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Uncertainty and information : foundations of generalized information theory / / George J. Klir
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Autore Klir George J. <1932->
Pubbl/distr/stampa Hoboken, New Jersey : , : Wiley-Interscience, , c2006
Descrizione fisica 1 online resource (519 p.)
Disciplina 003.54
003/.54
Soggetto topico Uncertainty (Information theory)
Fuzzy systems
ISBN 1-280-24298-1
9786610242986
0-470-31574-1
0-471-75557-5
0-471-75556-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Acknowledgments -- 1 Introduction -- 1.1. Uncertainty and Its Significance -- 1.2. Uncertainty-Based Information -- 1.3. Generalized Information Theory -- 1.4. Relevant Terminology and Notation -- 1.5. An Outline of the Book -- Notes -- Exercises -- 2 Classical Possibility-Based Uncertainty Theory -- 2.1. Possibility and Necessity Functions -- 2.2. Hartley Measure of Uncertainty for Finite Sets -- 2.2.1. Simple Derivation of the Hartley Measure -- 2.2.2. Uniqueness of the Hartley Measure -- 2.2.3. Basic Properties of the Hartley Measure -- 2.2.4. Examples -- 2.3. Hartley-Like Measure of Uncertainty for Infinite Sets -- 2.3.1. Definition -- 2.3.2. Required Properties -- 2.3.3. Examples -- Notes -- Exercises -- 3 Classical Probability-Based Uncertainty Theory -- 3.1. Probability Functions -- 3.1.1. Functions on Finite Sets -- 3.1.2. Functions on Infinite Sets -- 3.1.3. Bayes' Theorem -- 3.2. Shannon Measure of Uncertainty for Finite Sets -- 3.2.1. Simple Derivation of the Shannon Entropy -- 3.2.2. Uniqueness of the Shannon Entropy -- 3.2.3. Basic Properties of the Shannon Entropy -- 3.2.4. Examples -- 3.3. Shannon-Like Measure of Uncertainty for Infinite Sets -- Notes -- Exercises -- 4 Generalized Measures and Imprecise Probabilities -- 4.1. Monotone Measures -- 4.2. Choquet Capacities -- 4.2.1. Mbius Representation -- 4.3. Imprecise Probabilities: General Principles -- 4.3.1. Lower and Upper Probabilities -- 4.3.2. Alternating Choquet Capacities -- 4.3.3. Interaction Representation -- 4.3.4. Mbius Representation -- 4.3.5. Joint and Marginal Imprecise Probabilities -- 4.3.6. Conditional Imprecise Probabilities -- 4.3.7. Noninteraction of Imprecise Probabilities -- 4.4. Arguments for Imprecise Probabilities -- 4.5. Choquet Integral -- 4.6. Unifying Features of Imprecise Probabilities -- Notes -- Exercises -- 5 Special Theories of Imprecise Probabilities -- 5.1. An Overview -- 5.2. Graded Possibilities -- 5.2.1. Mbius Representation -- 5.2.2. Ordering of Possibility Profiles.
5.2.3. Joint and Marginal Possibilities -- 5.2.4. Conditional Possibilities -- 5.2.5. Possibilities on Infinite Sets -- 5.2.6. Some Interpretations of Graded Possibilities -- 5.3. Sugeno l-Measures -- 5.3.1. Mbius Representation -- 5.4. Belief and Plausibility Measures -- 5.4.1. Joint and Marginal Bodies of Evidence -- 5.4.2. Rules of Combination -- 5.4.3. Special Classes of Bodies of Evidence -- 5.5. Reachable Interval-Valued Probability Distributions -- 5.5.1. Joint and Marginal Interval-Valued Probability Distributions -- 5.6. Other Types of Monotone Measures -- Notes -- Exercises -- 6 Measures of Uncertainty and Information -- 6.1. General Discussion -- 6.2. Generalized Hartley Measure for Graded Possibilities -- 6.2.1. Joint and Marginal U-Uncertainties -- 6.2.2. Conditional U-Uncertainty -- 6.2.3. Axiomatic Requirements for the U-Uncertainty -- 6.2.4. U-Uncertainty for Infinite Sets -- 6.3. Generalized Hartley Measure in Dempster-Shafer Theory -- 6.3.1. Joint and Marginal Generalized Hartley Measures -- 6.3.2. Monotonicity of the Generalized Hartley Measure -- 6.3.3. Conditional Generalized Hartley Measures -- 6.4. Generalized Hartley Measure for Convex Sets of Probability Distributions -- 6.5. Generalized Shannon Measure in Dempster-Shafer Theory -- 6.6. Aggregate Uncertainty in Dempster-Shafer Theory -- 6.6.1. General Algorithm for Computing the Aggregate Uncertainty -- 6.6.2. Computing the Aggregated Uncertainty in Possibility Theory -- 6.7. Aggregate Uncertainty for Convex Sets of Probability Distributions -- 6.8. Disaggregated Total Uncertainty -- 6.9. Generalized Shannon Entropy -- 6.10. Alternative View of Disaggregated Total Uncertainty -- 6.11. Unifying Features of Uncertainty Measures -- Notes -- Exercises -- 7 Fuzzy Set Theory -- 7.1. An Overview -- 7.2. Basic Concepts of Standard Fuzzy Sets -- 7.3. Operations on Standard Fuzzy Sets -- 7.3.1. Complementation Operations -- 7.3.2. Intersection and Union Operations -- 7.3.3. Combinations of Basic Operations.
7.3.4. Other Operations -- 7.4. Fuzzy Numbers and Intervals -- 7.4.1. Standard Fuzzy Arithmetic -- 7.4.2. Constrained Fuzzy Arithmetic -- 7.5. Fuzzy Relations -- 7.5.1. Projections and Cylindric Extensions -- 7.5.2. Compositions, Joins, and Inverses -- 7.6. Fuzzy Logic -- 7.6.1. Fuzzy Propositions -- 7.6.2. Approximate Reasoning -- 7.7. Fuzzy Systems -- 7.7.1. Granulation -- 7.7.2. Types of Fuzzy Systems -- 7.7.3. Defuzzification -- 7.8. Nonstandard Fuzzy Sets -- 7.9. Constructing Fuzzy Sets and Operations -- Notes -- Exercises -- 8 Fuzzification of Uncertainty Theories -- 8.1. Aspects of Fuzzification -- 8.2. Measures of Fuzziness -- 8.3. Fuzzy-Set Interpretation of Possibility Theory -- 8.4. Probabilities of Fuzzy Events -- 8.5. Fuzzification of Reachable Interval-Valued Probability Distributions -- 8.6. Other Fuzzification Efforts -- Notes -- Exercises -- 9 Methodological Issues -- 9.1. An Overview -- 9.2. Principle of Minimum Uncertainty -- 9.2.1. Simplification Problems -- 9.2.2. Conflict-Resolution Problems -- 9.3. Principle of Maximum Uncertainty -- 9.3.1. Principle of Maximum Entropy -- 9.3.2. Principle of Maximum Nonspecificity -- 9.3.3. Principle of Maximum Uncertainty in GIT -- 9.4. Principle of Requisite Generalization -- 9.5. Principle of Uncertainty Invariance -- 9.5.1. Computationally Simple Approximations -- 9.5.2. Probability-Possibility Transformations -- 9.5.3. Approximations of Belief Functions by Necessity Functions -- 9.5.4. Transformations Between l-Measures and Possibility Measures -- 9.5.5. Approximations of Graded Possibilities by Crisp Possibilities -- Notes -- Exercises -- 10 Conclusions -- 10.1. Summary and Assessment of Results in Generalized Information Theory -- 10.2. Main Issues of Current Interest -- 10.3. Long-Term Research Areas -- 10.4. Significance of GIT -- Notes -- Appendix A Uniqueness of the U-Uncertainty -- Appendix B Uniqueness of Generalized Hartley Measure in the Dempster-Shafer Theory -- Appendix C Correctness of Algorithm 6.1.
Appendix D Proper Range of GeneralizedShannon Entropy -- Appendix E Maximum of GSa in Section 6.9 -- Appendix F Glossary of Key Concepts -- Appendix G Glossary of Symbols -- Bibliography -- Subject Index -- Name Index.
Record Nr. UNINA-9910143425103321
Klir George J. <1932->  
Hoboken, New Jersey : , : Wiley-Interscience, , c2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Autore Klir George J. <1932->
Pubbl/distr/stampa Hoboken, New Jersey : , : Wiley-Interscience, , c2006
Descrizione fisica 1 online resource (519 p.)
Disciplina 003.54
003/.54
Soggetto topico Uncertainty (Information theory)
Fuzzy systems
ISBN 1-280-24298-1
9786610242986
0-470-31574-1
0-471-75557-5
0-471-75556-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Acknowledgments -- 1 Introduction -- 1.1. Uncertainty and Its Significance -- 1.2. Uncertainty-Based Information -- 1.3. Generalized Information Theory -- 1.4. Relevant Terminology and Notation -- 1.5. An Outline of the Book -- Notes -- Exercises -- 2 Classical Possibility-Based Uncertainty Theory -- 2.1. Possibility and Necessity Functions -- 2.2. Hartley Measure of Uncertainty for Finite Sets -- 2.2.1. Simple Derivation of the Hartley Measure -- 2.2.2. Uniqueness of the Hartley Measure -- 2.2.3. Basic Properties of the Hartley Measure -- 2.2.4. Examples -- 2.3. Hartley-Like Measure of Uncertainty for Infinite Sets -- 2.3.1. Definition -- 2.3.2. Required Properties -- 2.3.3. Examples -- Notes -- Exercises -- 3 Classical Probability-Based Uncertainty Theory -- 3.1. Probability Functions -- 3.1.1. Functions on Finite Sets -- 3.1.2. Functions on Infinite Sets -- 3.1.3. Bayes' Theorem -- 3.2. Shannon Measure of Uncertainty for Finite Sets -- 3.2.1. Simple Derivation of the Shannon Entropy -- 3.2.2. Uniqueness of the Shannon Entropy -- 3.2.3. Basic Properties of the Shannon Entropy -- 3.2.4. Examples -- 3.3. Shannon-Like Measure of Uncertainty for Infinite Sets -- Notes -- Exercises -- 4 Generalized Measures and Imprecise Probabilities -- 4.1. Monotone Measures -- 4.2. Choquet Capacities -- 4.2.1. Mbius Representation -- 4.3. Imprecise Probabilities: General Principles -- 4.3.1. Lower and Upper Probabilities -- 4.3.2. Alternating Choquet Capacities -- 4.3.3. Interaction Representation -- 4.3.4. Mbius Representation -- 4.3.5. Joint and Marginal Imprecise Probabilities -- 4.3.6. Conditional Imprecise Probabilities -- 4.3.7. Noninteraction of Imprecise Probabilities -- 4.4. Arguments for Imprecise Probabilities -- 4.5. Choquet Integral -- 4.6. Unifying Features of Imprecise Probabilities -- Notes -- Exercises -- 5 Special Theories of Imprecise Probabilities -- 5.1. An Overview -- 5.2. Graded Possibilities -- 5.2.1. Mbius Representation -- 5.2.2. Ordering of Possibility Profiles.
5.2.3. Joint and Marginal Possibilities -- 5.2.4. Conditional Possibilities -- 5.2.5. Possibilities on Infinite Sets -- 5.2.6. Some Interpretations of Graded Possibilities -- 5.3. Sugeno l-Measures -- 5.3.1. Mbius Representation -- 5.4. Belief and Plausibility Measures -- 5.4.1. Joint and Marginal Bodies of Evidence -- 5.4.2. Rules of Combination -- 5.4.3. Special Classes of Bodies of Evidence -- 5.5. Reachable Interval-Valued Probability Distributions -- 5.5.1. Joint and Marginal Interval-Valued Probability Distributions -- 5.6. Other Types of Monotone Measures -- Notes -- Exercises -- 6 Measures of Uncertainty and Information -- 6.1. General Discussion -- 6.2. Generalized Hartley Measure for Graded Possibilities -- 6.2.1. Joint and Marginal U-Uncertainties -- 6.2.2. Conditional U-Uncertainty -- 6.2.3. Axiomatic Requirements for the U-Uncertainty -- 6.2.4. U-Uncertainty for Infinite Sets -- 6.3. Generalized Hartley Measure in Dempster-Shafer Theory -- 6.3.1. Joint and Marginal Generalized Hartley Measures -- 6.3.2. Monotonicity of the Generalized Hartley Measure -- 6.3.3. Conditional Generalized Hartley Measures -- 6.4. Generalized Hartley Measure for Convex Sets of Probability Distributions -- 6.5. Generalized Shannon Measure in Dempster-Shafer Theory -- 6.6. Aggregate Uncertainty in Dempster-Shafer Theory -- 6.6.1. General Algorithm for Computing the Aggregate Uncertainty -- 6.6.2. Computing the Aggregated Uncertainty in Possibility Theory -- 6.7. Aggregate Uncertainty for Convex Sets of Probability Distributions -- 6.8. Disaggregated Total Uncertainty -- 6.9. Generalized Shannon Entropy -- 6.10. Alternative View of Disaggregated Total Uncertainty -- 6.11. Unifying Features of Uncertainty Measures -- Notes -- Exercises -- 7 Fuzzy Set Theory -- 7.1. An Overview -- 7.2. Basic Concepts of Standard Fuzzy Sets -- 7.3. Operations on Standard Fuzzy Sets -- 7.3.1. Complementation Operations -- 7.3.2. Intersection and Union Operations -- 7.3.3. Combinations of Basic Operations.
7.3.4. Other Operations -- 7.4. Fuzzy Numbers and Intervals -- 7.4.1. Standard Fuzzy Arithmetic -- 7.4.2. Constrained Fuzzy Arithmetic -- 7.5. Fuzzy Relations -- 7.5.1. Projections and Cylindric Extensions -- 7.5.2. Compositions, Joins, and Inverses -- 7.6. Fuzzy Logic -- 7.6.1. Fuzzy Propositions -- 7.6.2. Approximate Reasoning -- 7.7. Fuzzy Systems -- 7.7.1. Granulation -- 7.7.2. Types of Fuzzy Systems -- 7.7.3. Defuzzification -- 7.8. Nonstandard Fuzzy Sets -- 7.9. Constructing Fuzzy Sets and Operations -- Notes -- Exercises -- 8 Fuzzification of Uncertainty Theories -- 8.1. Aspects of Fuzzification -- 8.2. Measures of Fuzziness -- 8.3. Fuzzy-Set Interpretation of Possibility Theory -- 8.4. Probabilities of Fuzzy Events -- 8.5. Fuzzification of Reachable Interval-Valued Probability Distributions -- 8.6. Other Fuzzification Efforts -- Notes -- Exercises -- 9 Methodological Issues -- 9.1. An Overview -- 9.2. Principle of Minimum Uncertainty -- 9.2.1. Simplification Problems -- 9.2.2. Conflict-Resolution Problems -- 9.3. Principle of Maximum Uncertainty -- 9.3.1. Principle of Maximum Entropy -- 9.3.2. Principle of Maximum Nonspecificity -- 9.3.3. Principle of Maximum Uncertainty in GIT -- 9.4. Principle of Requisite Generalization -- 9.5. Principle of Uncertainty Invariance -- 9.5.1. Computationally Simple Approximations -- 9.5.2. Probability-Possibility Transformations -- 9.5.3. Approximations of Belief Functions by Necessity Functions -- 9.5.4. Transformations Between l-Measures and Possibility Measures -- 9.5.5. Approximations of Graded Possibilities by Crisp Possibilities -- Notes -- Exercises -- 10 Conclusions -- 10.1. Summary and Assessment of Results in Generalized Information Theory -- 10.2. Main Issues of Current Interest -- 10.3. Long-Term Research Areas -- 10.4. Significance of GIT -- Notes -- Appendix A Uniqueness of the U-Uncertainty -- Appendix B Uniqueness of Generalized Hartley Measure in the Dempster-Shafer Theory -- Appendix C Correctness of Algorithm 6.1.
Appendix D Proper Range of GeneralizedShannon Entropy -- Appendix E Maximum of GSa in Section 6.9 -- Appendix F Glossary of Key Concepts -- Appendix G Glossary of Symbols -- Bibliography -- Subject Index -- Name Index.
Record Nr. UNISA-996202351503316
Klir George J. <1932->  
Hoboken, New Jersey : , : Wiley-Interscience, , c2006
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Autore Klir George J. <1932->
Pubbl/distr/stampa Hoboken, New Jersey : , : Wiley-Interscience, , c2006
Descrizione fisica 1 online resource (519 p.)
Disciplina 003.54
003/.54
Soggetto topico Uncertainty (Information theory)
Fuzzy systems
ISBN 1-280-24298-1
9786610242986
0-470-31574-1
0-471-75557-5
0-471-75556-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Acknowledgments -- 1 Introduction -- 1.1. Uncertainty and Its Significance -- 1.2. Uncertainty-Based Information -- 1.3. Generalized Information Theory -- 1.4. Relevant Terminology and Notation -- 1.5. An Outline of the Book -- Notes -- Exercises -- 2 Classical Possibility-Based Uncertainty Theory -- 2.1. Possibility and Necessity Functions -- 2.2. Hartley Measure of Uncertainty for Finite Sets -- 2.2.1. Simple Derivation of the Hartley Measure -- 2.2.2. Uniqueness of the Hartley Measure -- 2.2.3. Basic Properties of the Hartley Measure -- 2.2.4. Examples -- 2.3. Hartley-Like Measure of Uncertainty for Infinite Sets -- 2.3.1. Definition -- 2.3.2. Required Properties -- 2.3.3. Examples -- Notes -- Exercises -- 3 Classical Probability-Based Uncertainty Theory -- 3.1. Probability Functions -- 3.1.1. Functions on Finite Sets -- 3.1.2. Functions on Infinite Sets -- 3.1.3. Bayes' Theorem -- 3.2. Shannon Measure of Uncertainty for Finite Sets -- 3.2.1. Simple Derivation of the Shannon Entropy -- 3.2.2. Uniqueness of the Shannon Entropy -- 3.2.3. Basic Properties of the Shannon Entropy -- 3.2.4. Examples -- 3.3. Shannon-Like Measure of Uncertainty for Infinite Sets -- Notes -- Exercises -- 4 Generalized Measures and Imprecise Probabilities -- 4.1. Monotone Measures -- 4.2. Choquet Capacities -- 4.2.1. Mbius Representation -- 4.3. Imprecise Probabilities: General Principles -- 4.3.1. Lower and Upper Probabilities -- 4.3.2. Alternating Choquet Capacities -- 4.3.3. Interaction Representation -- 4.3.4. Mbius Representation -- 4.3.5. Joint and Marginal Imprecise Probabilities -- 4.3.6. Conditional Imprecise Probabilities -- 4.3.7. Noninteraction of Imprecise Probabilities -- 4.4. Arguments for Imprecise Probabilities -- 4.5. Choquet Integral -- 4.6. Unifying Features of Imprecise Probabilities -- Notes -- Exercises -- 5 Special Theories of Imprecise Probabilities -- 5.1. An Overview -- 5.2. Graded Possibilities -- 5.2.1. Mbius Representation -- 5.2.2. Ordering of Possibility Profiles.
5.2.3. Joint and Marginal Possibilities -- 5.2.4. Conditional Possibilities -- 5.2.5. Possibilities on Infinite Sets -- 5.2.6. Some Interpretations of Graded Possibilities -- 5.3. Sugeno l-Measures -- 5.3.1. Mbius Representation -- 5.4. Belief and Plausibility Measures -- 5.4.1. Joint and Marginal Bodies of Evidence -- 5.4.2. Rules of Combination -- 5.4.3. Special Classes of Bodies of Evidence -- 5.5. Reachable Interval-Valued Probability Distributions -- 5.5.1. Joint and Marginal Interval-Valued Probability Distributions -- 5.6. Other Types of Monotone Measures -- Notes -- Exercises -- 6 Measures of Uncertainty and Information -- 6.1. General Discussion -- 6.2. Generalized Hartley Measure for Graded Possibilities -- 6.2.1. Joint and Marginal U-Uncertainties -- 6.2.2. Conditional U-Uncertainty -- 6.2.3. Axiomatic Requirements for the U-Uncertainty -- 6.2.4. U-Uncertainty for Infinite Sets -- 6.3. Generalized Hartley Measure in Dempster-Shafer Theory -- 6.3.1. Joint and Marginal Generalized Hartley Measures -- 6.3.2. Monotonicity of the Generalized Hartley Measure -- 6.3.3. Conditional Generalized Hartley Measures -- 6.4. Generalized Hartley Measure for Convex Sets of Probability Distributions -- 6.5. Generalized Shannon Measure in Dempster-Shafer Theory -- 6.6. Aggregate Uncertainty in Dempster-Shafer Theory -- 6.6.1. General Algorithm for Computing the Aggregate Uncertainty -- 6.6.2. Computing the Aggregated Uncertainty in Possibility Theory -- 6.7. Aggregate Uncertainty for Convex Sets of Probability Distributions -- 6.8. Disaggregated Total Uncertainty -- 6.9. Generalized Shannon Entropy -- 6.10. Alternative View of Disaggregated Total Uncertainty -- 6.11. Unifying Features of Uncertainty Measures -- Notes -- Exercises -- 7 Fuzzy Set Theory -- 7.1. An Overview -- 7.2. Basic Concepts of Standard Fuzzy Sets -- 7.3. Operations on Standard Fuzzy Sets -- 7.3.1. Complementation Operations -- 7.3.2. Intersection and Union Operations -- 7.3.3. Combinations of Basic Operations.
7.3.4. Other Operations -- 7.4. Fuzzy Numbers and Intervals -- 7.4.1. Standard Fuzzy Arithmetic -- 7.4.2. Constrained Fuzzy Arithmetic -- 7.5. Fuzzy Relations -- 7.5.1. Projections and Cylindric Extensions -- 7.5.2. Compositions, Joins, and Inverses -- 7.6. Fuzzy Logic -- 7.6.1. Fuzzy Propositions -- 7.6.2. Approximate Reasoning -- 7.7. Fuzzy Systems -- 7.7.1. Granulation -- 7.7.2. Types of Fuzzy Systems -- 7.7.3. Defuzzification -- 7.8. Nonstandard Fuzzy Sets -- 7.9. Constructing Fuzzy Sets and Operations -- Notes -- Exercises -- 8 Fuzzification of Uncertainty Theories -- 8.1. Aspects of Fuzzification -- 8.2. Measures of Fuzziness -- 8.3. Fuzzy-Set Interpretation of Possibility Theory -- 8.4. Probabilities of Fuzzy Events -- 8.5. Fuzzification of Reachable Interval-Valued Probability Distributions -- 8.6. Other Fuzzification Efforts -- Notes -- Exercises -- 9 Methodological Issues -- 9.1. An Overview -- 9.2. Principle of Minimum Uncertainty -- 9.2.1. Simplification Problems -- 9.2.2. Conflict-Resolution Problems -- 9.3. Principle of Maximum Uncertainty -- 9.3.1. Principle of Maximum Entropy -- 9.3.2. Principle of Maximum Nonspecificity -- 9.3.3. Principle of Maximum Uncertainty in GIT -- 9.4. Principle of Requisite Generalization -- 9.5. Principle of Uncertainty Invariance -- 9.5.1. Computationally Simple Approximations -- 9.5.2. Probability-Possibility Transformations -- 9.5.3. Approximations of Belief Functions by Necessity Functions -- 9.5.4. Transformations Between l-Measures and Possibility Measures -- 9.5.5. Approximations of Graded Possibilities by Crisp Possibilities -- Notes -- Exercises -- 10 Conclusions -- 10.1. Summary and Assessment of Results in Generalized Information Theory -- 10.2. Main Issues of Current Interest -- 10.3. Long-Term Research Areas -- 10.4. Significance of GIT -- Notes -- Appendix A Uniqueness of the U-Uncertainty -- Appendix B Uniqueness of Generalized Hartley Measure in the Dempster-Shafer Theory -- Appendix C Correctness of Algorithm 6.1.
Appendix D Proper Range of GeneralizedShannon Entropy -- Appendix E Maximum of GSa in Section 6.9 -- Appendix F Glossary of Key Concepts -- Appendix G Glossary of Symbols -- Bibliography -- Subject Index -- Name Index.
Record Nr. UNINA-9910830850103321
Klir George J. <1932->  
Hoboken, New Jersey : , : Wiley-Interscience, , c2006
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Uncertainty and information : foundations of generalized information theory / / George J. Klir
Autore Klir George J. <1932->
Pubbl/distr/stampa Hoboken, N.J., : Wiley-Interscience, c2006
Descrizione fisica 1 online resource (519 p.)
Disciplina 003/.54
Soggetto topico Uncertainty (Information theory)
Fuzzy systems
ISBN 1-280-24298-1
9786610242986
0-470-31574-1
0-471-75557-5
0-471-75556-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Acknowledgments -- 1 Introduction -- 1.1. Uncertainty and Its Significance -- 1.2. Uncertainty-Based Information -- 1.3. Generalized Information Theory -- 1.4. Relevant Terminology and Notation -- 1.5. An Outline of the Book -- Notes -- Exercises -- 2 Classical Possibility-Based Uncertainty Theory -- 2.1. Possibility and Necessity Functions -- 2.2. Hartley Measure of Uncertainty for Finite Sets -- 2.2.1. Simple Derivation of the Hartley Measure -- 2.2.2. Uniqueness of the Hartley Measure -- 2.2.3. Basic Properties of the Hartley Measure -- 2.2.4. Examples -- 2.3. Hartley-Like Measure of Uncertainty for Infinite Sets -- 2.3.1. Definition -- 2.3.2. Required Properties -- 2.3.3. Examples -- Notes -- Exercises -- 3 Classical Probability-Based Uncertainty Theory -- 3.1. Probability Functions -- 3.1.1. Functions on Finite Sets -- 3.1.2. Functions on Infinite Sets -- 3.1.3. Bayes' Theorem -- 3.2. Shannon Measure of Uncertainty for Finite Sets -- 3.2.1. Simple Derivation of the Shannon Entropy -- 3.2.2. Uniqueness of the Shannon Entropy -- 3.2.3. Basic Properties of the Shannon Entropy -- 3.2.4. Examples -- 3.3. Shannon-Like Measure of Uncertainty for Infinite Sets -- Notes -- Exercises -- 4 Generalized Measures and Imprecise Probabilities -- 4.1. Monotone Measures -- 4.2. Choquet Capacities -- 4.2.1. Mbius Representation -- 4.3. Imprecise Probabilities: General Principles -- 4.3.1. Lower and Upper Probabilities -- 4.3.2. Alternating Choquet Capacities -- 4.3.3. Interaction Representation -- 4.3.4. Mbius Representation -- 4.3.5. Joint and Marginal Imprecise Probabilities -- 4.3.6. Conditional Imprecise Probabilities -- 4.3.7. Noninteraction of Imprecise Probabilities -- 4.4. Arguments for Imprecise Probabilities -- 4.5. Choquet Integral -- 4.6. Unifying Features of Imprecise Probabilities -- Notes -- Exercises -- 5 Special Theories of Imprecise Probabilities -- 5.1. An Overview -- 5.2. Graded Possibilities -- 5.2.1. Mbius Representation -- 5.2.2. Ordering of Possibility Profiles.
5.2.3. Joint and Marginal Possibilities -- 5.2.4. Conditional Possibilities -- 5.2.5. Possibilities on Infinite Sets -- 5.2.6. Some Interpretations of Graded Possibilities -- 5.3. Sugeno l-Measures -- 5.3.1. Mbius Representation -- 5.4. Belief and Plausibility Measures -- 5.4.1. Joint and Marginal Bodies of Evidence -- 5.4.2. Rules of Combination -- 5.4.3. Special Classes of Bodies of Evidence -- 5.5. Reachable Interval-Valued Probability Distributions -- 5.5.1. Joint and Marginal Interval-Valued Probability Distributions -- 5.6. Other Types of Monotone Measures -- Notes -- Exercises -- 6 Measures of Uncertainty and Information -- 6.1. General Discussion -- 6.2. Generalized Hartley Measure for Graded Possibilities -- 6.2.1. Joint and Marginal U-Uncertainties -- 6.2.2. Conditional U-Uncertainty -- 6.2.3. Axiomatic Requirements for the U-Uncertainty -- 6.2.4. U-Uncertainty for Infinite Sets -- 6.3. Generalized Hartley Measure in Dempster-Shafer Theory -- 6.3.1. Joint and Marginal Generalized Hartley Measures -- 6.3.2. Monotonicity of the Generalized Hartley Measure -- 6.3.3. Conditional Generalized Hartley Measures -- 6.4. Generalized Hartley Measure for Convex Sets of Probability Distributions -- 6.5. Generalized Shannon Measure in Dempster-Shafer Theory -- 6.6. Aggregate Uncertainty in Dempster-Shafer Theory -- 6.6.1. General Algorithm for Computing the Aggregate Uncertainty -- 6.6.2. Computing the Aggregated Uncertainty in Possibility Theory -- 6.7. Aggregate Uncertainty for Convex Sets of Probability Distributions -- 6.8. Disaggregated Total Uncertainty -- 6.9. Generalized Shannon Entropy -- 6.10. Alternative View of Disaggregated Total Uncertainty -- 6.11. Unifying Features of Uncertainty Measures -- Notes -- Exercises -- 7 Fuzzy Set Theory -- 7.1. An Overview -- 7.2. Basic Concepts of Standard Fuzzy Sets -- 7.3. Operations on Standard Fuzzy Sets -- 7.3.1. Complementation Operations -- 7.3.2. Intersection and Union Operations -- 7.3.3. Combinations of Basic Operations.
7.3.4. Other Operations -- 7.4. Fuzzy Numbers and Intervals -- 7.4.1. Standard Fuzzy Arithmetic -- 7.4.2. Constrained Fuzzy Arithmetic -- 7.5. Fuzzy Relations -- 7.5.1. Projections and Cylindric Extensions -- 7.5.2. Compositions, Joins, and Inverses -- 7.6. Fuzzy Logic -- 7.6.1. Fuzzy Propositions -- 7.6.2. Approximate Reasoning -- 7.7. Fuzzy Systems -- 7.7.1. Granulation -- 7.7.2. Types of Fuzzy Systems -- 7.7.3. Defuzzification -- 7.8. Nonstandard Fuzzy Sets -- 7.9. Constructing Fuzzy Sets and Operations -- Notes -- Exercises -- 8 Fuzzification of Uncertainty Theories -- 8.1. Aspects of Fuzzification -- 8.2. Measures of Fuzziness -- 8.3. Fuzzy-Set Interpretation of Possibility Theory -- 8.4. Probabilities of Fuzzy Events -- 8.5. Fuzzification of Reachable Interval-Valued Probability Distributions -- 8.6. Other Fuzzification Efforts -- Notes -- Exercises -- 9 Methodological Issues -- 9.1. An Overview -- 9.2. Principle of Minimum Uncertainty -- 9.2.1. Simplification Problems -- 9.2.2. Conflict-Resolution Problems -- 9.3. Principle of Maximum Uncertainty -- 9.3.1. Principle of Maximum Entropy -- 9.3.2. Principle of Maximum Nonspecificity -- 9.3.3. Principle of Maximum Uncertainty in GIT -- 9.4. Principle of Requisite Generalization -- 9.5. Principle of Uncertainty Invariance -- 9.5.1. Computationally Simple Approximations -- 9.5.2. Probability-Possibility Transformations -- 9.5.3. Approximations of Belief Functions by Necessity Functions -- 9.5.4. Transformations Between l-Measures and Possibility Measures -- 9.5.5. Approximations of Graded Possibilities by Crisp Possibilities -- Notes -- Exercises -- 10 Conclusions -- 10.1. Summary and Assessment of Results in Generalized Information Theory -- 10.2. Main Issues of Current Interest -- 10.3. Long-Term Research Areas -- 10.4. Significance of GIT -- Notes -- Appendix A Uniqueness of the U-Uncertainty -- Appendix B Uniqueness of Generalized Hartley Measure in the Dempster-Shafer Theory -- Appendix C Correctness of Algorithm 6.1.
Appendix D Proper Range of GeneralizedShannon Entropy -- Appendix E Maximum of GSa in Section 6.9 -- Appendix F Glossary of Key Concepts -- Appendix G Glossary of Symbols -- Bibliography -- Subject Index -- Name Index.
Record Nr. UNINA-9910877790403321
Klir George J. <1932->  
Hoboken, N.J., : Wiley-Interscience, c2006
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