In this paper we enlarge the language of MV-algebras by a unary operation σ equationally described so as to preserve the basic properties of a state in its original meaning. The resulting class of algebras will be called MV-algebras with internal state (or SMV-algebras for short). After discussing some basic algebraic properties of SMV-algebras, we apply them to the study of the coherence problem for rational assessments on many-valued events. Then we propose an algebraic treatment of the Lebesgue integral and we show that internal states defined on a divisible MVΔ-algebra can be represented by means of this more general notion of integral. © 2008 Elsevier Inc. All rights reserved.
Flaminio, T., Montagna, F. (2009). MV-algebras with internal states and probabilistic fuzzy logic. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 50(1), 138-152 [10.1016/j.ijar.2008.07.006].
MV-algebras with internal states and probabilistic fuzzy logic
MONTAGNA F.
2009-01-01
Abstract
In this paper we enlarge the language of MV-algebras by a unary operation σ equationally described so as to preserve the basic properties of a state in its original meaning. The resulting class of algebras will be called MV-algebras with internal state (or SMV-algebras for short). After discussing some basic algebraic properties of SMV-algebras, we apply them to the study of the coherence problem for rational assessments on many-valued events. Then we propose an algebraic treatment of the Lebesgue integral and we show that internal states defined on a divisible MVΔ-algebra can be represented by means of this more general notion of integral. © 2008 Elsevier Inc. All rights reserved.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/7167
Attenzione
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo