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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

2.5K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
2.5K
Interval Level of Measurement00:55

Interval Level of Measurement

13.0K
For effective statistical analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

502
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
502
Confidence Intervals01:21

Confidence Intervals

9.3K
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
9.3K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

9.9K
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
9.9K
Types of Limits I01:23

Types of Limits I

299
Limits are a key mathematical concept for understanding how functions behave as their input approaches specific values, particularly when the function is undefined. They help reveal trends and discontinuities by examining the values a function approaches rather than its actual value.One-sided limits focus on the direction from which a value is approached. When a function behaves differently depending on whether the input approaches from the left or the right, the two one-sided limits may not...
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Related Experiment Videos

Simplified interval type-2 fuzzy neural networks.

Yang-Yin Lin, Shih-Hui Liao, Jyh-Yeong Chang

    IEEE Transactions on Neural Networks and Learning Systems
    |May 9, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a self-evolving interval type-2 fuzzy neural network (FNN) that efficiently handles uncertainty. This novel FNN reduces errors and computational complexity compared to existing type-2 FNNs.

    Related Experiment Videos

    Area of Science:

    • Artificial Intelligence
    • Computational Intelligence
    • Machine Learning

    Background:

    • Type-1 fuzzy systems struggle with inherent uncertainties in knowledge bases.
    • Interval type-2 fuzzy sets offer enhanced capability for managing uncertainty.

    Purpose of the Study:

    • To propose a novel self-evolving interval type-2 fuzzy neural network (FNN).
    • To address limitations of type-1 fuzzy systems in handling uncertainty.
    • To improve upon existing type-2 FNNs in terms of accuracy and efficiency.

    Main Methods:

    • Utilizes interval type-2 fuzzy sets in the premise and Takagi-Sugeno-Kang (TSK) type in the consequent.
    • Employs on-line type-2 fuzzy clustering for rule generation from an empty rule-base.
    • Applies a gradient descent algorithm to learn design factors (ql, qr) for adaptive output adjustment.

    Main Results:

    • Achieves fewer test errors compared to other type-2 FNNs.
    • Demonstrates reduced computational complexity.
    • Successfully generates rules and adapts parameters adaptively.

    Conclusions:

    • The proposed self-evolving interval type-2 FNN effectively handles uncertainty.
    • The method offers a more efficient and accurate alternative to existing approaches.
    • This FNN is suitable for various applications requiring robust uncertainty management.