New Probabilistic Model for Pseudo-BCK Algebras and Pseudo-hoops
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.
pseudo-bck algebra pseudo-hoop wajsberg pseudo-hoop generalized bosbach state generalized state-morphism generalized riecan state glivenko property state operator