scholarly journals BiOWA for Preference Aggregation with Bipolar Scales: Application to Fair Optimization in Combinatorial Domains

2019 ◽  
Author(s):  
Hugo Martin ◽  
Patrice Perny
Keyword(s):  
Rating Scales ◽  
Optimization Problems ◽  
Multicriteria Decision Making ◽  
Weighted Averaging ◽  
Preference Aggregation ◽  
Ranking Algorithm ◽  
Pareto Optimal Solutions ◽  
Ordered Weighted Averaging ◽  
Numerical Tests ◽  
Gains And Losses

We study the biOWA model for preference aggregation and multicriteria decision making from bipolar rating scales. A biOWA is an ordered doubly weighted averaging extending standard ordered weighted averaging (OWA) and allowing a finer control of the importance attached to positive and negative evaluations in the aggregation. After establishing some useful properties of biOWA to generate balanced Pareto-optimal solutions, we address fair biOWA-optimization problems in combinatorial domains. We first consider the use of biOWA in multi-winner elections for aggregating graded approval and disapproval judgements. Then we consider the use of biOWA for solving robust path problems with costs expressing gains and losses. A linearization of biOWA is proposed, allowing both problems to be solved by MIP. A path-ranking algorithm for biOWA optimization is also proposed. Numerical tests are provided to show the practical efficiency of our models.

scholarly journals Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Akram ◽  
Naveed Yaqoob ◽  
Ghous Ali ◽  
Wathek Chammam
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Electre I ◽  
Geometric Operator

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

scholarly journals Applying Hybrid Decision-Making Method Based on Fuzzy AHP-WOWA Operator for Emergency Alternative Evaluation of Unattended Train Operation Metro System

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Bobo Zhao ◽  
Tao Tang ◽  
Bin Ning
Keyword(s):  
Decision Making ◽  
Fuzzy Ahp ◽  
Multicriteria Decision Making ◽  
Emergency Situation ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Train Operation ◽  
Emergency Decision ◽  
Response Task ◽  
Metro System

Optimal alternative selection to address the emergency situation is critical for dispatcher group in Unattended Train Operation (UTO) to guide emergency process. It is difficult to provide the precise decision value under one criterion and to evaluate the emergency alternatives among multiple dispatchers. This paper presents a hybrid emergency decision-making method integrating fuzzy analytic hierarchy process (FAHP) described by linguistic terms with enhanced weighted ordered weighted averaging (WOWA) operator. The enhanced WOWA operator aggregates the preference matrices of multidispatcher through the constructed emergency response task model of dispatcher group in OCC. This calculation approach takes into consideration the relations of emergency tasks to derive the importance weights of dispatchers and integrates them into the ordered weighted averaging (OWA) operator weights based on a fuzzy membership relation. A case study of applying the method in an emergency of a train fire is given to demonstrate the feasibility and usefulness of the methods associated with the group multicriteria decision-making (GMCDM) theory in emergency management of UTO metro system.

OWA aggregation with dual preferences for basic uncertain information

2021 ◽  
pp. 1-10
Author(s):  
LeSheng Jin ◽  
Ronald R. Yager ◽  
Jana Špirková ◽  
Radko Mesiar ◽  
Daniel Paternain ◽  
...  
Keyword(s):  
Decision Makers ◽  
Input Vector ◽  
Weighted Averaging ◽  
Preference Aggregation ◽  
Uncertain Information ◽  
Interval Vector ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Wide Range ◽  
Original Information

Basic Uncertain Information (BUI) as a newly introduced concept generalized a wide range of uncertain information. The well-known Ordered Weighted Averaging (OWA) operators can flexibly and effectively model bipolar preferences of decision makers over given real valued input vector. However, there are no extant methods for OWA operators to be carried out over given BUI vectors. Against this background, this study firstly discusses the interval transformation for BUI and elaborately explains the reasonability within it. Then, we propose the corresponding preference aggregations for BUI in two different decisional scenarios, the aggregation for BUI vector without original information influencing and the aggregation for BUI vector with original information influencing after interval transformation. For each decisional scenario, we also discuss two different orderings of preference aggregation, namely, interval-vector and vector-interval orderings, respectively. Hence, we will propose four different aggregation procedures of preference aggregation for BUI vector. Some illustrative examples are provided immediately after the corresponding aggregation procedures.

scholarly journals Linguistic Weighted Aggregation under Confidence Levels

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Chonghui Zhang ◽  
Weihua Su ◽  
Shouzhen Zeng ◽  
Linyun Zhang
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
New Approach ◽  
Confidence Levels ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Wide Range ◽  
Information Providers

We develop some new linguistic aggregation operators based on confidence levels. Firstly, we introduce the confidence linguistic weighted averaging (CLWA) operator and the confidence linguistic ordered weighted averaging (CLOWA) operator. These two new linguistic aggregation operators are able to consider the confidence level of the aggregated arguments provided by the information providers. We also study some of their properties. Then, based on the generalized means, we introduce the confidence generalized linguistic ordered weighted averaging (CGLOWA) operator. The main advantage of the CGLOWA operator is that it includes a wide range of special cases such as the CLOWA operator, the confidence linguistic ordered weighted quadratic averaging (CLOWQA) operator, and the confidence linguistic ordered weighted geometric (CLOWG) operator. Finally, we develop an application of the new approach in a multicriteria decision-making under linguistic environment and illustrate it with a numerical example.

THE RELATIONSHIPS BETWEEN TWO VARIABILITY AND ORNESS OPTIMIZATION PROBLEMS FOR OWA OPERATOR WITH RIM QUANTIFIER EXTENSIONS

2010 ◽  
Vol 18 (05) ◽  
pp. 515-538
Author(s):  
XINWANG LIU
Keyword(s):  
Analytical Solution ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Optimal Solutions ◽  
Ordered Weighted Averaging ◽  
Solution Methods ◽  
Points Of View ◽  
Free Dimension

The paper considers the analytical solution methods of the maximizing entropy or minimizing variance with fixed orness level problems and the maximizing orness with fixed entropy or variance value problems together. It proves that both of these two kinds of problems have common necessary conditions for their optimal solutions. The optimal solutions have the same forms and can be seen as the same OWA (ordered weighted averaging) weighting vectors from different points of view. The problems of minimizing orness problems with fixed entropy or variance constraints and their analytical solutions are proposed. Then these conclusions are extended to the corresponding RIM (regular increasing monotone) quantifier problems, which can be seen as the continuous case of OWA problems with free dimension. The analytical optimal solutions are obtained with variational methods.

scholarly journals A Study of OWA Operators Learned in Convolutional Neural Networks

2021 ◽  
Vol 11 (16) ◽  
pp. 7195
Author(s):  
Iris Dominguez-Catena ◽  
Daniel Paternain ◽  
Mikel Galar
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Practical Method ◽  
Local Information ◽  
Weighted Averaging ◽  
Global Information ◽  
Owa Operator ◽  
Owa Operators ◽  
Ordered Weighted Averaging

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this integration, the OWA layer becomes a practical method for the determination of OWA operator weights, which is usually a difficult task that complicates the integration of these operators in other fields. In this paper, we explore the weights learned for the OWA operators inside the OWA layer, characterizing them through their basic properties of orness and dispersion. We also compare them to some families of OWA operators, namely the Binomial OWA operator, the Stancu OWA operator and the exponential RIM OWA operator, finding examples that are currently impossible to generalize through these parameterizations.

Sign in / Sign up

Export Citation Format

Share Document