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New probabilistic model for pseudo-BCK algebras and pseudo-hoops. (English) Zbl 1393.06021
Summary: 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.

MSC:
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
03G25 Other algebras related to logic
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