Constructing an Outranking Relation with Weighted OWA for Multi-criteria Decision Analysis

We briefly describe the Ordered Weighted Averaging (OWA) operator and discuss a methodology for learning the associated weighting vector from observational data. We then introduce a more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator. These operators take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are then aggregated. A number of different aggregation situations have been shown to be representable in this framework. We then show how this tool can be used to represent different types of aggregation models.

Vector Induced OWA Operators

The classification accuracy of a classifier depends largely on the aggregation operator it uses in fusion of information. This paper presents a similarity classifier that utilizes a weighted ordered weighted averaging (WOWA) operator. The applicability of the WOWA operator for aggregation of similarities is studied and tested with several Regular Increasing Monotonic (RIM) type weight generators. The RIM quantifiers used here are of the basic, polynomial, trigonometric, exponential, and of the logarithmic type. The proposed approach is tested on three real world data sets. Results obtained with the new method are compared with those obtained using two previously presented similarity classifiers. The proposed new classifier shows better performance on the data sets studied, which indicates that benefits can be gained from using a WOWA operator in the aggregation.

Determination of the weights of an ordered weighted averaging (OWA) operator is a vital constituent of the operator's aggregation procedure. Consequently, several weight generation techniques have evolved in the literature. Here, using inverse hypergeometric distribution, we use a novel parametric function to generate the weight vector of an OWA operator. The proposed inverse hypergeometric OWA (InHyp-OWA) operator generates a unique weight vector for every choice of its parameter. Also, using the proposed weight function, OWA weight vectors can be generated without solving any complicated optimization problem. An important property of InHyp-OWA operator is that for a given parameter value, its orness value remains constant, regardless of the number of objectives aggregated. Hence, InHyp-OWA operator is a new member of the family of OWA operators with constant orness. This class of OWA operators can utilize a prejudiced preference to determine the corresponding weight vector. The proposed approach provides a number of advantages over existing weight generating methods for OWA operators. One of the remarkable advantages of the InHyp-OWA operator is the fact that it generates weight vectors with strictly monotonic components. It also generalizes the well-known Borda-Kendall OWA operator.

Ontology matching is an essential operation in many application domains, such as the Semantic Web, ontology merging or integration. So far, quite a few ontology matching approaches or matchers have been proposed. It has been observed that combining the results of multiple matchers is a promising technique to get better results than just using one matcher at a time. Many aggregation operators, such as Max, Min, Average and Weighted, have been developed. The limitations of these operators are studied. To overcome the limitations and provide a semantic interpretation for each aggregation operator, in this paper, we propose a linguistic combination system (LCS), where a linguistic aggregation operator (LAO), based on the ordered weighted averaging (OWA) operator, is used for the aggregation. A weight here is not associated with a specific matcher but a particular ordered position. A large number of LAOs can be developed for different uses, and the existing aggregation operators Max, Min and Average are the special cases in LAOs. For each LAO, there is a corresponding semantic interpretation. The experiments show the strength of our system.KeywordsAggregation OperatorSemantic InterpretationOrdered Weighted AverageOrdered Weighted Average OperatorOntology MatchThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This study proposes a site location assessment model for citrus cropland using multi-criteria evaluation (MCE) and the combination of a set of factors for suitability mapping and delineating the suitable areas for citrus production in Ramsar, Iran. It defines an incorporated method for the suitability mapping of the most appropriate sites for citrus cultivars with an emphasis on the multi-criteria decision analysis (MCDA) process. The combination of geographic information system (GIS) and a modified version of the analytic hierarchy process (AHP) based on the ordered weighted averaging (OWA) technique is also emphasized. The OWA is based on two principles, namely: the weights of relative criterion significance and the order weights. Therefore, the participatory technique was employed to outline the set of standards and the important criterion. The results derived from the GIS–OWA technique indicate that the cultivation of citrus is feasible only in limited areas, which make up 6.7% of the total area near the Caspian Sea. This investigation has shown that the GIS–OWA model can be integrated into MCDA to select the optimal site for citrus production. The present research highlights how multi-criteria in GIS can play a considerable role in decision making for evaluating the suitability of selected sites for citrus production.

Interval numbers multiple attribute decision-making (MADM) is an important branch of uncertainty decision theory, and the decision result largely depends on the selection of the aggregation operator. In this paper, we analyze the ordered weighted average (OWA) operator, which is an averaging aggregation operator. The OWA operator provides an aggregation method between the minimum and maximum operators. Moreover, we further analyze some of extensions about OWA operator, and pay special attention to the Bonferroni means and OWA (BON-OWA) operator. Note that the BON-OWA operator only aggregate the input arguments which are exact numbers. Under normal circumstances, decision makers is difficult to provide a clear evaluation value for attribute and most of them are described by vague information. When the decision information is an interval numbers, the BON-OWA operator cannot describe decision result accurately. Under these environments, we proposed the interval numbers BON-OWA (IBr,q-OWA) operator to deal with the vague decision information in this paper. Then we consider their main properties, such as idempotence, monotonicity, and boundedness and prove them. Besides, a wide range of special aggregation operators are found in changing parameter values, such as the square mean and max operator, and so on. We also compare the ranking method of the interval numbers based on Boolean matrix. As a result, the combination of IBr,q-OWA operator makes the decision result more scientific. Finally, a new approach for decision-making problem is developed based on the IBr,q-OWA operator, which shows the effectiveness in practical examples.

Flood hazard zone mapping incorporating geographic information system (GIS) and multi-criteria analysis (MCA) techniques

In group decision making (GDM), to facilitate an acceptable consensus among the experts from different fields, time and resources are paid for persuading experts to modify their opinions. Thus, consensus costs are important for the GDM process. Notwithstanding, the unit costs in the common linear cost functions are always fixed, yet experts will generally express more resistance if they have to make more compromises. In this study, we use the quadratic cost functions, the marginal costs of which increase with the opinion changes. Aggregation operators are also considered to expand the applications of the consensus methods. Moreover, this paper further analyzes the minimum cost consensus models under the weighted average (WA) operator and the ordered weighted average (OWA) operators, respectively. Corresponding approaches are developed based on strictly convex quadratic programming and some desirable properties are also provided. Finally, some examples and comparative analyses are furnished to illustrate the validity of the proposed models.

Kerman Province in Iran is known as an earthquake prone area, with different serious damages. In this study, GIS-based ordered weight averaging (OWA) with fuzzy quantifier algorithm is used to model earthquake events in north of Kerman Province, Iran. For this aim, at first using attraction model was tried to increase DEM resolution from 30 to 10 m. Then, using the mentioned DEM, three layers such as aspect, slope, and elevation was prepared. Also, different layers including lithology, land use, river, road, fault, and earthquake occurrences were prepared in ArcGIS software. Subsequently, the importance of each factor in earthquake events was defined using trapezoidal membership function. Finally, the earthquake events map with different risk level (six levels) was prepared using OWA method. The results showed that with decreasing risk (no trade-off), many parts of the study area had not earthquake events hazard. While, with increasing risk (no trade-off), all of the study area had earthquake events hazard. Low level of risk and no trade-off had the highest area in the very low class (98%), while high level of risk and average trade-off had the highest area in the very low class (15.62%). So, for the study where has high earthquake should use low level risk maps in order to better management and damage decreasing.

Integrating multi-criteria evaluation techniques with geographic information systems for landfill site selection: A case study using ordered weighted average

A unified model between the weighted average and the induced OWA operator

A fuzzy MCDM approach for personnel selection

Developing effective, fairness-preserving optimization algorithms is of considerable importance in systems which serve many users. In this paper we show the results of the threshold accepting procedure applied to extremely difficult problem of fair resource allocation in wireless mesh networks (WMN). The fairness is modeled by allowing preferences with regard to distribution of Internet traffic between network participants. As aggregation operator we utilize weighted ordered weighted averaging (WOWA). In the underlaying optimization problem, the physical medium properties cause strong interference among simultaneously operating node devices, leading to nonlinearities in the mixed-integer pricing subproblem. That is where the threshold accepting procedure is applied. We show that, the threshold accepting heuristic performs much better than the widely utilized simulated annealing algorithm.

This article introduces the uncertain ordered weighted averaging adequacy coefficient (UOWAAC) operator. This novel operator uses the ordered weighted averaging (OWA) operator, the adequacy coefficient, and the interval numbers in a single formulation. This article also extends the UOWAAC operator by using order-inducing variables in the reordering process of the input arguments. This new extension is called the uncertain induced ordered weighted averaging adequacy coefficient (UIOWAAC) operator. The article also presents an application of the new approach in a multi-criteria group decision making (MCGDM) problem about international expansion. In addition, a comparative analysis is conducted with the purpose of demonstrating the superiority of the UOWAAC and UIOWAAC aggregation operators in specific situations. Likewise, the use of basic uncertain information (BUI) is discussed. The results show the usefulness of these new aggregation operators in real-life decision making problems under uncertainty, particularly when the decision maker wants to compare different alternatives with an ideal but without giving any penalty or reward in the case that the ideal levels are exceeded.