On probabilistic averaging in bounded commutative residuated l-monoids

DOI

10.2991/iske.2007.14How to use a DOI?

Keywords

Non-classical Logics; Bounded commutative commutative residuated l-monoids;State; State-morphism; MV-algebras;BL-algebras; Probability measure; Satisfiability degree; BCRl-metric space

Abstract

Bounded commutative R`-monoids are a generalization of MV-algebras as well as of BLalgebras.With the probability measure on the set of states on bounded commutative `-monoids, we introduce the satisfiability degrees of propositions as their average truth degrees. If we consider the probability measure only on the set of state-morphisms, the concept of satisfiability degrees will naturally induce a similarity degree between two propositions of any bounded commutative R`-monoid. Then we can define a pseudometric on a bounded commutative R`-monoid and study the properties of such a metric space. Our result is an algebraic counterpart as well as a generalization of the integrated semantics for fuzzy logic.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Hongjun Zhou
AU  - Guojun Wang
PY  - 2007/10
DA  - 2007/10
TI  - On probabilistic averaging in bounded commutative residuated l-monoids
BT  - Proceedings of the 2007 International Conference on Intelligent Systems and Knowledge Engineering (ISKE 2007)
PB  - Atlantis Press
SP  - 72
EP  - 79
SN  - 1951-6851
UR  - https://doi.org/10.2991/iske.2007.14
DO  - 10.2991/iske.2007.14
ID  - Zhou2007/10
ER  -