Ordered Weighted Averaging Operator Research Articles

A Bibliometric Review of the Ordered Weighted Averaging Operator

The ordered weighted averaging (OWA) operator was proposed by Yager back in 1988 and constitutes a parameterized family of aggregation functions between the minimum and the maximum. The purpose of this paper is to perform a bibliometric review of this aggregation operator during the last 35 years through the Web of Science (WoS) Core Collection database and the Visualization of Similarities (VOS) viewer software. The results show that the OWA operator is an increasingly popular aggregation operator, especially in Computer Science. The results also allow the assertion that Yager, as expected, is still the most influential and productive author. Moreover, the study reveals that institutions from over 80 countries have contributed to OWA research, highlighting the high presence of Chinese universities and the emergence of Pakistani ones. Other interesting findings are presented to provide a comprehensive and up-to-date analysis of the OWA operator literature.

Risk measurement of aggregation approaches in multiple attribute decision making under uncertain information

The decision-maker's judgment deviates from uncertain attribute information will lead to decision risk in multiple attribute decision making (MADM), and different aggregation approaches result in different risk levels. This paper aims to study the risk levels of aggregation operators in MADM with uncertain attribute information. We use the signal detection theory to characterize the decision-maker's noisy perceptions of multiple attributes to present his/her judgment deviation. Then, we establish the aggregation models to aggregate these perceptions based on the weighted averaging (WA) and the ordered weighted averaging (OWA) operators. Furthermore, a risk measurement model of each aggregation approach is constructed to measure the risk levels of the commission risk (CR), the omission risk (OR), and the overall risk. A numerical example is used to verify the validity of the proposed model, while simulation experiments are designed to compare the risk levels of the WA and OWA operators. The results reveal that the overall risk level of the WA operator is higher than that of the OWA operator when judging the quality of the alternative with high standards; otherwise, the WA operator is lower. This finding provides a scientific reference for aggregation approach selection under uncertain information. Code metadataPermanent link to reproducible Capsule: https://doi.org/10.24433/CO.0911610.v1.

A generalized form of the distance-induced OWA operators – Demonstrating its use for evaluation indicator system in China

Using multi-criteria decision making (MCDM) technique to rank alternatives is a well-known area of study in which aggregation operators, such as ordered weighted averaging (OWA) and induced OWA (IOWA) operators, play an important role in merging information and producing an overall ranking. The distance measures from ideal argument values in aggregation operators have gained attention in recent literature. Distance measures are traditionally used as argument variables, which leads to the depiction that the attribute cannot be aggregated directly. In this paper, a generalized form of distance-induced OWA (DIOWA) operators is proposed with distance measures used as order-inducing variables. A distinctive benefit of DIOWA operators is that they permit us to consider ideal argument values while simultaneously also taking the attribute values as argument variables. Three variants of DIOWA operators are proposed and investigated, namely a) the Hamming distance-induced OWA (HDIOWA) operator, b) the normalized Hamming distance-induced OWA (NHDIOWA) operator, and c) the weighted Hamming distance-induced OWA (WHDIOWA) operator. We highlight their important properties and provide proofs to necessary theorems, and also suggest the determination methods for calculating their associated weights. We discuss further extensions of the proposed DIOWA operators with the help of generalized and quasi-arithmetic means. We discuss the use of our proposed family of operators for two different decision making situations, and demonstrate their validity by an illustrative numerical example. Finally, we apply the proposed operators to a real-life problem of ranking Chinese provinces for their science and technology (S&T) development levels. The proposed operators are shown to be a useful addition to the aggregation toolbox for decision analysts.

Admissible OWA operators for fuzzy numbers

Ordered Weighted Averaging (OWA) operators are some of the most widely used aggregation functions in classic literature, but their application to fuzzy numbers has been limited due to the complexity of defining a total order in fuzzy contexts. However, the recent notion of admissible order for fuzzy numbers provides an effective method to totally order them by refining a given partial order. Therefore, this paper is devoted to defining OWA operators for fuzzy numbers with respect to admissible orders and investigating their properties. Firstly, we define the OWA operators associated with such admissible orders and then we show their main properties. Afterward, an example is presented to illustrate the applicability of these AOWA operators in linguistic decision-making. In this regard, we also develop an admissible order for trapezoidal fuzzy numbers that can be efficiently applied in practice.

A Generalized Family of Constant Orness Ordered Weighted Averaging Operators

A Generalized Family of Constant Orness Ordered Weighted Averaging Operators

An integrated method for multi-attribute group decision-making based on the linguistic Z-number and MSM operators

This article extends the ordered weighted average operator (OWA) in the linguistic Z-number (LZN) environment, increasing attention to the distribution of data itself, and this idea can also be combined with other operators. Specifically, for the weight of data, this paper gives consideration to both the preference of attributes and the distribution of data itself, gives the interval distribution induced OWA operator (IDIOWA), and combines the weight of attributes to obtain the LZN interval distribution induced hybrid weighted average operator (LZIDIHWA) in LZN environment. Then, it introduces some good properties of this operator. At the same time, the LZN interval distribution induced weighted Maclaurin symmetric means operator (LZIDIWMSM) is obtained by combining LZN interval distribution induced OWA operator (LZIDIOWA) with the LZN weighted Maclaurin symmetric means operator (LZWMSM), which makes up for the defect that LZWMSM cannot be used for data integration alone. Finally, the two operators are used for multi-attribute group decision-making (MAGDM), and their effectiveness is verified by comparative analysis.

OWAdapt: An adaptive loss function for deep learning using OWA operators

In this paper, we propose a novel adaptive loss function for enhancing deep learning performance in classification tasks. Specifically, we redefine the cross-entropy loss to effectively address class-level noise conditions, including the challenging problem of class imbalance. Our approach introduces aggregation operators to improve classification accuracy. The rationale behind our proposed method lies in the iterative up-weighting of class-level components within the loss function, focusing on those with larger errors. To achieve this, we employ the ordered weighted average (OWA) operator and combine it with an adaptive scheme for gradient-based learning. The main finding is that our method outperforms other commonly used loss functions, such as the standard cross-entropy or focal loss, across various binary and multiclass classification tasks. Furthermore, we explore the influence of hyperparameters associated with the OWA operators and propose a default configuration that performs well across different experimental settings.

Advanced Fuzzy Sets and Genetic Algorithm Optimizer for Mammographic Image Enhancement

A well-researched field is the development of Computer Aided Diagnosis (CADx) Systems for the benign-malignant classification of abnormalities detected by mammography. Due to the nature of the breast parenchyma, there are significant uncertainties about the shape and geometry of the abnormalities that may lead to an inaccurate diagnosis. These same uncertainties give mammograms a fuzzy character that is essential to the application of fuzzy processing. Fuzzy set theory considers uncertainty in the form of a membership function, and therefore fuzzy sets can process imperfect data if this imperfection originates from vagueness and ambiguity rather than randomness. Fuzzy contrast enhancement can improve edge detection and, by extension, the quality of related classification features. In this paper, classical (Linguistic hedges and fuzzy enhancement functions), advanced fuzzy sets (Intuitionistic fuzzy set (ΙFS), Pythagorean fuzzy set (PFS), and Fermatean fuzzy sets (FFS)), and a Genetic Algorithm optimizer are proposed to enhance the contrast of mammographic features. The advanced fuzzy sets provide better information on the uncertainty of the membership function. As a result, the intuitionistic method had the best overall performance, but most of the techniques could be used efficiently, depending on the problem that needed to be solved. Linguistic methods could provide a more manageable way of spreading the histogram, revealing more extreme values than the conventional methods. A fusion technique of the enhanced mammography images with Ordered Weighted Average operators (OWA) achieves a good-quality final image.

Ordered weighted averaging operators for basic uncertain information granules

Yager's Ordered Weighted Averaging (OWA) operators have been extensively employed in academic literature as a means of aggregating information through the comparison of inputs. However, in cases where the inputs consist of basic uncertain information (BUI), which is partially unreliable, it becomes impractical to compare these inputs. As a result, the traditional method of OWA aggregation cannot be utilized. Hence, this study introduces a novel approach to establishing BUI OWA operators by employing problem factorization and integration techniques, akin to the principles underlying the Choquet integral. In addition, we engage in an examination of related properties and present a numerical illustration to showcase the practicality of the suggested approach. Finally, we discuss various methodologies for determining specific weights that can be used to define BUI OWA operators.

Fuzzy evaluation of ecological vulnerability based on the SRP-SES method and analysis of multiple decision-making attitudes based on OWA operators: A case of Fujian Province, China

Evaluation of the ecological vulnerability facilitates ecological protection and management. We presented a well-organized and comprehensive evaluation system and analysis method of ecological vulnerability. We used Fujian Province, China, as a case study and validated the reliability of evaluation results. The details are as follows. Based on the framework of sensitivity-resilience-pressure (SRP) coupled with the “social-environmental” system (SES), this study selected 23 indicators and determined their weights by a combination of subjective and objective weighting methods to systematically construct the ecological vulnerability evaluation system. By establishing a fuzzy evaluation model, the indicator data were fuzzily mapped into evaluation scores for the calculation of the ecological vulnerability index (EVI). Following the calculation results, the spatial clustering analysis based on K-means, driving factor analysis based on GeoDetector and spatial autocorrelation analysis were conducted. Finally, an ecological vulnerability analysis under multiple decision-making attitudes was conducted based on the ordered weighted average (OWA) operators. The results were as follows. (1) The ecological vulnerability of Fujian Province showed a trend of higher in the east and lower in the west, and there is an obvious spatial aggregation effect. The high-high aggregation areas mainly distributed in the eastern coastal areas of Fujian Province, and the low-low aggregation areas mainly distributed in the western and central areas. (2) Landscape pattern sensitivity had the highest degree of explanation for the EVI. The main driving factors of the EVI in coastal cities were different from those of the EVI in inland cities. (3) We divided the study area into four categories: high-quality development areas, transformational development areas, ecological-economic synergy areas and ecological function areas. (4) With an increase in the decision-making risk coefficient, the ecological vulnerability of Fujian Province gradually increased. The results of the study provide important guidance for ecological protection and sustainable development in Fujian Province. Moreover, the study framework has reference value for related studies of regional ecological vulnerability evaluation.

Weighted OWA (Ordered Weighted Averaging Operator) Preference Aggregation for Group Multicriteria Decisions

Group decision making is an integral part of operations and management functions in almost every business domain with substantial applications in finance and economics. In parallel to human decision makers, software agents operate in business systems and environments, collaborate, compete and perform algorithmic decision-making tasks as well. In both settings, information aggregation of decision problem parameters and agent preferences is a necessary step to generate group decision outcome. Although plenty aggregation information approaches exist, overcomplexity of the underlying aggregating operation, in most of them, is a drawback, especially for human based group decisions in practice. In this work we introduce an aggregation method for group decision setting, based on the Weighted Ordered Averaging Operator (WOWA). The aggregation is applied on decision maker preferences, following the majority concept to generate a unique set of preferences as input for the decision algorithm. We present the theoretical construction of the model and an application at a group multicriteria assignment decision problem, along with detailed numerical results. The proposed method contributes in the field, as it offers a novel approach that is simple and intuitive, and avoids overcomplexity during group decision process. The method can be also easily deployed into artificial environments and algorithmic decision-making mechanisms.

Entropy and probability based Fuzzy Induced Ordered Weighted Averaging operator

The traditional Ordered Weighting Average (OWA) operator is suitable for aggregating numerical attributes. However, this method fails when the attribute values are given in a linguistic form. In this paper, a novel aggregating method named Entropy and Probability based Fuzzy Induced Ordered Weighted Averaging (EPFIOWA) is proposed for Gaussian-fuzzy-number-based linguistic attributes. A method is first designed to obtain a reasonable weighting vector based on probability distribution and maximal entropy. Such optimal weighting vectors can be obtained under any given level of optimism, and the symmetric properties of the proposed model are proven. The linguistic attributes of EPFIOWA are represented by Gaussian fuzzy numbers because of their concise form and good operational properties. In particular, the arithmetic operations and distance measures of Gaussian fuzzy numbers required by EPFIOWA are given systematically. A novel method to obtain the order-inducing variables of linguistic attribute values is proposed in the EPFIOWA operators by calculating the distances between any Gaussian fuzzy number and a set of ordered grades. Finally, two numerical examples are used to illustrate the proposed approach, with evaluation results consistent with the observed situation.

On the orders of OWA operators

In this paper, we propose a partial ordering ⪯ on the set of ordered weighted averaging (OWA) operators. Based on this relation ⪯, we introduce the negation, conjunction and disjunction operations, and establish a bounded De Morgan lattice equipped with an involutive negation for OWA operators. Finally, we develop a similarity measure between OWA operators based on the ordering ⪯.

A GIS-Based Probabilistic Spatial Multicriteria Roof Water Inrush Risk Evaluation Method Considering Decision Makers’ Risk-Coping Attitude

A combination of geographic information system (GIS) and spatial multicriteria decision making (MCDA) in mine water inrush risk evaluation is widely used, but the randomness in the process of index weight determination and the risk-coping attitude of decision makers are not considered in the decision making process. Therefore, this paper proposes a probability-based roof water inrush risk evaluation method (GIS-MCDA) by combining the Monte Carlo analytic hierarchy process (MAHP) and ordered weighted averaging (OWA) operator. This method uses MAHP to determine the weight of the evaluation indicators, reducing the randomness of the analytic hierarchy process (AHP) to determine the weight of the evaluation indicators using the OWA operator to quantify the five risk-coping attitudes of decision makers and incorporate the risk attitude of decision makers into the evaluation process. Taking the Liangshuijing Coal Mine in northern Shaanxi as an example, the application of the GIS-MCDA method showed that the method makes the risk results of roof water inrush more objective and comprehensive and reduces or avoids the risk of decision making due to human subjective tendency change.

Information Fusion for the Development of a Composite Indicator of Criminogenic Factors Using OWA Operators

In this study, the issue of criminogenic factors in the Lizarzaburu parish of Riobamba-Ecuador is addressed, an area marked by a notable increase in crime. Recognizing the complexity of these factors and the need for an integrated approach for their analysis, the use of Ordered Weighted Averaging (OWA) operators for information fusion is proposed, aiming to create a composite indicator that allows for a holistic and accurate measure of criminality in the area. The implementation of OWA operators facilitates effective weighting of these factors, resulting in the creation of a composite indicator that more faithfully reflects the criminogenic dynamics of Lizarzaburu. This study not only provides a valuable tool for diagnosing crime in urban areas but also establishes a methodological foundation for future research and intervention policies in the field of public security.

An Aggregation Metric Based on Partitioning and Consensus for Asymmetric Distributions in Likert Scale Responses

A questionnaire is a basic tool for collecting information in survey research. Often, these questions are measured using a Likert scale. With multiple items on the same broad object, these codes could be summed or averaged to give an indication of each respondent’s overall positive or negative orientation towards that object. This is the basis for Likert scales. Aggregation methods have been widely used in different research areas. Most of them are mathematical methods, such as the arithmetic mean, the weighted arithmetic mean, or the OWA (Ordered Weighted Averaging) operator. The usual presentation of Likert scale derived data are Mean. This paper presents a new approach to compute an aggregate value that represents Likert scale responses as a histogram adequate to treat better than Mean with asymmetric distributions. This method generates a set of partitions using an approach based on successive division. After every division, each partition is evaluated using a consensus measure and the one with the best value is then selected. Once the process of division has finished, the aggregate value is computed using the resulting partitions. Promising results have been obtained. Experiments show that our method is appropriate for distributions with large asymmetry and is not far from the behavior of the arithmetic mean for symmetric distributions. Overall, the article sheds light on the need to consider other presentations of Likert scale derived data beyond Mean more suitable for asymmetric distributions.

Cloud Risk Management With OWA-LSTM and Fuzzy Linguistic Decision Making

In a cloud environment, the indemnity of service level agreement (SLA) violations has an adverse effect on the service provider. It leads to the penalty fee, credit amount, license extension, and reputation decline that could significantly impact future business outcomes. Existing approaches are unable to handle complex predictions that can accommodate the temporal influence of Quality of Service (QoS) data. Moreover, no method in a cloud environment considers all possible attitudinal behavior of the service provider to mitigate the risk of an actual violation. This article proposes an SLA violation risk mitigation model that uses ordered weighted average (OWA) in long short-term memory for complex QoS prediction. The OWA operator is weighted with a minimax disparity approach to manage the risk of SLA violation. The approach intelligently predicts deviation in custom prioritized QoS parameter and recommend exigency of mitigating action by considering all possible attitudinal behavior of the service provider. This article uses linguistic variables, fuzzy and interval numbers to handle imprecise information. The analysis results demonstrate the applicability and efficiency of the proposed approach to address complex risk mitigation actions.

Exploring 2-rank strategic weight manipulation in multiple attribute decision making and its applications in project review and university ranking

In some real multiple attribute decision making (MADM) problems, sometimes, it is time-consuming and unnecessary to obtain a complete ranking of alternatives, thus, a decision maker would classify the alternatives into two ordered categories, forming a 2-rank MADM problem. Occasionally, a decision maker can manipulate the desired 2-rank results by strategically setting attribute weights. This process is called 2-rank strategic weight manipulation (2RSWM). First, this study defines the 2-rank range of alternatives. Subsequently, several mixed 0–1 linear programming models (MLPMs) are constructed to obtain the 2-rank range and the strategic attribute weight vector of the desired 2-rank result of the alternative(s) of the decision maker. Furthermore, we provide conditions for the existence of the strategic attribute weight vector based on the 2-rank range of the alternatives and the proposed MLPMs. Finally, two illustrative examples and two simulation experiments are conducted to validate the effectiveness of our proposed models. Due to the ordered weighted averaging (OWA) operator having smaller average width of the 2-rank range, and a larger minimum distance between the impersonal and strategic attribute weight vectors, we argue that the OWA operator has a better performance than the weighted averaging (WA) operator in defending against 2RSWM.

Beta-Bézier OWA operator

Determination of associated weight vectors for an ordered weighted averaging (OWA) operator is always a crucial issue, and for this purpose, several weight vector determination models have been introduced in the literature. In this article, we propose a new biparametric OWA operator, called a “beta-Bézier OWA operator”. The beta-Bézier OWA operator provides an infinite number of weight vectors for a fixed degree of orness. The orness value of this class of OWA operators is its most essential characteristic, which always depends on one of its parameters, and can be prefixed according to the decision-maker choice and also irrespective of the number of arguments aggregated. The optimum OWA weight vector can be calculated without solving a complicated optimization problem. It becomes the same as several other OWA operators at particular values of parameters. The maximum Bayesian entropy OWA operator weight vector is measured with use of the proposed OWA operator for a given level of optimism/pessimism (orness). It is also compared with many other OWA operators.

Expert system and entropy‐ordered weighted average method in cold supply chain risk evaluation

AbstractIf not well identified and controlled, risks in systematically engineered cold supply chains can lead directly to food safety incidents. In current approaches to cold supply chain risk evaluation, there is a lack of systematic classification and quantitative analysis of the influences of risk factors in the chain. To accurately evaluate unknown risks that can exert a fluctuating influence and result in great losses, this study builds a knowledge base of expert systems based on expertise and extensive experience and modifies the expert weights in conjunction with entropy weights to reduce subjective error. An ordered weighted average (OWA) operator is used to evaluate risk in a cold supply chain effectively. First, in combination with a case study of a typical fresh food e‐commerce enterprise, a typical fresh food e‐commerce enterprise, this paper identifies the risks in a food refrigeration supply chain. Second, relying on an expert group with professional knowledge and rich experience, an expert system knowledge base is constructed, risks are assigned, and the expert weight is modified in combination with the entropy weight method. Finally, based on the OWA operator, the modified risk assignment is effectively evaluated, and the risk value is obtained and sorted. Specific risk control measures are put forward according to the results of the calculation. The results show that an evaluation method combining an expert system knowledge base and the entropy‐OWA method can effectively depict and process the evaluation information needed for risk rankings and solve the problems of supply chain risks more rapidly and effectively.