Symmetric weights for OWA operators prioritizing intermediate values. The EVR-OWA operator.

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.

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

Tatra Mountains Mathematical Publications ◽

10.1515/tmmp-2017-0017 ◽

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.

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The General Least Square Deviation OWA Operator Problem

Mathematics ◽

10.3390/math7040326 ◽

2019 ◽

Vol 7 (4) ◽

pp. 326 ◽

Cited By ~ 3

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.

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On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

Tatra Mountains Mathematical Publications ◽

10.1515/tmmp-2016-0026 ◽

2016 ◽

Vol 66 (1) ◽

pp. 137-149

Author(s):

Zdenko Takáč

Keyword(s):

Fuzzy Sets ◽

Weighted Averaging ◽

Owa Operator ◽

Complete Lattices ◽

Owa Operators ◽

Averaging Operator ◽

16Th World ◽

Starting Point ◽

Algebraic Properties ◽

Ordered Weighted Averaging Operator

Abstract We deal with an ordered weighted averaging operator (OWA operator) on the set of all fuzzy sets. Our starting point is OWA operator on any lattice introduced in Lizasoain, I.-Moreno,C.: OWA operators defined on complete lattices, Fuzzy Sets and Systems 224 (2013), 36-52; Ochoa, G.-Lizasoain, I.- -Paternain, D.-Bustince, H.-Pal, N. R.: Some properties of lattice OWA operators and their importance in image processing, in: Proc. of the 16th World Congress of the Internat. Systems Assoc.-IFSA ’15 and the 9th Conf. of the European Soc. for Fuzzy Logic and Technology-EUSFLAT ’15 (J. M. Alonso et al., eds.), Atlantis Press, Gijón, Spain, 2015, pp. 1261-1265. We focus on a particular case of lattice, namely that of all normal convex fuzzy sets in [0,1], and study algebraic properties and linearity of the proposed OWA operator. It is shown that the operator is an extension of standard OWA operator for real numbers and it possesses similar algebraic properties as standard one, however, it is neither homogeneous nor shift-invariant, i.e., it is not linear in contrast to the standard OWA operator.

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Human Focused Summarizing Statistics Using OWA Operators

Scalable Fuzzy Algorithms for Data Management and Analysis ◽

10.4018/978-1-60566-858-1.ch009 ◽

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.

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PARAMETERIZED 2-TUPLE LINGUISTIC MOST PREFERRED OWA OPERATORS AND THEIR APPLICATION IN DECISION MAKING

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488513500384 ◽

2013 ◽

Vol 21 (06) ◽

pp. 799-819 ◽

Cited By ~ 2

Author(s):

XIUZHI SANG ◽

XINWANG LIU

Keyword(s):

Decision Making ◽

Recommender System ◽

Preference Assessment ◽

Decision Makers ◽

Owa Operator ◽

Maximum Frequency ◽

Preference Information ◽

Preference Relations ◽

Owa Operators ◽

Weighting Vector

The most preferred OWA (MP-OWA) operator is a new method to aggregate preference information with crisp numbers, whose weights are related with the frequency of the most preferred assessment to each criteria. However, people are usually not able to estimate their preference degrees with crisp number, since they have a vague knowledge about the preference assessment. In this paper, we propose a 2-tuple linguistic MP-OWA (LMP-OWA) operator. It is useful because it can be used to make decision with linguistic preference relations, and the weighting vector is not only connected to the maximum frequency of the assessment to the criteria, but also to the assessment values. Meanwhile, we introduce the parameterized 2-tuple LMP-OWA operator and the parameterized 2-tuple LMP-OWA operator with power function, which provide multiple aggregation results for decision makers to select. The paper ends up with an example of decision making with linguistic preference relations in movie recommender system.

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A NOTE ON THE MINIMAL VARIABILITY OWA OPERATOR WEIGHTS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488506004308 ◽

2006 ◽

Vol 14 (06) ◽

pp. 747-752 ◽

Cited By ~ 11

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.

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