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 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 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.

scholarly journals On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

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.

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 The General Model for Least Convex Disparity RIM Quantifier Problems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 576
Author(s):  
Dug Hun Hong
Keyword(s):  
Least Squares ◽  
General Model ◽  
Least Square ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Ordered Weighted Averaging ◽  
Full Solution

Hong (Mathematics 2019, 7, 326) recently introduced the general least squares deviation (LSD) model for ordered weighted averaging (OWA) operator weights. In this paper, we propose the corresponding generalized least square disparity model for regular increasing monotone (RIM) quantifier determination under a given orness level. We prove this problem mathematically. Using this result, we provide the full solution of the least square disparity RIM quantifier model as an illustrative example.

Inverse problem of Mueller polarimetry for metrological applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tatiana Novikova ◽  
Pavel Bulkin
Keyword(s):  
Inverse Problem ◽  
Nonlinear Problem ◽  
Optimization Problem ◽  
Global Minimum ◽  
Mueller Matrix ◽  
Least Square ◽  
Marquardt Algorithm ◽  
Geometrical Features ◽  
Levenberg Marquardt

Abstract Inverse problem of Mueller polarimetry is defined as a determination of geometrical features of the metrological structures (i.e. 1D diffraction gratings) from its experimental Mueller polarimetric signature. This nonlinear problem was considered as an optimization problem in a multi-parametric space using the least square criterion and the Levenberg–Marquardt algorithm. We demonstrated that solving optimization problem with the experimental Mueller matrix spectra taken in conical diffraction configuration helps finding a global minimum and results in smaller variance values of reconstructed dimensions of the grating profile.

Multi-Criteria Decision Making Analysis Based on Target-Oriented OWA Operator

2020 ◽  
Vol 28 (06) ◽  
pp. 911-938
Author(s):  
Meimei Xia
Keyword(s):  
Decision Making ◽  
Decision Analysis ◽  
Weight Vector ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Owa Operator ◽  
Ordered Weighted Averaging ◽  
The Impact

The target-oriented multi-criteria decision making is investigated based on the ordered weighted averaging (OWA) operator. The criteria evaluations are measured by using the likelihood of satisfying the targets of criteria. To aggregate the target-oriented criteria evaluations, the target-oriented OWA operator is firstly introduced, in which the target-oriented criteria evaluations are reordered and then aggregated by using the weight vector associated with the position of criteria evaluations. Four types of targets about criteria evaluations and four types of attitudinal characters about criteria weight vector are introduced, based on which, models are given to identify the potential best alternative(s), and estimate the ranges of attitudinal characters about criteria weight vector for each potential best alternative. The proposed models can not only analyze the sensitivity of each potential best alternative, but also can explore the impact of targets about criteria evaluations and attitudinal characters about criteria weight vector on the decision results. Models are further established to find the best and worst ranking orders of each alternative based on targets about criteria evaluations, and give decision analysis by considering specific ranking orders of alternatives. The proposed method considers the targets about criteria evaluations and attitudinal character about criteria weight vector at the same time and can provide decision makers more choices. Several examples are given to illustrate the proposed methods.

Least-square refinement of structure parameters from CBED integrated intensities: application to determination of temperature factors in Y BA2CU3O7

1992 ◽  
Vol 50 (2) ◽  
pp. 1456-1457
Author(s):  
Kjersti Gjønnes ◽  
Jon Gjønnes
Keyword(s):  
Least Square ◽  
Measured Intensity ◽  
Structure Information ◽  
Accurate Temperature ◽  
Least Square Fit ◽  
Case Application ◽  
Integrated Intensities ◽  
Temperature Factors ◽  
Narrow Bands

Electron diffraction intensities can be obtained at large scattering angles (sinθ/λ ≥ 2.0), and thus structure information can be collected in regions of reciprocal space that are not accessable with other diffraction methods. LACBED intensities in this range can be utilized for determination of accurate temperature factors or for refinement of coordinates. Such high index reflections can usually be treated kinematically or as a pertubed two-beam case. Application to Y Ba2Cu3O7 shows that a least square refinememt based on integrated intensities can determine temperature factors or coordinates.LACBED patterns taken in the (00l) systematic row show an easily recognisable pattern of narrow bands from reflections in the range 15 < l < 40 (figure 1). Integrated intensities obtained from measured intensity profiles after subtraction of inelastic background (figure 2) were used in the least square fit for determination of temperature factors and refinement of z-coordinates for the Ba- and Cu-atoms.

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