Ordered Weighted Averaging Method Research Articles

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

A hybrid GIS-MCDM approach for multi-level risk assessment and corresponding effective criteria in optimal solar power plant.

This study aims to propose a hybrid method for suitability assessment with different risk levels to construct solar power plants (CSPPs) in southern Iran. The fuzzy-analytic hierarchy process (AHP) and fuzzy were applied to forecast and determine the suitable location for CSPPs. To extract suitable location maps with different risk levels for CSPPs, ordered weighted averaging (OWA) was implemented. In addition, the best subset regression method was used to determine the most effective factors in CSPPs. Based on the results of the fuzzy-AHP method, 42% of the southern regions of the area was suitable for CSPPs. Based on the results of the OWA method, the most suitable areas were located in the north and south in all of the risk areas with increasing values. The results demonstrated that the FCM and sub-clustering approaches can accurately predict land suitability classes (LSCs) for CSPPs. Moreover, the best subsets regression (BSR) results showed that distance to power transmission line (PTL) and temperature exhibited the strongest correlation. Finally, receiver operating characteristics (ROC) were used to determine the accuracy of these methods. The results showed that the area under the curve (AUC) values were highly accurate (AUCFuzzy-AHP = 85.0%, AUCOWA = 83.0%).

Spatial priorities for biodiversity and ecosystem services considering theoretical decision-makers’ attitudes to risk

Choosing appropriate spatial priorities for protected areas (PAs) to conserve ecosystem services (ESs) and biodiversity is a challenge for decision makers under limited land resources, especially when facing uncertain protection consequences or conflicting protection objectives. Attitudes toward risk will influence actions, which will, in turn, impact consequences. To understand how theoretical decision-makers’ attitudes towards risk impact protection effectiveness for biodiversity and ESs (e.g., water retention, soil retention, flood mitigation, water purification and carbon sequestration) and how this information can be integrated into effective PAs management, we examined Hainan Island as a case study. We used the ordered weighted averaging (OWA) algorithm to assess the impact of attitude towards risk in PA management. Decision-makers’ attitude towards risk scenarios (from risk-averse and risk-taking) showed higher mean protection effectiveness (2.41–2.85) than existing PAs (2.37), indicating that there is still room for improvement in biodiversity and ESs conservation in existing PAs. In addition, among the seven examined risk scenarios, the higher risk aversion scenario showed the best outcome. In comparison to existing PAs, this scenario improved mean protection effectiveness (20.13%) as well as the protection effectiveness of water retention (24.84%), water purification (11.46%), flood mitigation (8.84%), soil retention (16.63%), carbon sequestration (5.31%), and biodiversity (12.84%). Thus, our research shows that the influence of theoretical decision-makers’ attitudes towards risk could be considered by OWA method which could provide a normative model of what the right choice given theoretical risk attitudes is while selecting priority area for biodiversity and ESs.

Developing a GIS-Based Decision Rule for Sustainable Marine Aquaculture Site Selection: An Application of the Ordered Weighted Average Procedure

Fish consumption is on the increase due to the increase in growth of the global population. Therefore, taking advantage of new methods such as marine aquaculture can be a reliable source for the production of fish in the world. It is necessary to allocate suitable sites from environmental, economic, and social points of view in the decision-making process. In this study, in order to specify suitable areas for marine aquaculture by the Ordered Weighted Averaging (OWA) methodology in the Caspian Sea (Iran), efforts were made to incorporate the concept of risk into the GIS-based analysis. By using the OWA-based method, a model was provided which can generate marine aquaculture maps with various pessimistic or optimistic strategies. Eighteen modeling criteria (14 factors and 4 constraints) were considered to determine the appropriate areas for marine aquaculture. This was done in 6 scenarios using multi-criteria evaluation (MCE) and ordered weighted average (OWA) methodologies. The results of the sensitivity analysis showed that most of the parameters affecting the marine aquaculture location in the region were as follows: Social-Economic, Water Quality, and Physical–Environmental parameters. In addition, based on Cramer’s V coefficient values for each parameter, bathymetry and distance from the coastline with the most effective and maximum temperature had the least impact on site selection of marine aquaculture. Finally, the final aggregated suitability image (FASI) of weighted linear combination (WLC) scenario was compared with existing sites for cage culture on the southern part of the Caspian Sea and the ROC (Relative Operating Characteristics) value turned out to be equal to 0.69. Although the existing sites (9 farms) were almost compatible with the results of the study, their locations can be transferred to more favorable areas with less risk and the mapping risk level can be controlled and low- or high-risk sites for marine aquaculture could be determined by using the OWA method.

Corneal nerve tortuosity grading via ordered weighted averaging-based feature extraction.

Tortuosity of corneal nerve fibers acquired by in vivo Confocal Microscopy (IVCM) are closely correlated to numerous diseases. While tortuosity assessment has conventionally been conducted through labor-intensive manual evaluation, this warrants an automated and objective tortuosity assessment of curvilinear structures. This paper proposes a method that extracts the image-level features for corneal nerve tortuosity grading. For an IVCM image, all corneal nerve fibers are first segmented and then, their tortuosity are calculated by morphological measures. The ordered weighted averaging (OWA) approach, and the k-Nearest-Neighbor guided dependent ordered weighted averaging (kNNDOWA) approach are proposed to aggregate the tortuosity values and form a set of extracted features. This is followed by running the Wrapper method, a supervised feature selection, with an aim to identify the most informative attributes for tortuosity grading. Validated on a public and an in-house benchmark data sets, experimental results demonstrate superiority of the proposed method over the conventional averaging and length-weighted averaging methods with performance gain in accuracy (15.44% and 14.34%, respectively). The simultaneous use of multiple aggregation operators could extract the image-level features that lead to more stable and robust results compared with that using average and length-weighted average. The OWA method could facilitate the explanation of derived aggregation behavior through stress functions. The kNNDOWA method could mitigate the effects of outliers in the image-level feature extraction.

Mobile Phone Recommender System Using Information Retrieval Technology by Integrating Fuzzy OWA and Gray Relational Analysis

With the advancement and diversification of information retrieval technology, such technology has been widely applied in recent years in personalized information recommender systems (RSs) and e-commerce RSs in addition to data-mining applications, especially with respect to mobile phone purchases. By integrating the weights of fuzzy ordered weighted averaging (OWA) and gray relational analysis, this research calculated the recommended F1 indices of three weight calculation methods to be 20.5%, 14.36%, and 16.43% after an examination by 30 experimenters. According to the operational results attained by the 30 experimenters, the recommended products obtained by the fuzzy OWA and gray relational analysis calculation method covered the products recommended by the other two weight calculation methods with a higher recommendation effect.

A Spatially Explicit Multi-Criteria Analysis Method on Solving Spatial Heterogeneity Problems for Flood Hazard Assessment

Flood hazard assessment and mapping of flood prone area are of great importance for flood management, as well as the reduction of potential losses of life and property caused by flooding. In this study, a spatially explicit multi-criteria analysis approach which emphasizes on spatial heterogeneity in decision-making process is developed for flood hazard assessment, and it has been applied to the area including Hanyang, Caidian and Hannan of Wuhan, China, where flood events occur frequently. Factors associated with flood mechanism and characteristics of the watershed itself were selected, and primary analysis was implemented to make the factors concise and essential. This paper emphasized the spatial heterogeneity problem in flood hazard assessment by incorporating spatial ordered weighted averaging (OWA) method into windows-based local spatial multi-criteria analysis (MCA). On one hand, the local normalization was applied to normalize the criteria, and entropy-based local criteria weights were calculated to adjust the criteria weight at local level. On the other hand, spatial OWA method with spatially variable risk preference was applied to assign different order weights at different locations. The results indicate that the proposed approach focused on the flood hazard at local level, and the flood hazard map presented more dispersive distribution of the high and very high hazard area than that derived by global MCA. Furthermore, flood hazard in important and unimportant area was distinguished by paying more attention to the former one. And the distribution of high hazard area tends to be mainly located in populated and developed areas.

Integrated flood hazard assessment based on spatial ordered weighted averaging method considering spatial heterogeneity of risk preference

Flood is the most common natural hazard in the world and has caused serious loss of life and property. Assessment of flood prone areas is of great importance for watershed management and reduction of potential loss of life and property. In this study, a framework of multi-criteria analysis (MCA) incorporating geographic information system (GIS), fuzzy analytic hierarchy process (AHP) and spatial ordered weighted averaging (OWA) method was developed for flood hazard assessment. The factors associated with geographical, hydrological and flood-resistant characteristics of the basin were selected as evaluation criteria. The relative importance of the criteria was estimated through fuzzy AHP method. The OWA method was utilized to analyze the effects of different risk attitudes of the decision maker on the assessment result. The spatial ordered weighted averaging method with spatially variable risk preference was implemented in the GIS environment to integrate the criteria. The advantage of the proposed method is that it has considered spatial heterogeneity in assigning risk preference in the decision-making process. The presented methodology has been applied to the area including Hanyang, Caidian and Hannan of Wuhan, China, where flood events occur frequently. The outcome of flood hazard distribution presents a tendency of high risk towards populated and developed areas, especially the northeast part of Hanyang city, which has suffered frequent floods in history. The result indicates where the enhancement projects should be carried out first under the condition of limited resources. Finally, sensitivity of the criteria weights was analyzed to measure the stability of results with respect to the variation of the criteria weights. The flood hazard assessment method presented in this paper is adaptable for hazard assessment of a similar basin, which is of great significance to establish counterplan to mitigate life and property losses.

Siting MSW landfills using MCE methodology in GIS environment (Case study: Birjand plain, Iran)

The rapid municipal solid waste growth of Birjand plain causes to find an appropriate site selection for the landfill. In order to reduce the negative impacts of waste, the use of novel tools and technologies to gain a suitable site for landfill seems imperative. The present paper aimed to exhibits the Multi Criteria Evaluation (MCE) for the landfill site selection of the Birjand plain because till date a suitable action has not been implicated. In the present research, the parameters such as environmental and socio-economical factors have been used. The factors like slope, water resources, soil parameters, landuse, fault and protected areas in the model of effective environmental criteria and the factors viz. distance from road, urban areas, village, airport, historical place, and industries in the model of socio-economic criteria were investigated and with the use of Weighted Linear Combination (WLC) and Analytical Network Process (ANP) models were compounded and according to the Ordered Weighted Averaging (OWA) and Fuzzy Linguistic Quantifier (LQ) were aggregated. The paper focuses on the OWA method as well as an approach for integrating Geographic Information System (GIS) and OWA. OWA has been developed as a generalization of multi-criteria combination. In this study we attained comparable data via the technique of ANP and five scenarios of OWA method were used. The results of field studies, fifth scenario for the study area proposed. Based on the research findings, OWA method had a great potential and flexibility in the modeling of the complex decision-making problems.

A combined OWA–DEA method for dispatching rule selection

Dispatching rule selection is an important issue in dynamic scheduling of production systems. When there are multiple performance criteria, identification of the most efficient dispatching rule is not an easy task. This paper considers an ordered weighted averaging (OWA) methodology combined with a data envelopment analysis (DEA) model for identifying the best dispatching rule in a flowshop environment. Standard DEA cannot be used directly, due to ambiguity in the inputs and outputs that may be specified in the flowshop scheduling problem. To overcome this drawback, an OWA method is used to first assess the dispatching rules, measured in terms of multiple factors, for different decision making optimism levels. This is followed by using a DEA model to aggregate the OWA assessments, in order to identify the dispatching rule(s) with the best overall performance. A computational analysis is performed by using randomly generated test problems, and different scenarios involving different factor priorities. The results demonstrate that the proposed OWA–DEA approach successfully identifies which dispatching rules are efficient, and which are not.

Ecohydrologically Driven Catchment Evaluation and Prioritization

This study develops information based on index, and termed hydro-ecological-index, to represent the need of a riverine ecosystem characterized through a biologically relevant flow regime. The flow regime is defined by a set of parameters, called Indicators of Hydrologic Alteration. These parameters are predicted at the catchment scale by a hydrologic model, called Soil and Water Assessment Tool. Then the Maximum Entropy Ordered Weighted Averaging method is employed to aggregate non-commensurable biologically relevant flow regimes to develop hydro-ecological- index at the catchment scale. The resulting index reflects the variability of the need of the riverine ecosystem at catchment scale and thus different catchments can be evaluated and compared.

Application of the Ordered Weighted Averaging (OWA) method to the Caspian Sea conflict

This study proposes a promising allocation mechanism of the Caspian Sea natural resources, which are presently shared among five countries. To date, these nations have been unable to reach an allocation agreement. We apply a methodology to propose the most appropriate solution under different risk attitudes of the states. This research is different from other studies regarding the Caspian Sea negotiations in that it employs risk-based fuzzy multi attribute decision making methods for simulating the risk attitudes or optimism/pessimism degrees of the decision makers. The ordered weighted averaging (OWA) approach, which considers the optimism/pessimism degree quantitatively, is used to take into account the effects of different risk attitudes of the negotiators on the final outcome. We demonstrate how one could obtain a range of alternatives under different multi attribute and risk attitudes. The induced OWA (IOWA) method is also used to determine the relative power of these states bordering the Caspian Sea by considering several attributes, including different risk attitudes of agents. Results indicate that taking into account the risk attitude (prone, neutral, averse) of the states can affect the overall ranking of the proposed solutions. The findings from this study may facilitate negotiation regarding the most preferred allocation mechanism for the Caspian Sea.

The use of ordered weighted averaging method for decision making under uncertainty

AbstractA decision making under uncertainty (DMUU) prevails at the outset and often evolves into a decision making under partial uncertainty as information on the states of nature, for example, a probability distribution, is advanced. Many methods have emerged for solving the DMUU problems, which includes the classical decision criteria and the domain criterion. Yager (1988) introduced a new approach, the so‐called ordered weighted averaging (OWA) as a viable method for solving the DMUU problems. The OWA weights to be used in the aggregation are generated under the degree of optimism provided by a decision maker and then combined with the reordered payoffs to produce aggregated payoffs for each strategy. The reordering process, one of the characterizing features of the OWA method, enables us to perform various types of aggregations including maximax, maximin, and Hurwicz‐α index in conjunction with the generated weights. The OWA method obviously extends the Hurwicz approach by taking into account the tradeoffs among the entire payoffs while the Hurwicz approach considers a tradeoff only between the two extremes, the maximum and the minimum payoffs. In this paper, we examine the features of the OWA method in light of Milnor's set of requirements for reasonable decision criteria, thus providing a solid methodological foundation for the DMUU. The OWA method can also be used to solve a group DMUU problem by exploiting individual decision results in the situation when the use of a fuzzy majority is advocated.

OWA Analysis for Ecological Capability Assessment in Watersheds

Fuzzylogic computes a multi-criteria evaluation by means of either a Boolean analysis, WeightedLinear Combination (WLC) and Ordered Weighted Averaging (OWA) of factor images. OWA works withstandardized factor images and employs a variant of the WLC. It takes into account the risk associated withthe decision and degree of tradeoff associated with the variables in the analysis. In this research, for Ecological Capability Assessment and watersheds management in study area, we have studied 22 biological and physiological factors. For ecological capability evaluation, the method of OWA was deployed. This method involves criterion weights and order weights. The generality of OWA is related to its capability to implement different combination operators by selecting appropriate order weights. By specifying suitable order weights, it is possible to change the form of aggregation from the minimum-type combination through all intermediate types including the conventional weighted linear combination, to the maximum-type combination. The paper focuses on the OWA method as well as an approach for integrating Geographic Information System (GIS) and OWA. OWA has been developed as a generalization of multi-criteria combination. The OWA concept has been extended to the GIS applications as part of a decision support module in GIS. In this study to obtain the criteria weights, comparisons were made by evaluating 22 criteria against each other, therefore we attained comparable data via the technique of Analytical Hierarchy Process (AHP) and five scenarios of OWA method were used. The results of field studies, third scenario for the study area proposed.

GIS-based ordered weighted averaging and Dempster–Shafer methods for landslide susceptibility mapping in the Urmia Lake Basin, Iran

In this paper, GIS-based ordered weighted averaging (OWA) is applied to landslide susceptibility mapping (LSM) for the Urmia Lake Basin in northwest Iran. Nine landslide causal factors were used, whereby the respective parameters were extracted from an associated spatial database. These factors were evaluated, and then the respective factor weight and class weight were assigned to each of the associated factors using analytic hierarchy process (AHP). A landslide susceptibility map was produced based on OWA multicriteria decision analysis. In order to validate the result, the outcome of the OWA method was qualitatively evaluated based on an existing inventory of known landslides. Correspondingly, an uncertainty analysis was carried out using the Dempster–Shafer theory. Based on the results, very strong support was determined for the high susceptibility category of the landslide susceptibility map, while strong support was received for the areas with moderate susceptibility. In this paper, we discuss in which respect these results are useful for an improved understanding of the effectiveness of OWA in LSM, and how the landslide prediction map can be used for spatial planning tasks and for the mitigation of future hazards in the study area.

Choosing the best Twenty20 cricket batsmen using ordered weighted averaging

This paper provides a way to evaluate and choose the best Twenty20 (T20) cricket batsmen using ordered weighted averaging (OWA) operator. The paper suggests an OWA evaluation method for a cricket batsman using multiple attributes related to the player’s performance. A dataset consisting of ten important attributes for 24 T20 Indian Premier League 4 (IPL 4) cricket batsmen is used to choose the best players. Also, a comparison result shows the advantage of using the proposed OWA method. The proposed method in this paper can also be used for evaluation of T20 bowlers in turn in the selection of a T20 cricket team.

Autologistic regression and multicriteria evaluation models for the prediction of forest expansion

Land use changes are complex ecological processes driven by the interaction of biophysical and human related factors. The prediction of forest land use changes is important for sustainable forest management and biodiversity conservation. This study investigates the modelling process of the spatial dynamics of a forest ecosystem in north eastern Greece. For the prediction of forest expansion, based on land use data of the study area, a deterministic approach using logistic regression and heuristic methods of multi-criteria evaluation is adopted. The set of factors driving forest expansion are: the slope, the distance to roads, the distance to urban areas, the distance to forest, the soil depth, the soil erosion and the influence from the land uses of the neighbourhood. The spatial autocorrelation of driving factors is addressed using an autologistic regression model. The multicriteria evaluation approach is developed using weighted linear combination (WLC) and ordered weighted averaging (OWA) methods. In WLC method the relative importance of each factor was estimated using the analytical hierarchy process. In the OWA method, decision strategies are generated using a selection of relative linguistic quantifiers, which allow different Risk in decisions. The accuracy of the models produced was tested with real data for the year 2001 using the ROC validation method. All the methods produced satisfactory results. Autologistic regression showed slightly better performance than multicriteria evaluation methods due to higher degree of objectivity in defining the importance of driving factors for forest expansion.

Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach

In a situation where imprecise attribute weights such as a rank order are captured, various approximate weighting methods have been proposed to aid multiattribute decision analysis. Among others, it is well known that the rank order centroid (ROC) weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights. In this paper, we aim to reinterpret the meaning of the ROC weights and to develop a compatible weighting method that is based on other well-established academic disciplines. The ordered weighted averaging (OWA) method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process. Some interesting semantics can be attached to the approximate weights in view of the measure developed in the OWA method. Furthermore, the weights generated by the maximum entropy method show equally compatible performance with the ROC weights under some condition, which is demonstrated by theoretical and simulation analysis.

Multi-Objective Decision Making for Land Use Planning with Ordered Weighted Averaging Method

Multi-objective decision making is common in environmental engineering management. A compromise solution to the multi-objective problems under conditions of conflicting objectives with GIS-based Ordered Weighted Averaging (OWA) method is investigated. In some instances, decisions may be based on a single criterion, but commonly several criteria are required to define the decision set. Ordered Weighted Averaging (OWA) is a relatively new Multi-Criteria Evaluation (MCE) method. In GIS-based OWA method, both criteria weights and order weights are considered. Calculation method of order weights based on Orness, and construction method of comparison matrix for criteria weights based on analytical hierarchy program (AHP), are introduced; Multi-objective decision making of this method is investigated. As an example, GIS-based OWA method is applied to Tangshan City, and some advice is proposed for engineering design.

Some remarks on the LSOWA approach for obtaining OWA operator weights

One of the key issues in the theory of ordered-weighted averaging (OWA) operators is the determination of their associated weights. To this end, numerous weighting methods have appeared in the literature, with their main difference occurring in the objective function used to determine the weights. A minimax disparity approach for obtaining OWA operator weights is one particular case, which involves the formulation and solution of a linear programming model subject to a given value of orness and the adjacent weight constraints. It is clearly easier for obtaining the OWA operator weights than from previously reported OWA weighting methods. However, this approach still requires solving linear programs by a conventional linear program package. Here, we revisit the least-squared OWA method, which intends to produce spread-out weights as much as possible while strictly satisfying a predefined value of orness, and we show that it is an equivalent of the minimax disparity approach. The proposed solution takes a closed form and thus can be easily used for simple calculations. © 2009 Wiley Periodicals, Inc.