Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables

A single constrained ordered weighted averaging aggregation (COWA) problem is of considerable importance in many disciplines. Two models are considered: the maximization COWA problem with lower bounded variables and the minimization COWA problem with upper bounded variables. For a three-dimensional case of these models, we present the explicitly optimal solutions theoretically and empirically. The bounds and weights can affect the optimal solution(x1',x2',x3') of the three-dimensional COWA problem with bounded variables.

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A Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Lower Bounded Variables

Symmetry ◽

10.3390/sym10080339 ◽

2018 ◽

Vol 10 (8) ◽

pp. 339

Author(s):

Yi-Fang Chen ◽

Hui-Chin Tang

Keyword(s):

Lower Bounds ◽

Three Dimensional ◽

Optimal Solution ◽

Weighted Averaging ◽

Ordered Weighted Averaging ◽

Single Constraint ◽

Bounded Variables ◽

Aggregation Problem

We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution(x1',x2',x3') depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution(x1',x2',x3') types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables.

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

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488510006684 ◽

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.

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A Study of OWA Operators Learned in Convolutional Neural Networks

Applied Sciences ◽

10.3390/app11167195 ◽

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.

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Temporal concatenation for Markov decision processes

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964821000206 ◽

2021 ◽

pp. 1-28

Author(s):

Ruiyang Song ◽

Kuang Xu

Keyword(s):

Markov Decision Processes ◽

Large Scale ◽

Optimal Solution ◽

Upper Bounds ◽

Black Box ◽

Decision Processes ◽

Optimal Solutions ◽

Wide Range ◽

Markov Decision ◽

Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

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Effects of 3D Printing-Line Directions for Stretchable Sensor Performances

Materials ◽

10.3390/ma14071791 ◽

2021 ◽

Vol 14 (7) ◽

pp. 1791

Author(s):

Chi Cuong Vu ◽

Thanh Tai Nguyen ◽

Sangun Kim ◽

Jooyong Kim

Keyword(s):

3D Printing ◽

Thermoplastic Polyurethane ◽

Three Dimensional ◽

Optimal Solution ◽

Human Motion ◽

Repeated Measurements ◽

Fused Filament Fabrication ◽

And Performance ◽

The Times ◽

Stretchable Sensors

Health monitoring sensors that are attached to clothing are a new trend of the times, especially stretchable sensors for human motion measurements or biological markers. However, price, durability, and performance always are major problems to be addressed and three-dimensional (3D) printing combined with conductive flexible materials (thermoplastic polyurethane) can be an optimal solution. Herein, we evaluate the effects of 3D printing-line directions (45°, 90°, 180°) on the sensor performances. Using fused filament fabrication (FDM) technology, the sensors are created with different print styles for specific purposes. We also discuss some main issues of the stretch sensors from Carbon Nanotube/Thermoplastic Polyurethane (CNT/TPU) and FDM. Our sensor achieves outstanding stability (10,000 cycles) and reliability, which are verified through repeated measurements. Its capability is demonstrated in a real application when detecting finger motion by a sensor-integrated into gloves. This paper is expected to bring contribution to the development of flexible conductive materials—based on 3D printing.

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