Related Experiment Videos
Some properties of the weighted OWA operator
1School of Economics and Management, Southeast University, Nanjing 210096, China. xwliu@seu.edu.cn
Summary
This study enhances the weighted ordered average (WOWA) operator using regular increasing monotone (RIM) quantifiers for improved decision-making. New parameterized RIM quantifiers ensure aggregation values align with optimism levels, aiding preference representation.
Area of Science:
- Fuzzy Logic and Decision Theory
- Aggregation Operators
- Mathematical Optimization
Background:
- The ordered weighted average (OWA) and weighted OWA (WOWA) operators are foundational in aggregation techniques.
- Quantifier guided aggregation and regular increasing monotone (RIM) quantifiers offer methods for incorporating preference levels.
- Recent advancements include continuous OWA and WOWA operators, expanding applicability.
Purpose of the Study:
- To investigate the properties of the WOWA operator with RIM quantifiers, focusing on orness.
- To propose an improvement on continuous OWA and WOWA operators.
- To develop parameterized RIM quantifiers for the WOWA operator that align aggregation with decision-maker preferences.
Main Methods:
- Extension of WOWA properties from discrete to continuous cases.
- Development of two families of parameterized RIM quantifiers: exponential and piecewise linear generating functions.
- Analysis of aggregation consistency with orness levels.
Main Results:
- Established properties of WOWA operators with RIM quantifiers concerning orness.
- Proposed improved continuous OWA and WOWA operators.
- Introduced parameterized RIM quantifiers that ensure aggregation values reflect specified orness levels.
- Demonstrated that these quantifiers can represent decision-maker preferences for fuzzy sets and random variables.
Conclusions:
- The proposed parameterized RIM quantifiers for WOWA operators provide a robust method for decision analysis.
- These quantifiers effectively bridge the gap between aggregation mechanics and subjective preference levels (orness).
- The framework allows for flexible preference elicitation and consistent aggregation of fuzzy sets or random variables.
Related Concept Videos
00:57Weighted Mean
While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
01:16Properties of the z-Transform II
The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
01:17Properties of the z-Transform I
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
01:17Convolution Properties II
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
01:20Convolution Properties I
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
01:05Properties of the Root Locus
The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on the...
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on the...