Probabilistic averaging in bounded commutative residuated \(\ell\)-monoids

DOI10.1016/j.disc.2005.12.024zbMath1105.06011OpenAlexW2036118857MaRDI QIDQ2497469

Anatolij Dvurečenskij, Jiří Rachůnek

Publication date: 4 August 2006

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2005.12.024

zbMATH Keywords

MV-algebraBL-algebraBosbach stateextremal statemaximal filterbounded commutative Rl-monoid

Mathematics Subject Classification ID

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

Related Items (29)

Characterizations and new subclasses of \(\mathcal{I}\)-filters in residuated lattices ⋮ The prime state ideal theorem in state residuated lattices ⋮ States on semi-divisible generalized residuated lattices reduce to states on MV-algebras ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Extended filters in bounded commutative \(Rl\)-monoids ⋮ Unnamed Item ⋮ Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices ⋮ Measures, states and de Finetti maps on pseudo-BCK algebras ⋮ Stone-like representation theorems and three-valued filters in \(R_{0}\)- algebras (nilpotent minimum algebras) ⋮ On state pseudo-hoops ⋮ Generalized Bosbach and Riečan states based on relative negations in residuated lattices ⋮ States and internal states on semihoops ⋮ Interior and closure operators on bounded residuated lattices ⋮ A note on some filters in residuated lattices ⋮ States on \(R_{0}\) algebras ⋮ Generalized state operators on residuated lattices ⋮ Unnamed Item ⋮ States, state operators and quasi-pseudo-MV algebras ⋮ Modal operators on bounded commutative residuated ℓ-monoids ⋮ States on finite monoidal t-norm based algebras ⋮ Ideals and involutive filters in generalizations of fuzzy structures ⋮ Effectible residuated lattices and \(n\)-th roots ⋮ Aglianò-Montagna type decomposition of linear pseudo hoops and its applications ⋮ On state pseudo-hoops ⋮ Direct product decompositions of bounded commutative residuated ℓ-monoids ⋮ Perfect residuated lattice ordered monoids ⋮ Algebras on subintervals of pseudo-hoops ⋮ Unnamed Item

Cites Work

• Bosbach states on fuzzy structures
• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Metamathematics of fuzzy logic
• Varieties of BL-algebras. I: General properties.
• Algebraic foundations of many-valued reasoning
• Averaging the truth-value in Łukasiewicz logic
• Dually residuated lattice ordered semigroups
• Dually residuated lattice ordered semigroups. III
• Algebraic Analysis of Many Valued Logics
• Negation in bounded commutative DRℓ-monoids
• DRl-semigroups and MV-algebras
• MV-algebras are categorically equivalent to a class of $\scr{DR}l\sb {1(i)}$-semigroups
• States on pseudo MV-algebras
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