States on Generalization of Fuzzy Structures

Bounded residuated lattice ordered monoids (Rl-monoids) form a large class of bounded residuated lattices which contains important classes of algebras behind fuzzy reasoning (MV-algebras, GMV-algebras, BL-algebras, pseudo BL-algebras) and algebras of the intuitionistic logic (Heyting algebras). States, which are mappings into the real interval [0,1], are analogues of probability measures. The book presents the theory of Bosbach and Riečan states on bounded Rl-monoids.