Ebook: Fundamentals of Fuzzy Sets

Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field.
The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

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Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field.
The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

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Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field.
The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.
Content:
Front Matter....Pages i-xxi
General Introduction....Pages 1-18
Front Matter....Pages 19-19
Fuzzy Sets: History and Basic Notions....Pages 21-124
Fuzzy Set-Theoretic Operators and Quantifiers....Pages 125-193
Measurement of Membership Functions: Theoretical and Empirical Work....Pages 195-227
Front Matter....Pages 231-231
An Introduction to Fuzzy Relations....Pages 233-259
Fuzzy Equivalence Relations: Advanced Material....Pages 261-290
Analytical Solution Methods for Fuzzy Relational Equations....Pages 291-340
Front Matter....Pages 341-341
Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps....Pages 343-438
Measures of Uncertainty and Information....Pages 439-457
Quantifying Different Facets of Fuzzy Uncertainty....Pages 459-480
Front Matter....Pages 481-481
Fuzzy Interval Analysis....Pages 483-581
Metric Topology of Fuzzy Numbers and Fuzzy Analysis....Pages 583-641
Back Matter....Pages 643-647

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Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field.
The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.
Content:
Front Matter....Pages i-xxi
General Introduction....Pages 1-18
Front Matter....Pages 19-19
Fuzzy Sets: History and Basic Notions....Pages 21-124
Fuzzy Set-Theoretic Operators and Quantifiers....Pages 125-193
Measurement of Membership Functions: Theoretical and Empirical Work....Pages 195-227
Front Matter....Pages 231-231
An Introduction to Fuzzy Relations....Pages 233-259
Fuzzy Equivalence Relations: Advanced Material....Pages 261-290
Analytical Solution Methods for Fuzzy Relational Equations....Pages 291-340
Front Matter....Pages 341-341
Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps....Pages 343-438
Measures of Uncertainty and Information....Pages 439-457
Quantifying Different Facets of Fuzzy Uncertainty....Pages 459-480
Front Matter....Pages 481-481
Fuzzy Interval Analysis....Pages 483-581
Metric Topology of Fuzzy Numbers and Fuzzy Analysis....Pages 583-641
Back Matter....Pages 643-647
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