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E-raamat: Fuzzy Logic in Action: Applications in Epidemiology and Beyond

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Fuzzy Logic in Action: Applications in Epidemiology and Beyond, co-authored by Eduardo Massad, Neli Ortega, Laécio Barros, and Cláudio Struchiner is a remarkable achievement. The book brings a major paradigm shift to medical sciences exploring the use of fuzzy sets in epidemiology and medical diagnosis arena. The volume addresses the most significant topics in the broad areas of epidemiology, mathematical modeling and uncertainty, embodying them within the framework of fuzzy set and dynamic systems theory.





Written by leading contributors to the area of epidemiology, medical informatics and mathematics, the book combines a very lucid and authoritative exposition of the fundamentals of fuzzy sets with an insightful use of the fundamentals in the area of epidemiology and diagnosis. The content is clearly illustrated by numerous illustrative examples and several real world applications. Based on their profound knowledge of epidemiology and mathematical modeling, and on their keen understanding of the role played by uncertainty and fuzzy sets, the authors provide insights into the connections between biological phenomena and dynamic systems as a mean to predict, diagnose, and prescribe actions. An example is the use of Bellman-Zadeh fuzzy decision making approach to develop a vaccination strategy to manage measles epidemics in São Paulo.



The book offers a comprehensive, systematic, fully updated and self- contained treatise of fuzzy sets in epidemiology and diagnosis. Its content covers material of vital interest to students, researchers and practitioners and is suitable both as a textbook and as a reference. The authors present new results of their own in most of the chapters. In doing so, they reflect the trend to view fuzzy sets, probability theory and statistics as an association of complementary and synergetic modeling methodologies.
Introduction
1(10)
Uncertainty versus Precision in Biomedicine and Epidemiology
1(2)
Epidemiological Modeling
3(1)
Mathematical Modeling
4(1)
Fuzzy Logic in Biomedicine and Epidemiology
5(3)
Chapter Descriptions
8(1)
The Authors
9(2)
Basic Concepts of Fuzzy Sets Theory
11(30)
Fuzzy Sets
11(3)
Operations with Fuzzy Sets
14(9)
Triangular Norms and Conorms
20(2)
Cartesian Product
22(1)
Fuzzy Sets and Membership Functions
23(7)
Properties and Characteristics of Fuzzy Sets
27(2)
α - cut or α - level
29(1)
Extension Principle and Fuzzy Numbers
30(7)
Zadeh Extension Principle
30(2)
Fuzzy Numbers
32(2)
Arithmetic Operations on Fuzzy Numbers
34(3)
Fuzzy Relations
37(4)
Composition of Fuzzy Relations
38(3)
Modern Epidemiology
41(18)
Statistical Models in Epidemiology
42(2)
Mathematical Models in Epidemiology
44(13)
The Reproduction of an Infection
44(3)
Analytical Models
47(7)
Computer Simulation Models
54(3)
What Lies in the Future?
57(2)
Probability, Possibility and Fuzzy Events
59(20)
Probability and Fuzzy Measures
60(7)
Probability Measure
60(1)
Fuzzy Measure
61(1)
Possibility Measure
62(4)
Probability/Possibility Transformations Applied to the Prostate Cancer Analysis
66(1)
Fuzzy Integrals
67(7)
The Integral of Choquet
67(1)
The Integral of Sugeno
67(5)
Fuzzy Expected Value Applied to the Accidents of Traffic Analysis, in the Sao Paulo City, Brazil
72(2)
Probability of Fuzzy Events
74(4)
Fuzzy Probabilities of Epidemic Events
76(2)
Final Considerations
78(1)
Fuzzy Logic and Risk Estimators
79(18)
Risk and Common Measures of Association Used in Epidemiology
79(3)
Potential Outcomes
80(2)
Infectious Diseases and Violation of the Stability Assumption
82(3)
Vaccine Efficacy
83(2)
Measures of Association for Non-observable Subsets of the Target Population
85(6)
Randomization and Baseline Transmission
87(4)
Fuzzy Logic and Risk Estimators
91(6)
Fuzzy Conditional Probability
91(1)
Fuzzy Measures of Association
92(5)
Fuzzy Decision Making in Public Health Strategies
97(14)
Designing a Vaccination Strategy
98(4)
The Measles Epidemic in Sao Paulo
102(1)
The Impact of the Vaccination
103(8)
Forecasting and Projection Models
104(1)
The Case of the Measles Epidemic in Sao Paulo
105(6)
Fuzzy Rule-Based Models in Epidemiology
111(40)
Linguistic Variables
112(3)
Fuzzy Rules
115(2)
Inference Procedure in Fuzzy Rule-Based Models
117(5)
Defuzzification Methods
122(3)
Center of Maximum Method
123(1)
Mean of Maximum Method
123(1)
Center of Area Method
124(1)
Some Types of Fuzzy Rule-Based Models
125(8)
The Mamdani Model
126(3)
The Takagi-Sugeno-Kang Model
129(2)
The Standard Additive Model
131(2)
Modeling Health Decisions through Fuzzy Linguistic Systems
133(18)
A Fuzzy Model for HIV Natural History
133(7)
A Fuzzy Model to Estimate the Risk of Neonatal Death
140(5)
A Fuzzy Model to Quality of Life Evaluation
145(6)
Fuzzy Rule-Based Dynamical Models
151(30)
The Fuzzy Rule Dynamic Structure
152(2)
A Model for Canine Rabies Seroprevalence
154(13)
A TSK Model for Canine Rabies
156(5)
A Mamdani Model for Canine Rabies
161(6)
A Fuzzy Dynamical Model for a SIR Epidemic
167(6)
A Fuzzy Linguistic Dynamical Model Based on the Extension Principle
173(8)
Dealing with the Opinions of Experts
174(1)
The Extension Principle Methodology Applied in the Canine Rabies Study
175(6)
Fuzzy Dynamical Systems in Epidemic Modeling
181(26)
Demographic Fuzziness
181(2)
Environmental Fuzziness
183(3)
Epidemiology with Heterogeneity
186(16)
The SI Model
187(9)
The SIS Model
196(6)
Fuzzy Differential Inclusion
202(5)
The SI Fuzzy Model by Fuzzy Differential Inclusion
202(5)
Classical Dynamical Systems with Fuzzy Rule-Based Parameters
207(18)
Fuzzy Modeling in Symptomatic a HIV Infected Population
208(11)
Classical HIV/AIDS Models
208(4)
A Fuzzy Rule-Based Model to Estimate
212(5)
Fuzzy Expectancy of Symptomatic Individuals and Real Data
217(2)
Fuzzy Model to Compute the Life Expectancy of HIV Infected Individuals
219(6)
The Influence of AIDS on the Mortality Rate
220(1)
Average Number and the Life Expectancy of Individuals
221(4)
Fuzzy Reed-Frost Model
225(28)
The Classical Reed-Frost Model
225(2)
The Stochastic Reed-Frost Model
227(12)
The Probabilistic Structure
229(9)
Theoretical Remarks
238(1)
Fuzzy Reed-Frost Model
239(3)
The Possibilistic Structure
240(1)
Theoretical Remarks
241(1)
Simulations
242(7)
Discussion
249(4)
Hybrid Models in Epidemiology
253(24)
A Fuzzy Model for the Estimation of Optimal Age for Vaccination Against Measles
255(14)
A Bayesian Approach to Fuzzy Hypotheses Testing
256(2)
Estimating the Optimal Age to Vaccinate Against Measles
258(5)
A Fuzzy Rule-Based Model
263(5)
Discussion
268(1)
A Fuzzy Model to Study a Predator-Prey Dynamics
269(8)
The Predator-Prey Model
270(1)
Aphids versus Ladybugs
270(1)
Formulation of the Predator-Prey Fuzzy Model
271(2)
Fitting the Holling-Tanner Model
273(3)
Discussion
276(1)
...and Beyond: Fuzzy Logic in Medical Diagnosis
277(34)
The Diagnostic Process
278(1)
Computer Models and Expert Systems for Medical Diagnosis
279(8)
Mathematical Models in Medical Diagnosis
279(5)
The Stanford Certainty Factor Algebra
284(1)
Expert Systems for Medical Diagnosis
284(3)
Fuzzy Diagnostic Systems
287(24)
Fuzzy Relations Diagnostic Models
289(2)
Fuzzy Cluster Analysis Models
291(1)
Smets' Model for Fuzzy Diagnosis
292(2)
Bellamy's State-Space Approach
294(3)
Other Fuzzy Diagnostic Systems
297(9)
Hybrid Diagnostic Systems
306(5)
Final Reflexions
311(2)
References 313(22)
Index 335