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 post-graduated courses.
Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 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. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices.
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-7908-1221-3 (9783790812213)
Schweitzer Klassifikation
Residuated Lattices: Lattices and Equivalence Relations; Lattice Filters; Residuated Lattices ; BL-Algebras; Exercises.- MV-Algebras: MV-Algebras and Wajsberg Algebras; Complete MV-Algebras; Pseudo-Boolean Algebras; Exercises.- Fuzzy Propositional Logic: Semantics of Fuzzy Propositional Logic; Exercises.- Fuzzy Relations: Solvability of Fuzzy Relation Equations; On Fuzzy Similiarity Relations; Fuzzy Similiarity and Approximate Reasoning; Maximal Similiarity and Fuzzy Reasoning; Exercises.- Solutions to Exercises.
