Data Uncertainty and Important Measures.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Simon, Christophe
Otros Autores: Weber, Philippe, Sallak, Mohamed
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : John Wiley & Sons, Incorporated, 2016.
Temas:
Uncertainty (Information theory)
Incertitude (Théorie de l'information)
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Half-Title Page; Title Page; Copyright Page; Contents; Foreword; Acknowledgments; 1. Why and Where Uncertainties; 1.1. Sources and forms of uncertainty; 1.2. Types of uncertainty; 1.3. Sources of uncertainty; 1.4. Conclusion; 2. Models and Language of Uncertainty; 2.1. Introduction; 2.2. Probability theory; 2.2.1. Interpretations; 2.2.2. Fundamental notions; 2.2.3. Discussion; 2.3. Belief functions theory; 2.3.1. Representation of beliefs; 2.3.2. Combination rules; 2.3.3. Extension and marginalization; 2.3.4. Pignistic transformation; 2.3.5. Discussion; 2.4. Fuzzy set theory.
  • 2.4.1. Basic definitions2.4.2. Operations on fuzzy sets; 2.4.3. Fuzzy relations; 2.5. Fuzzy arithmetic; 2.5.1. Fuzzy numbers; 2.5.2. Fuzzy probabilities; 2.5.3. Discussion; 2.6. Possibility theory; 2.6.1. Definitions; 2.6.2. Possibility and necessity measures; 2.6.3. Operations on possibility and necessity measures; 2.7. Random set theory; 2.7.1. Basic definitions; 2.7.2. Expectation of random sets; 2.7.3. Random intervals; 2.7.4. Confidence interval; 2.7.5. Discussion; 2.8. Confidence structures or c-boxes; 2.8.1. Basic notions; 2.8.2. Confidence distributions; 2.8.3. P-boxes and C-boxes.
  • 2.8.4. Discussion2.9. Imprecise probability theory; 2.9.1. Definitions; 2.9.2. Basic properties; 2.9.3. Discussion; 2.10. Conclusion; 3. Risk Graphs and Risk Matrices: Application of Fuzzy Sets and Belief Reasoning; 3.1. SIL allocation scheme; 3.1.1. Safety instrumented systems (SIS); 3.1.2. Conformity to standards ANSI/ISA S84.01-1996 and IEC 61508; 3.1.3. Taxonomy of risk/SIL assessment methods; 3.1.4. Risk assessment; 3.1.5. SIL allocation process; 3.1.6. The use of expertsâ#x80;#x99; opinions; 3.2. SIL allocation based on possibility theory; 3.2.1. Eliciting the expertsâ#x80;#x99; opinions.
  • 3.2.2. Rating scales for parameters3.2.3. Subjective elicitation of the risk parameters; 3.2.4. Calibration of expertsâ#x80;#x99; opinions; 3.2.5. Aggregation of the opinions; 3.3. Fuzzy risk graph; 3.3.1. Input fuzzy partition and fuzzification; 3.3.2. Risk/SIL graph logic by fuzzy inference system; 3.3.3. Output fuzzy partition and defuzzification; 3.3.4. Illustration case; 3.4. Risk/SIL graph: belief functions reasoning; 3.4.1. Elicitation of expert opinions in the belief functions theory; 3.4.2. Aggregation of expert opinions; 3.5. Evidential risk graph; 3.6. Numerical illustration.
  • 3.6.1. Clustering of expertsâ#x80;#x99; opinions3.6.2. Aggregation of preferences; 3.6.3. Evidential risk/SIL graph; 3.7. Conclusion; 4. Dependability Assessment Considering Interval-valued Probabilities; 4.1. Interval arithmetic; 4.1.1. Interval-valued parameters; 4.2. Constraint arithmetic; 4.3. Fuzzy arithmetic; 4.3.1. Application example; 4.3.2. Monte Carlo sampling approach; 4.4. Discussion; 4.4.1. Markov chains; 4.4.2. Multiphase Markov chains; 4.4.3. Markov chains with fuzzy numbers; 4.4.4. Fuzzy modeling of SIS characteristic parameters; 4.5. Illustration; 4.5.1. Epistemic approach.

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