Enumerative combinatorics
Bosbach states on fuzzy structures
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Every Linear Pseudo BL-Algebra Admits a State
Soft Computing - A Fusion of Foundations, Methodologies and Applications
On fuzzy filters of pseudo BL-algebras
Fuzzy Sets and Systems
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If A is a bounded R@?-monoid or a pseudo-BL algebra, then it was proved that a subinterval [a,b] of A can be endowed with a structure of an algebra of the same kind as A. Similar results were obtained if A is a residuated lattice and a,b belong to the Boolean center of A. Given a bounded pseudo-hoop A, in this paper we will give conditions for a,b@?A for the subinterval [a,b] of A to be endowed with a structure of a pseudo-hoop. We will introduce the notions of Bosbach and Riecan states on a pseudo-hoop, we study their properties and we prove that any Bosbach state on a good pseudo-hoop is a Riecan state. For the case of a bounded Wajsberg pseudo-hoop we prove that the two states coincide. We also study the restrictions of Bosbach states on subinterval algebras of a pseudo-hoop.