Mathematics Behind Fuzzy Logic (Advances in Intelligent and Soft Computing (Closed)) - Softcover

Turunen, Esko

Softcover

ISBN 10: 3790812218 ISBN 13: 9783790812213

Publisher: Physica-Verlag GmbH & Co, 1999

Synopsis

Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook, the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and postgraduated courses. The first chapter starts from such basic concepts as order, lattice, equivalence and residuated lattice. It contains a full section on BL-algebras. Chapter two concerns MV-algebra and its basic properties, while chapter three applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details besides semantics, syntax and completeness of this logic, a lot of examples are given. The fourth chapter shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices.

Edition details

• Publisher: Physica-Verlag GmbH & Co
• Publication date: 1999
• ISBN 10: 3790812218
• ISBN 13: 9783790812213
• Binding: Paperback
• Language: English
• Number of pages: 201