Towards Efficient Fuzzy Information Processing Using the Principle of Information Diffusion 1st Edition by Chongfu Huang ISBN 9783790825114 3790825115
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ISBN 10: 3790825115
ISBN 13: 9783790825114
Author: Chongfu Huang
When we learn from books or daily experience, we make associations and draw inferences on the basis of information that is insufficient for under- standing. One example of insufficient information may be a small sample derived from observing experiments. With this perspective, the need for de- veloping a better understanding of the behavior of a small sample presents a problem that is far beyond purely academic importance. During the past 15 years considerable progress has been achieved in the study of this issue in China. One distinguished result is the principle of in- formation diffusion. According to this principle, it is possible to partly fill gaps caused by incomplete information by changing crisp observations into fuzzy sets so that one can improve the recognition of relationships between input and output. The principle of information diffusion has been proven suc- cessful for the estimation of a probability density function. Many successful applications reflect the advantages of this new approach. It also supports an argument that fuzzy set theory can be used not only in “soft” science where some subjective adjustment is necessary, but also in “hard” science where all data are recorded.
Table of contents:
Part I: Principle of Information Diffusion
1. Introduction
1.1 Information Sciences
1.2 Fuzzy Information
1.2.1 Some basic notions of fuzzy set theory
1.2.2 Fuzzy information defined by fuzzy entropy
1.2.3 Traditional fuzzy information without reference to entropy
1.2.4 Fuzzy information due to an incomplete data set
1.2.5 Fuzzy information and its properties
1.2.6 Fuzzy information processing
1.3 Fuzzy function approximation
1.4 Summary
Referencess
2. Information Matrix
2.1 Small-Sample Problem
2.2 Information Matrix
2.3 Information Matrix on Crisp Intervals
2.4 Information Matrix on Fuzzy Intervals
2.5 Mechanism of Information Matrix
2.6 Some Approaches Describing or Producing Relationships
2.6.1 Equations of mathematical physics
2.6.2 Regression
2.6.3 Neural networks
2.6.4 Fuzzy graphs
2.7 Conclusion and Discussion
References
Appendix 2.A: Some Earthquake Data
3. Some Concepts From Probability and Statistics
3.1 Introduction
3.2 Probability
3.2.1 Sample spaces, outcomes, and events
3.2.2 Probability
3.2.3 Joint, marginal, and conditional probabilities
3.2.4 Random variables
3.2.5 Expectation value, variance, functions of random variables
3.2.6 Continuous random variables
3.2.7 Probability density function
3.2.8 Cumulative distribution function
3.3 Some Probability Density Functions
3.3.1 Uniform distribution
3.3.2 Normal distribution
3.3.3 Exponential distribution
3.3.4 Lognormal distribution
3.4 Statistics and Some Traditional Estimation Methods
3.4.1 Statistics
3.4.2 Maximum likelihood estimate
3.4.3 Histogram
3.4.4 Kernel method
3.5 Monte Carlo Methods
3.5.1 Pseudo-random numbers
3.5.2 Uniform random numbers
3.5.3 Normal random numbers
3.5.4 Exponential random numbers
3.5.5 Lognormal random numbers
References
4. Information Distribution
4.1 Introduction
4.2 Definition of Information Distribution
4.3 1-Dimension Linear Information Distribution
4.4 Demonstration of Benefit for Probability Estimation
4.4.1 Model description
4.4.2 Normal experiment
4.4.3 Exponential experiment
4.4.4 Lognormal experiment
4.4.5 Comparison with maximum likelihood estimate
4.4.6 Results
4.5 Non-Linear Distribution
4.6 r-Dimension Distribution
4.7 Fuzzy Relation Matrix from Information Distribution
4.7.1 Rf based on fuzzy concepts
4.7.2 Rm based on fuzzy implication theory
4.7.3 Re based on conditional falling shadow
4.8 Approximate Inference Based on Information Distribution
4.8.1 Max-min inference for Rf
4.8.2 Similarity inference for R
4.8.3 Max-min inference for Rm
4.8.4 Total-falling-shadow inference for Re
4.9 Conclusion and Discussion
5. Information Diffusion
5.1 Problems in Information Distribution
5.2 Definition of Incomplete-Data Set
5.2.1 Incompleteness
5.2.2 Correct-data set
5.2.3 Incomplete-data set
5.3 Fuzziness of a Given Sample
5.3.1 Fuzziness in terms of fuzzy sets
5.3.2 Fuzziness in terms of philosophy
5.3.3 Fuzziness of an incomplete sample
5.4 Information Diffusion
5.5 Random Sets and Covering Theory
5.5.1 Fuzzy logic and possibility theory
5.5.2 Random sets
5.5.3 Covering function
5.5.4 Set-valuedization of observation
5.6 Principle of Information Diffusion
5.6.1 Associated characteristic function and relationships
5.6.2 Allocation function
5.6.3 Diffusion estimate
5.6.4 Principle of Information Diffusion
5.7 Estimating Probability by Information Diffusion
5.7.1 Asymptotically unbiased property
5.7.2 Mean squared consistent property
5.7.3 Asymptotically property of mean square error
5.7.4 Empirical distribution function, histogram and diffusion estimate
5.8 Conclusion and Discussion
References
6. Quadratic Diffusion
6.1 Optimal Diffusion Function
6.2 Choosing A Based on Kernel Theory
6.2.1 Mean integrated square error
6.2.2 References to a standard distribution
6.2.3 Least-squares cross-validation
6.2.4 Discussion
6.3 Searching for A by Golden Section Method
6.4 Comparison with Other Estimates
6.5 Conclusion
References
7. Normal Diffusion
7.1 Introduction
7.2 Molecule Diffusion Theory
7.2.1 Diffusion
7.2.2 Diffusion equation
7.3 Information Diffusion Equation
7.3.1 Similarities of molecule diffusion and information diffusion
7.3.2 Partial differential equation of information diffusion
7.4 Nearby Criteria of Normal Diffusion
7.5 The 0.618 Algorithm for Getting h
7.6 Average Distance Model
7.7 Conclusion and Discussion
References
Part II: Applications
8. Estimation of Epicentral Intensity
8.1 Introduction
8.2 Classical Methods
8.2.1 Linear regression
8.2.2 Fuzzy inference based on normal assumption
8.3 Self-Study Discrete Regression
8.3.1 Discrete regression
8.3.2 r-dimension diffusion
8.3.3 Self-study discrete regression
8.4 Linear Distribution Self-Study
Contents
8.5 Normal Diffusion Self-Study
8.6 Conclusion and Discussion
References
Appendix 8.A: Real and Estimated Epicentral Intensities
Appendix 8.B: Program of NDSS
9. Estimation of Isoseismal Area
9.1 Introduction
9.2 Some Methods for Constructing Fuzzy Relationships
9.2.1 Fuzzy relation and fuzzy relationship
9.2.2 Multivalued logical-implication operator
9.2.3 Fuzzy associative memories
9.2.4 Self-study discrete regression
9.3 Multitude Relationships Given by Information Diffusion
9.4 Patterns Smoothening
9.5 Learning Relationships by BP Neural Networks
9.6 Calculation
9.7 Conclusion and Discussion
References
10. Fuzzy Risk Analysis
10.1 Introduction
10.2 Risk Recognition and Management for Environment, Health, and Safety
10.3 A Survey of Fuzzy Risk Analysis
10.4 Risk Essence and Fuzzy Risk
10.5 Some Classical Models
10.5.1 Histogram
10.5.2 Maximum likelihood method
10.5.3 Kernel estimation
10.6 Model of Risk Assessment by Diffusion Estimate
10.7 Application in Risk Assessment of Flood Disaster
10.7.1 Normalized normal-diffusion estimate
10.7.2 Histogram estimate
10.7.3 Soft histogram estimate
10.7.4 Maximum likelihood estimate
10.7.5 Gaussian kernel estimate
10.7.6 Comparison
10.8 Conclusion and Discussion
References
11. System Analytic Model for Natural Disasters
11.1 Classical System Model for Risk Assessment of Natural Disasters
11.1.1 Risk assessment of hazard
11.1.2 From magnitude to site intensity
11.1.3 Damage risk
11.1.4 Loss risk
11.2 Fuzzy Model for Hazard Analysis
11.2.1 Calculating primary information distribution
11.2.2 Calculating exceeding frequency distribution
11.2.3 Calculating fuzzy relationship between magnitude and probability
11.3 Fuzzy Systems Analytic Model
11.3.1 Fuzzy attenuation relationship
11.3.2 Fuzzy dose-response relationship
11.3.3 Fuzzy loss risk
11.4 Application in Risk Assessment of Earthquake Disaster
11.4.1 Fuzzy relationship between magnitude and probability
11.4.2 Intensity risk
11.4.3 Earthquake damage risk
11.4.4 Earthquake loss risk
11.5 Conclusion and Discussion
References
12. Fuzzy Risk Calculation
12.1 Introduction
12.1.1 Fuzziness and probability
12.1.2 Possibility-probability distribution
12.2 Interior-outer-set Model
12.2.1 Model description
12.2.2 Calculation case
12.2.3 Algorithm and Fortran program
12.3 Ranking Alternatives Based on a PPD
12.3.1 Classical model of ranking alternatives
12.3.2 Fuzzy expected value
12.3.3 Center of gravity of a fuzzy expected value
12.3.4 Ranking alternatives by FEV
12.4 Application in Risk Management of Flood Disaster
12.4.1 Outline of Huarong county
12.4.2 PPD of flood in Huarong county
12.4.3 Benefit-output functions of farming alternatives
12.4.4 Ranking farming alternative based on the PPD
12.4.5 Comparing with the traditional probability method
12.5 Conclusion and Discussion
References
Appendix 12.A: Algorithm Program for Interior-outer-set Model
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Tags: Chongfu Huang, Towards Efficient, Fuzzy Information, the Principle