Towards Efficient Fuzzy Information Processing: Using the Principle of Information Diffusion - Softcover

Huang, Chongfu; Shi, Yong

Softcover

ISBN 10: 3662003163 ISBN 13: 9783662003169

Verlag: Physica, 2014

Inhaltsangabe

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 Re

Details zur Ausgabe

• Verlag: Physica
• Erscheinungsdatum: 2014
• ISBN 10: 3662003163
• ISBN 13: 9783662003169
• Einband: Paperback
• Sprache: Englisch
• Kontakt zum Hersteller: Nicht verfügbar