We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a regular congruence relation and a inf-Bosbach state on . By inducing an inf-Bosbach state on the quotient structure / , we show that / 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 / by a reflexive hyper BCK-ideal . Further, we prove that / is a bounded commutative BCK-algebra.
"States and Measures on Hyper BCK-Algebras." J. Appl. Math. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/397265