Ordered Weighted Averaging Research Articles

Probabilistic Risk Assessment for Data Rate Maximization in Unmanned Aerial Vehicle-Assisted Wireless Networks

The evolution of beyond fifth generation (B5G) wireless networks poses significant technical and economic challenges across urban, suburban, and rural areas, demanding increased capacity for users whose positions continually change. This study investigated the dynamic positioning of an unmanned aerial vehicle (UAV), acting as a mobile base station (MoBS) to enhance network efficiency and meet ground terminals (GTs) expectations for data rates, particularly in emergency scenarios or temporary events. While UAVs show great promise, existing research often assumes certainty in network architecture, overlooking the complexities of unpredictable user movements. We introduce a decision-making framework utilizing the ordered weighted averaging (OWA) operator to address uncertainties in GT locations, enabling the optimization of UAV trajectories to maximize the overall network data rate. An optimization problem is formulated by modeling GT dynamics through a Markov process and discretizing UAV movements while accounting for communication thresholds and movement constraints. Extensive simulations reveal that our approach significantly improves expected data rates by up to 48% compared to traditional fixed base stations (BSs) and predefined UAV movement patterns. This research underscores the potential of UAV-assisted networks to bolster communication reliability while effectively managing dynamic user movements to maintain optimal quality of service (QoS).

Urban growth simulation guided by ecosystem service trade-offs in Wuhan metropolitan area: Methods and implications for spatial planning

The effective integration of ecosystem services (ESs) and urban growth simulation is crucial for spatial planning decisions that support sustainable and high-quality development. Interactions (i.e., trade-offs, synergies, and irrelevance) generally exist among ESs, however, few studies have been done on the methodology for simulating urban growth that optimizes the synergistic effect of ESs. In this study, the Wuhan metropolitan area was taken as the research area. Four key ESs in 2000, 2010, and 2020: water yield (WY), carbon storage (CS), habitat quality (HQ), and soil retention (SR) were evaluated by using the InVEST model. Then the ordered weighted averaging (OWA) method was applied to optimally allocate ESs trade-offs and identify ecological priority protection areas (EPPAs). Finally, the PLUS model was used to simulate urban growth scenarios under different levels of ESs protection constraints and propose spatial planning strategies. The results revealed the following. (1) From 2000 to 2020, the three ESs (i.e., WY, CS, and HQ) exhibited the spatial distribution pattern with high in the east and low in the west, and higher in the woodland than in built-up areas, except SR, which remained at a weak level throughout the region. (2) During the 20 years, SR and the other three ESs, HQ and CS showed a synergistic relationship; WY exhibited a very weak trade-off with HQ; and WY and CS changed from a very weak trade-off to a weak synergy. (3) Seven ecosystem service patterns (ESPs) were generated, and ESP 5 was compared as the ideal option. The weights of SR, WY, CS, and HQ in this pattern were 0.063, 0.187, 0.313, and 0.437, respectively. (4) By 2030, the built-up areas will exhibit edge expansion and interconnection development trends, with the high-constraint ecological protection scenario as the most compact mode, and the spatial structure of “two districts, one axis, four cities as one” is consistent with the development tendency. Our findings can help to enrich the method of urban growth management oriented by ecological protection, and provide a scientific basis for ecological environment restoration and land use spatial planning practices.

Evaluation of ecological network resilience using OWA and attack scenario simulation in the Gansu section of the Yellow River Basin, NW China

Regional ecosystem quality has been rapidly declining as a result of rapid urbanization, which has also fragmented landscapes and reduced ecosystem connectedness. Strengthening ecological network resilience helps improve the ecological environment’s quality, protect biodiversity, and maximize ecological benefits. To quantitatively assess ecological network resilience based on 2020 data, we have selected the Gansu region of the Yellow River Basin as a case study in this study due to its significant ecological condition and sensitive vulnerability. Firstly, based on four ecosystem services (ESs)—water yield, carbon storage, soil conservation, and habitat quality—the ordered weighted averaging (OWA) method is introduced to determine ecological sources by calculating ordered weights under different risk coefficients to weigh multiple ESs. Two node attack simulations—random attack and deliberate attack—are used for quantitatively evaluating ecological network resilience, which can simulate the impact of external interference. The concept of a resilience threshold is introduced into the evaluation process of network resilience to improve the objectivity and accuracy of results. The findings indicate that (1) 156 ecological corridors spanning a total distance of 6,569.3 km and 73 ecological sources totalling 20,840 km2 were found in the study area. These findings generally demonstrate a concentrated and contiguous configuration in the southwestern region and a broken and scattered configuration in other regions. (2) With a mean degree of 4.27, a mean path length of 4.08, and a clustering coefficient of 0.47, an undirected and unweighted complex network with improved connectivity and no discernible clustering characteristics was established. (3) The ecological network is more resilient to perturbations from natural disasters when compared to assault simulations in two scenarios; the resilience threshold is 0.34. Considering the final results of node global features and resilience curves, ecological protection suggestions are proposed.

Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems

Objectives: To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. Methods: A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The proposed improved class of aggregation operators will aggregate the IFS matrix data sets appearing in the form of matrices and then the revised input vectors which is then fed into the ANN algorithm following Delta, Perceptron, and Hebb Learning Rule for the next phase. Findings: Aggregating the Intuitionistic Fuzzy set information or data in today’s digital world is a tedious task in the field of MAGDM problem-solving. In this work, two new classes of operators for aggregating the data sets are proposed namely the IM-IFWAA operator and the IM-IFOWA operator which will improve the performance of the ANN. Necessary theorems for the proposed operators are proved to provide consistency of the same. The input created using the aforementioned operators is then fed into the novel ANN algorithm for further computations. Varieties of learning rules are then engaged for ranking of the best alternative for the decision problem. The developed theory is supported by a numerical example which is computed using all the proposed techniques. Novelty: Most of the research done on Intuitionistic Fuzzy Artificial Neural Network models are based on learning rules or using some other calculations. The proposed methods of using novel and improvised aggregation operators for ANN are used to find the inputs for ANN where varieties of learning rules for ANN are employed for effective decision analysis. Keywords: ANN, Learning Rules, MAGDM, Intuitionistic Fuzzy Sets, Weighted Aggregation Operator

Associated Probabilities’ Aggregations in Fuzzy Collaborative Filtering Recommender System Prediction

AbstractIn this article, the expert evaluations transformed in the multi-attribute decision-making (MADM) model are presented in the discrimination q-rung picture linguistic fuzzy numbers (q-RPLFNs). In the construction of a second-order additive fuzzy measure (TOAFM) the attributes’ interaction indexes and Shapley values are taken into account. The Shapley entropy maximum principle for identification of associated probabilities class (APC) of a TOAFM is constructed. Based on the APC of the TOAFM, a new aggregation operators’ class is constructed which represents some hybrid extensions of ordered weighted averaging (OWA), geometric (OWG), the Choquet integral averaging (CA) and geometric (CG) operators under discrimination q-rung orthopair fuzzy (q-ROF) and q-rung picture linguistic fuzzy (q-RPLF) information. These operators, constructed for the q-RPLF and q-ROF environments, take into account the overall pair interactions among attributes. Main properties on the correctness of extensions are proved: for the lower and upper capacities of order 2, all constructed operators consequently coincide with q-ROF and q-RPLF Choquet averaging and geometric operators, respectively. Constructed operators in the evaluation of prediction of fuzzy Collaborative Filtering Recommender Systems (CFRS) are used. New symmetric discrimination measures as some extensions of discrimination measures for the fuzzy CFRS are proposed. Users’ profile data by the constructed operators in the new similarity measure under q-rung picture linguistic environment are aggregated. The developed new approach is schematically described in such a way that it can be “embedded” in any existing CFRS model. An example is given to illustrate the results, for which the software designed to aggregate profile data for similarity comparison provides the use of new and well-known classical aggregation operators.

A three-step modification of the DRASTIC model using spatial multi criteria decision making methods to assess groundwater vulnerability

Groundwater vulnerability assessment, as a key tool, is essential for assisting decision-makers and experts in identifying highly vulnerable areas and devising efficient pollution reduction strategies. The widely utilized DRASTIC model for assessing groundwater vulnerability incorporates seven key geological and hydrological parameters. To address the limitations of the DRASTIC model, this study proposes a novel three-step modification by introducing an extra parameter, adjusting default weights, and utilizing alternative aggregation methods. These modifications aim to capture the unique characteristics of a specific region more accurately. The first step involves incorporating the Land Use (LU) parameter as the eighth parameter in the DRASTIC model, resulting in an updated 8-parameter model. The second step involves integrating the Analytic Hierarchy Process (AHP) to adjust parameter weights based on input from local experts. Lastly, while the Weighted Linear Combination (WLC) technique has conventionally been used for aggregating layers in the GIS environment, this study suggests employing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Furthermore, to consider decision makers' risk attitudes, the Ordered Weighted Averaging (OWA) method is utilized.To assess its effectiveness, the modified model was applied to Khoy County in Iran. Then, the results were compared to the DRASTIC model using correlation analysis based on nitrate concentrations. The results indicated a correlation coefficient of 0.67 for the modified model compared to 0.47 for the DRASTIC model. This suggests that the proposed modified model is an enhanced and highly effective approach for evaluating groundwater vulnerability.

A Fuzzy Decision Support System for Risk Prioritization in Fine Kinney-based Occupational Risk Analysis

Analyzing Occupational Health and Safety (OHS) risks requires prioritizing risk, a vital step in hazard and effect analysis (HEA). Currently, there is no existing approach to determine the priority of risk in HEA-based occupational risk analysis that incorporates interactive risk factors and spherical fuzzy risk information. This paper presents a novel approach to address the constraints by introducing a fresh framework for evaluating job-related hazards using HEA by combining the spherical fuzzy set (SFS), the multi-attributive border approximation area comparison (MABAC) technique, and the Ordered Weighted Averaging (OWA) operator, a more sophisticated approach is achieved within this framework. The SFS is utilized in this framework to depict the more ambiguous and unsure data given by specialists, offering a more efficient approach to handling the fuzzy risk information, encompassing the non-membership degree and hesitation. In addition, an advanced MABAC method is used to prioritize occupational risk. Afterward, we provide a practical instance of utilizing the MABAC technical-oriented risk prioritization approach for evaluating potential occupational dangers in risk analysis.

A Generalized Family of Constant Orness Ordered Weighted Averaging Operators

A Generalized Family of Constant Orness Ordered Weighted Averaging Operators

A multiple attribute group decision making model based on 2-tuple linguistic pythagorean fuzzy dombi aggregation operators for optimal selection of potential global suppliers

Multiple-Attribute Group Decision-Making (MAGDM) is a significant area of research in decision-making, and its principles and methodologies are widely implemented. A Pythagorean Fuzzy Set (PFS) is an extension of an Intuitionistic Fuzzy Set (IFS) that is highly valuable for representing uncertain information in real-world scenarios. The 2-Tuple Linguistic Pythagorean Fuzzy Number (2TLPFN) is a specific type of Pythagorean Fuzzy Number (PFN) that can be used to represent uncertainty in real-world decision making through the use of 2-Tuple Linguistic Terms (2TLTs). This paper focuses on the examination of Multiple Attribute Group Decision Making (MAGDM) using 2TLPFNs. Dombi's t-norm and t-conorm operations were commonly referred to as Dombi operations, which might have been greater degree of applicability if offered in a new form of flexibility within the general parameter. In this research, we implement Dombi operations to construct some 2-Tuple Linguistic Pythagorean Fuzzy (2TLPF) Dombi Aggregation operators. These operators include the 2TLPF Dombi Weighted Averaging (2TLPFDWA) operator, 2TLPF Dombi Ordered Weighted Averaging (2TLPFDOWA) operator, 2TLPF Dombi Weighted Geometric (2TLPFDWG) operator, and 2TLPF Dombi Ordered Weighted Geometric (2TLPFDOWA) operator. An analysis is conducted to examine the unique characteristics of these suggested operators. Subsequently, we leveraged the proposed operators to develop a model aimed at tackling the MAGDM problems in the 2TLPF environment. Eventually, a suitable instance has been demonstrated to validate the formation of the model as well as exhibit its implementation and resilience.

Preparation of Green Sustainable Cement Paste Mixture Based on Inorganic Additives: An Experimental and Modelling Approach

Using waste materials in the mixture of building materials is an approach aligned with the circular economy, a viewpoint that creates sustainable building industries, especially in developed countries. This study concentrated on the application of laponite (LAP), fly ash (FA), and bentonite (BENT) materials in the mixture of cement pastes. The first step used experimental practices to examine the metrics of toughness, three-point bending, and compressive strength with different percentages of added LAP, FA, and BENT after the characterization of samples by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS). The next step entailed assessment of cement paste specifications through some regressive equations obtained by the application of 2D curve fitting and sensitive analysis of additive (FA, LAP, and BENT) fluctuations in the structure of cement paste. The results show that linear polynomial equations are the best for the evaluation of cement paste terms as per different percentages of the additives. The environmental impact assessment (EIA) of nine prepared samples demonstrated that LAP created the safest condition in comparison to others. However, the ordered weighted averaging (OWA) computations applied for the sustainability assessment (SA) of the samples showed that the LAP is the most appropriate option for use in the structure of cement paste. Using experimental analysis and mathematical modeling, the behavior of cement paste interacting with mineral additives is evaluated. Sustainable mixtures are then presented based on EIA.

A Consensus-Based 360 Degree Feedback Evaluation Method with Linguistic Distribution Assessments

The 360 degree feedback evaluation method is a multidimensional, comprehensive assessment method. Evaluators may hesitate among multiple evaluation values and be simultaneously constrained by the biases and cognitive errors of the evaluators, evaluation results are prone to unfairness and conflicts. To overcome these issues, this paper proposes a consensus-based 360 degree feedback evaluation method with linguistic distribution assessments. Firstly, evaluators provide evaluation information in the form of linguistic distribution. Secondly, utilizing an enhanced ordered weighted averaging (OWA) operator, the model aggregates multi-source evaluation information to handle biased evaluation information effectively. Subsequently, a consensus-reaching process is established to coordinate conflicting viewpoints among the evaluators, and a feedback adjustment mechanism is designed to guide evaluators in refining their evaluation information, facilitating the attainment of a unanimous evaluation outcome. Finally, the improved 360 degree feedback evaluation method was applied to the performance evaluation of the project leaders in company J, thereby validating the effectiveness and rationality of the method.

A dynamic model for performance evaluations: an integrated approach based on P-AHP and aggregation operators

PurposeMulti-criteria methods represent an adequate tool for solving complex decision problems that provide real support to the decision maker in the choice process. This paper analyzes a decision problem that recurs over time using one of the newer methods as the Parsimonious AHP.Design/methodology/approachIn this paper we integrated the P-AHP with: (1) the weighted average which takes into account the objectivity of the data; (2) ordered weighted average (OWA) aggregation operators that address the subjective nature of the data; (3) the Choquet integral and (4) the Sugeno integral which also considers the uncertain nature of the final ranking as it is defined on a fuzzy measure.FindingsThe present paper proves that variations in the final ranking, due to the different mathematical properties of the selected aggregators, are fundamental to select the best alternative without neglecting any characteristic of the input data. In fact, it is discussed and underlined how and why the best alternative is one that never excels but has very good positions with respect to all aggregation operator rankings.Originality/valueThe aim and innovation presented in this work is the use of the Parsimonious AHP (P-AHP) method in a dynamic way with the use of different aggregation techniques.

On linear combinations of binomial OWA functions

We consider the binomial decomposition of ordered weighted averaging (OWA) functions proposed by Calvo and De Baets (1998) in the framework of Choquet integration. Our aim in the paper is to further investigate the equivalence between the two representations of OWA functions involved in the binomial decomposition: the usual canonical representation in terms of the order statistics, and the binomial representation in terms of the binomial OWA functions. We describe and discuss in detail the linear transformations that relate the coefficients of these two equivalent representations: the original expression of the weights in terms of the coefficients of the binomial representation, and its inverse, the expression of those coefficients in terms of the weights. In both cases simple and direct proofs are presented. Moreover, we consider the linear transformations between the two representations in the general linear algebra framework of unconstrained linear combinations of binomial OWA functions. In this perspective we obtain compact matrix expressions for the linear transformations, which also offer new insight on the geometry of the coefficient constraints in the binomial representation of OWA functions.

The Advantages of the OWA (Ordered Weighted Averaging) Method in Decision Making and Reliability Testing of Spatial Multi-Criteria Site Selection (SMCSS) Model

The Advantages of the OWA (Ordered Weighted Averaging) Method in Decision Making and Reliability Testing of Spatial Multi-Criteria Site Selection (SMCSS) Model

FORECASTING THE REAL AVERAGE RETIREMENT BENEFIT IN THE UNITED STATES USING OWA OPERATORS

The issue of pensions has become increasingly topical. This paper presents the ordered weighted averaging real average pension (OWARAP) operator. The OWARAP operator is based on the ordered weighted averaging (OWA) operator and calculates the future average retirement benefit taking into account price changes. Moreover, this work extends the OWARAP operator by using order-inducing variables, generalized means, and probabilities. This paper ends by analyzing the applicability of the OWARAP operator and its extensions in forecasting the real average Social Security benefits for retired workers in each state of the United States (U.S.). The results demonstrate the usefulness of the proposed approach in retirement decision making.

Flexible-dimensional L-statistic for mean estimation of symmetric distributions

Estimating the mean of a population is a recurrent topic in statistics because of its multiple applications. If previous data is available, or the distribution of the deviation between the measurements and the mean is known, it is possible to perform such estimation by using L-statistics, whose optimal linear coefficients, typically referred to as weights, are derived from a minimization of the mean squared error. However, such optimal weights can only manage sample sizes equal to the one used to derive them, while in real-world scenarios this size might slightly change. Therefore, this paper proposes a method to overcome such a limitation and derive approximations of flexible-dimensional optimal weights. To do so, a parametric family of functions based on extreme value reductions and amplifications is proposed to be adjusted to the cumulative optimal weights of a given sample from a symmetric distribution. Then, the application of Yager’s method to derive weights for ordered weighted average (OWA) operators allows computing the approximate optimal weights for sample sizes close to the original one. This method is justified from the theoretical point of view by proving a convergence result regarding the cumulative weights obtained for different sample sizes. Finally, the practical performance of the theoretical results is shown for several classical symmetric distributions.

Pearson Correlation and Ordered Weighted Average Operator in The World Stock Exchange Market

Due to the large number of transactions carried out in the stock market, it becomes of great importance for the financial development of a country. Analyzing the correlation between indices in the world helps us to know the way towards the variables that impact. This paper proposes the use of ordered weighted average (OWA) operators in combination with Pearson Coefficient to create a measure of correlation that can analyze a wide range of possible scenarios that go minimum to maximum. The new frameworks can add additional information to the process of correlation. The work presents an application in ten of the largest stock exchanges in the world. The results suggest a broad positive correlation between them that is reinforced in times of instability.

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.

Evaluating the feasibility of constructing shopping centers on urban vacant land through a spatial multi-criteria decision-making model

Shopping centers are among the major economic and commercial places in cities in terms of social function, urban sustainability, environment, etc. Therefore, it is crucial to determine suitable locations for building new shopping centers. In this regard, urban vacant lands can be considered as high-potential locations to transform the urban landscape and enhance socio-economic development. The main purpose of this study is to assess the potential of urban vacant lands based on a spatial multi-criteria decision-making (SMCDM) system for building shopping centers in 22 districts of Tehran. In this study, first, 16 effective spatial criteria for locating the new shopping centers were identified using expert opinions and a literature review. The best-worst method (BWM) and the Min/Max method were used to calculate the weight and standardized values of each criterion. Then, the ordered weighted averaging (OWA) method was used to prepare a potential map of urban vacant lands for the construction of a shopping center under different decision-making scenarios, including very optimistic, optimistic, intermediate, pessimistic, and very pessimistic. Finally, the spatial distribution of potential locations in the 22 districts of Tehran was investigated. The results showed that among the different criteria, the distance from the highway networks and distance from public transportation stations had the most weight, whereas the distance from fault and distance from stream networks had the least weight. The number of vacant lands with a very high potential for building a shopping center in Tehran based on very pessimistic, pessimistic, intermediate, optimistic and very optimistic scenarios was obtained at 29, 95, 105, 122, and 224, respectively. An increase in the degree of optimism in the attitude of decision-makers or investors increased the number of available options in the very high potential category. Under all scenarios, all vacant lands in 10 of Tehran’s 22 districts with very high potential for building shopping centers. The results of the proposed model in this study can be useful and practical for a wide range of planners, decision-makers, and investors with different mental attitudes and risk tolerance. Close attention to these results can contribute to achieving sustainable urban development.