weights estimated for the OWA operator also suggests that it might provide a good approximation to certain types of decision heuristics.