States and Measures on Hyper BCK-Algebras
We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra (H,∘,0,e) and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a ∘-compatibled regular congruence relation θ and a θ-compatib...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/397265 |
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| author | Xiao-Long Xin Pu Wang |
| author_facet | Xiao-Long Xin Pu Wang |
| author_sort | Xiao-Long Xin |
| collection | DOAJ |
| description | We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra (H,∘,0,e) and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a ∘-compatibled regular congruence relation θ and a θ-compatibled inf-Bosbach state s on (H,∘,0,e). By inducing an inf-Bosbach state s^ on the quotient structure H/[0]θ, we show that H/[0]θ is a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebra H/Ker(m) by a reflexive hyper BCK-ideal Ker(m). Further, we prove that H/Ker(m) is a bounded commutative BCK-algebra. |
| format | Article |
| id | doaj-art-12d27cee8d7b4e588f21a912efb0f497 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-12d27cee8d7b4e588f21a912efb0f4972025-02-03T05:59:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/397265397265States and Measures on Hyper BCK-AlgebrasXiao-Long Xin0Pu Wang1Department of Mathematics, Northwest University, Xi'an 710069, ChinaDepartment of Mathematics, Northwest University, Xi'an 710069, ChinaWe define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra (H,∘,0,e) and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a ∘-compatibled regular congruence relation θ and a θ-compatibled inf-Bosbach state s on (H,∘,0,e). By inducing an inf-Bosbach state s^ on the quotient structure H/[0]θ, we show that H/[0]θ is a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebra H/Ker(m) by a reflexive hyper BCK-ideal Ker(m). Further, we prove that H/Ker(m) is a bounded commutative BCK-algebra.http://dx.doi.org/10.1155/2014/397265 |
| spellingShingle | Xiao-Long Xin Pu Wang States and Measures on Hyper BCK-Algebras Journal of Applied Mathematics |
| title | States and Measures on Hyper BCK-Algebras |
| title_full | States and Measures on Hyper BCK-Algebras |
| title_fullStr | States and Measures on Hyper BCK-Algebras |
| title_full_unstemmed | States and Measures on Hyper BCK-Algebras |
| title_short | States and Measures on Hyper BCK-Algebras |
| title_sort | states and measures on hyper bck algebras |
| url | http://dx.doi.org/10.1155/2014/397265 |
| work_keys_str_mv | AT xiaolongxin statesandmeasuresonhyperbckalgebras AT puwang statesandmeasuresonhyperbckalgebras |