Handbook of Mathematical Fuzzy Logic

0372983 - ÚI 2012 RIV GB eng M - Monography Chapter
Horčík, Rostislav
Algebraic Semantics: Semilinear FL-Algebras. Chapter 4.
Handbook of Mathematical Fuzzy Logic. Vol. 1. London: College Publications, 2011 - (Cintula, P.; Hájek, P.; Noguera, C.), s. 283-353. Studies in Logic - Mathematical Logic and Foundations, 37. ISBN 978-1-84890-039-4
R&D Projects: GA ČR GEICC/08/E018; GA ČR GAP202/10/1826
Institutional research plan: CEZ:AV0Z10300504
Keywords : FL-algebra * semilinear FL-algebra * representable FL-algebra * residuated lattice * fuzzy logic
Subject RIV: BA - General Mathematics

The chapter summarizes the most important results in the theory of semilinear FL-algebras which form an equivalent algebraic semantics for most of fuzzy logics studied in the literature. The first part focuses on basic algebraic properties and constructions, e.g. structure theory, axiomatization of the variety of semilinear FL-algebras, or Dedekind-McNeille completion. The second part deals with various completeness properties for varieties of semilinear FL-algebras. The last part presents several results on the structure of the subvariety lattice of the variety of semilinear FL-algebras.
Permanent Link: http://hdl.handle.net/11104/0206166