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.

A NOTE ON THE MINIMAL VARIABILITY OWA OPERATOR WEIGHTS

2006 ◽  
Vol 14 (06) ◽  
pp. 747-752 ◽  
Author(s):  
DUG HUN HONG
Keyword(s):  
Second Order ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Weighting Vector ◽  
Sufficiency Conditions

One important issue in the theory of ordered weighted averaging (OWA) operators is the determination of the associated weighting vector. Recently, Fullér and Majlender2 derived the minimal variability weighting vector for any level of orness using the Kuhn-Tucker second-order sufficiency conditions for optimality. In this note, we give a new proof of the problem.

scholarly journals Three Ways of Defining Owa Operator on the Set of All Normal Convex Fuzzy Sets

2017 ◽  
Vol 69 (1) ◽  
pp. 101-118
Author(s):  
Zdenko Takáč
Keyword(s):  
Fuzzy Sets ◽  
Linear Order ◽  
Recent Literature ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Main Obstacle ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Algebraic Properties

Abstract We deal with an extension of ordered weighted averaging (OWA, for short) operators to the set of all normal convex fuzzy sets in [0, 1]. The main obstacle to achieve this goal is the non-existence of a linear order for fuzzy sets. Three ways of dealing with the lack of a linear order on some set and defining OWA operators on the set appeared in the recent literature. We adapt the three approaches for the set of all normal convex fuzzy sets in [0, 1] and study their properties. It is shown that each of the three approaches leads to operator with desired algebraic properties, and two of them are also linear.

scholarly journals The General Least Square Deviation OWA Operator Problem

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 326 ◽  
Author(s):  
Dug Hong ◽  
Sangheon Han
Keyword(s):  
Optimization Problem ◽  
Weight Vector ◽  
Least Square ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Crucial Issue ◽  
Absolute Deviation ◽  
Owa Operators ◽  
Operator Problem

A crucial issue in applying the ordered weighted averaging (OWA) operator for decision making is the determination of the associated weights. This paper proposes a general least convex deviation model for OWA operators which attempts to obtain the desired OWA weight vector under a given orness level to minimize the least convex deviation after monotone convex function transformation of absolute deviation. The model includes the least square deviation (LSD) OWA operators model suggested by Wang, Luo and Liu in Computers & Industrial Engineering, 2007, as a special class. We completely prove this constrained optimization problem analytically. Using this result, we also give solution of LSD model suggested by Wang, Luo and Liu as a function of n and α completely. We reconsider two numerical examples that Wang, Luo and Liu, 2007 and Sang and Liu, Fuzzy Sets and Systems, 2014, showed and consider another different type of the model to illustrate our results.

scholarly journals An approach to obtain the generalized mixed linear stress function for known owa weights with artificial bee colony algorithm

2017 ◽  
Vol 6 (3) ◽  
pp. 150-157
Author(s):  
Efsun Coşkun ◽  
Resmiye Nasiboglu ◽  
Baris Tekin Tezel
Keyword(s):  
Stress Function ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Piecewise Linear ◽  
Decision Function ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Ordered Weighted Averaging ◽  
Bee Colony

Abstract OWA (Ordered Weighted Averaging) is a flexible aggregation operator which is come up with Yager to create a decision function in multi-criteria decision making. It is possible to determine how optimistic or pessimistic the decision maker's opinion with the value obtained from the weights of this operator. The determination of OWA weights cannot provide characterization by itself. If it is desired to aggregate various sized objects in terms of generalization and reusability of OWA weights, a more general form is needed. In this study, we propose the parameterized piecewise linear stress function and the approach to characterize OWA weights. The stress function is expressed by parameters which are obtained by artificial bee colony algorithm. Also the weights are approximately found by using parameters. Keywords – OWA operator, aggregation, artificial bee colony algorithm.

Human Focused Summarizing Statistics Using OWA Operators

2010 ◽  
pp. 238-253
Author(s):  
Ronald R. Yager
Keyword(s):  
Generating Functions ◽  
Large Data ◽  
Large Data Sets ◽  
Weighted Averaging ◽  
Data Sets ◽  
Owa Operator ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Data Analyst ◽  
Computer Aided

The ordered weighted averaging (OWA) operator is introduced and the author discusses how it can provide a basis for generating summarizing statistics over large data sets. The author further notes how different forms of OWA operators, and hence different summarizing statistics, can be induced using weight-generating functions. The author shows how these weight-generating functions can provide a vehicle with which a data analyst can express desired summarizing statistics. Modern data analysis requires the use of more human focused summarizing statistics then those classically used. The author’s goal here is to develop to ideas to enable a human focused approach to summarizing statistics. Using these ideas we can envision a computer aided construction of the weight generating functions based upon a combination of graphical and linguistic specifications provided by a data analyst describing his desired summarization.

scholarly journals A method for decision making with the OWA operator

2012 ◽  
Vol 9 (1) ◽  
pp. 357-380 ◽  
Author(s):  
José Merigó ◽  
Anna Gil-Lafuente
Keyword(s):  
Decision Making ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Minimum Level ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Wide Range ◽  
Decision Making Problem ◽  
Parameterized Family

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

GENERALIZED MOVING AVERAGES, DISTANCE MEASURES AND OWA OPERATORS

2013 ◽  
Vol 21 (04) ◽  
pp. 533-559 ◽  
Author(s):  
JOSÉ M. MERIGÓ ◽  
RONALD R. YAGER
Keyword(s):  
Moving Average ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Wide Range ◽  
Moving Averaging ◽  
Generalized Distance ◽  
Weighted Moving Average

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making.

A Study on the Location Analysis Using Spatial Analysis and Ordered Weighted Averaging Operator Weighting Functions

2008 ◽  
Vol 12 (6) ◽  
pp. 529-536 ◽  
Author(s):  
Se-Woong Oh ◽  
◽  
Gyei-Kark Park ◽  
Jong-Min Park ◽  
Sang-Hyun Suh ◽  
...  
Keyword(s):  
Spatial Analysis ◽  
Spatial Data ◽  
Fuzzy Ahp ◽  
Selection Method ◽  
Total Order ◽  
Weighted Averaging ◽  
Decision Strategy ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Definition Of

In this thesis, we proposed the method combining spatial analysis, selection method of weighting values, aggregating decision strategy. To select a sites proposed for ship anchorage, we analyzed spatial data. Fuzzy AHP was used as selection method of weighting values to incorporate the fuzzy set theory and the basic nature of subjectivity due to ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environments. To obtain the score that corresponds to the best alternative or the ranking of the alternatives, we need to use a total order for the fuzzy numbers involved in the problem. In this paper, we consider a definition of such a total order: the degree of Orness (1, 3/4, 2/3, 1/2, 1/3, 1/4, 0) reflected with the ordered weighted averaging (OWA) operators. A numerical example was given to illustrate the approach.

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