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States and Measures on Hyper BCK-Algebras
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-13
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Xin, Xiao Long& Wang, Pu. 2014. States and Measures on Hyper BCK-Algebras. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-468919
Modern Language Association (MLA)
Xin, Xiao Long& Wang, Pu. States and Measures on Hyper BCK-Algebras. Journal of Applied Mathematics No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-468919
American Medical Association (AMA)
Xin, Xiao Long& Wang, Pu. States and Measures on Hyper BCK-Algebras. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-468919
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468919