BN.com Gift Guide

Towards Efficient Fuzzy Information Processing: Using the Principle of Information Diffusion / Edition 1

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $139.51
Usually ships in 1-2 business days
(Save 26%)
Other sellers (Paperback)
  • All (5) from $139.51   
  • New (4) from $139.51   
  • Used (1) from $220.74   

Overview

The need for developing a better understanding of the behaviour of small samples by observing experiments presents a problem far beyond purely academic interest. This monograph describes the character of incomplete fuzzy information, and proposes and proves the principle of information diffusion. The focus lies in changing a traditional sample-point into a fuzzy set to partly fill the gap caused by incomplete data, so that the recognition of relationships between input and output can be improved. Part 1 examines the origins of the principle of information diffusion and describes the mathematical concepts and proofs. Topics covered include: information matrix, demonstration of information distribution, and the kernel function in terms of information diffusion. Part 2 covers applications such as earthquake engineering and risk assessment of flood, and demonstrates that the new theory is useful for studying practical cases.

Read More Show Less

Product Details

  • ISBN-13: 9783790825114
  • Publisher: Physica-Verlag HD
  • Publication date: 12/15/2010
  • Series: Studies in Fuzziness and Soft Computing Series , #99
  • Edition description: Softcover reprint of hardcover 1st ed. 2002
  • Edition number: 1
  • Pages: 370
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.81 (d)

Table of Contents

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 Rc 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 Rf.- 4.8.3 Max-min inference for Rm.- 4.8.4 Total-falling-shadow inference for Rc.- 4.9 Conclusion and Discussion.- References.- Appendix 4.A: Linear Distribution Program.- Appendix 4.B: Intensity Scale.- 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— 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— 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.- 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.- 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.- List of Special Symbols.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)