New Probabilistic Model for Pseudo-BCK Algebras and Pseudo-hoops
Lavinia Corina Ciungu and Jan Kuhr
The notion of state is an analogue to probability measure and its basic idea is an averaging of events of a given algebraic structure. States on multiple-valued logic algebras proved to be the most suitable models for averaging the truth-value in their corresponding logics. They have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0, 1]. For the case of bounded residuated lattices, the states were generalized as functions with values in a bounded residuated lattice. In this paper we extend the generalized states for the cases of bounded pseudo-BCK algebras, involutive pseudo-BCK algebras and bounded pseudo-hoops.
Keywords: Pseudo-BCK algebra, pseudo-hoop, Wajsberg pseudo-hoop, generalized Bosbach state, generalized state-morphism, generalized Rieˇcan state, Glivenko property, state operator