Bounded pseudo-hoops with internal states

Abstract

Abstract State MV-algebras were introduced by Flaminio and Montagna as MV-algebras with internal states. Di Nola and Dvurečenskij presented the notion of state-morphism MV-algebra which is a stronger variation of a state MV-algebra. Rachůnek and Šalounová introduced state GMV-algebras (pseudo-MV algebras) and state-morphism GMV-algebras, while the state BL-algebras and state-morphism BL-algebras were defined by Ciungu, Dvurečenskij and Hyčko. Recently, Dvurečenskij, Rachůnek and Šalounová presented state Rℓ-monoids and state-morphism Rℓ-monoids. In this paper we study these concepts for more general fuzzy structures, namely pseudo-hoops and we present state pseudo-hoops and state-morphism pseudo-hoops.