On probabilistic averaging in bounded commutative residuated l-monoids
Hongjun Zhou, Guojun Wang · 2007
Bounded commutative Rℓ-monoids are a generalization of MV-algebras as well as of BL-algebras.With the probability measure on the set of states on bounded commutative ℓ-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 Rℓ-monoid.Then we can define a pseudo-metric on a bounded commutative Rℓ-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.