States on semi-divisible residuated lattices

Authors:
Esko Turunen;Janne Mertanen
Affiliations:
Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland;Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (pp 315-357) "Ordered structures in many-valued logic"
Year:
2007

Citing 0
Cited 7

Semi-divisible t-norms on discrete scales

Fuzzy Sets and Systems
States on semi-divisible generalized residuated lattices reduce to states on MV-algebras

Fuzzy Sets and Systems
States on finite monoidal t-norm based algebras

Information Sciences: an International Journal
Generalized Bosbach and Riečan states based on relative negations in residuated lattices

Fuzzy Sets and Systems
Some types of filters in MTL-algebras

Fuzzy Sets and Systems
On the existence of states on MTL-algebras

Information Sciences: an International Journal
Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices

Archive for Mathematical Logic

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a residuated lattice L, we prove that the subset MV(L) of complement elements x * of L generates an MV-algebra if, and only if L is semi-divisible. Riečan states on a semi-divisible residuated lattice L, and Riečan states on MV(L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states.