scientific article

zbMath1141.06005MaRDI QIDQ3421448

Anatolij Dvurečenskij, Jiří Rachůnek

Publication date: 13 February 2007

Full work available at URL: https://eudml.org/doc/32069

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zbMATH Keywords

Bosbach stateRiečan statebounded \(\roman {R}\ell \)-monoidpseudo \(\roman {BL}\)-algebra

Mathematics Subject Classification ID

MV-algebras (06D35) Ordered semigroups and monoids (06F05)

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States on quantum and algebraic structures and their integral representation ⋮ States on semi-divisible generalized residuated lattices reduce to states on MV-algebras ⋮ Generalized Bosbach states. I ⋮ Unnamed Item ⋮ Relationships between generalized Bosbach states and \(L\)-filters on residuated lattices ⋮ Generalized Bosbach states. II ⋮ How Do $$\ell $$-Groups and Po-Groups Appear in Algebraic and Quantum Structures? ⋮ Measures, states and de Finetti maps on pseudo-BCK algebras ⋮ An algebraic generalization of the notion of tribe ⋮ State operators on generalizations of fuzzy structures ⋮ Interior and closure operators on bounded residuated lattices ⋮ State hoops ⋮ Results in L-algebras ⋮ Generalized state operators on residuated lattices ⋮ Algebraic study to generalized Bosbach states on residuated lattices ⋮ States, state operators and quasi-pseudo-MV algebras ⋮ New types of generalized Bosbach states on non-commutative residuated lattices ⋮ States on finite monoidal t-norm based algebras ⋮ Aglianò-Montagna type decomposition of linear pseudo hoops and its applications ⋮ Involutive filters of pseudo-hoops ⋮ On the relationships between hybrid generalized Bosbach states and \(L\)-filters in non-commutative residuated lattices ⋮ Algebras on subintervals of pseudo-hoops ⋮ On residuated lattices with left and right internal state ⋮ Unnamed Item

Cites Work

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• Bosbach states on fuzzy structures
• Averaging the truth-value in Łukasiewicz logic
• Probabilistic averaging in bounded \(R\ell\)-monoids
• Cancellative residuated lattices
• Probabilistic averaging in bounded commutative residuated \(\ell\)-monoids
• Good and bad infinitesimals, and states on pseudo MV-algebras
• Some classes of pseudo-BL algebras
• Algebraic Analysis of Many Valued Logics
• A non-commutative generalization of MV-algebras
• Pseudo MV-algebras are intervals in ℓ-groups

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