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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.
List of contents
General Introduction.- I Fuzzy Sets: From Basic Concepts to Applications.- II The Role of Fuzzy Sets in Information Engineering.- III Conclusion: The Legitimacy of Fuzzy Sets.- References.- I Fuzzy Sets.- 1 Fuzzy Sets: History and Basic Notions.- 2 Fuzzy Set-Theoretic Operators and Quantifiers.- 3 Measurement of Membership Functions: Theoretical and Empirical Work.- II Fuzzy Relations.- 4 An Introduction to Fuzzy Relations.- 5 Fuzzy Equivalence Relations: Advanced Material.- 6 Analytical Solution Methods for Fuzzy Relational Equations.- III Uncertainty.- 7 Possibility Theory, Probability and Fuzzy Sets: Misunderstandings, Bridges and Gaps.- 8 Measures of Uncertainty and Information.- 9 Quantifying Different Facets of Fuzzy Uncertainty.- IV Fuzzy Sets on the Real Line.- 10 Fuzzy Interval Analysis.- 11 Metric Topology of Fuzzy Numbers and Fuzzy Analysis.
