Name
Abstract | ||
|---|---|---|
Bosbach and Rieă驴an states on residuated lattices both are generalizations of probability measures on Boolean algebras. Just from the observation that both of them can be defined by using the canonical structure of the standard MV-algebra on the unit interval [0, 1], generalized Rieă驴an states and two types of generalized Bosbach states on residuated lattices were recently introduced by Georgescu and Mure驴an through replacing the standard MV-algebra with arbitrary residuated lattices as codomains. In the present paper, the Glivenko theorem is first extended to residuated lattices with a nucleus, which gives several necessary and sufficient conditions for the underlying nucleus to be a residuated lattice homomorphism. Then it is proved that every generalized Bosbach state (of type I, or of type II) compatible with the nucleus on a nucleus-based-Glivenko residuated lattice is uniquely determined by its restriction on the nucleus image of the underlying residuated lattice, and every relatively generalized Rieă驴an state compatible with the double relative negation on an arbitrary residuated lattice is uniquely determined by its restriction on the double relative negation image of the residuated lattice. Our results indicate that many-valued probability theory compatible with nuclei on residuated lattices reduces in essence to probability theory on algebras of fixpoints of the underlying nuclei. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s00153-013-0338-7 | Arch. Math. Log. |
Keywords | Field | DocType |
arbitrary residuated lattice,generalized bosbach,residuated lattice homomorphism,generalized bosbach state,residuated lattice,underlying nucleus,generalized rie,underlying residuated lattice,nucleus-based-glivenko residuated lattice,nucleus image,standard mv-algebra,nucleus | Discrete mathematics,Residuated lattice,Combinatorics,Negation,Lattice (order),Generalization,Probability measure,Unit interval,Homomorphism,Probability theory,Mathematics | Journal |
Volume | Issue | ISSN |
52 | 7-8 | 1432-0665 |
Citations | PageRank | References |
6 | 0.41 | 20 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bin Zhao | 1 | 42 | 3.92 |
| Hongjun Zhou | 2 | 101 | 10.08 |