State operators on generalizations of fuzzy structures (Q427916)

Bounded residuated lattice-ordered monoids \(M\) are studied. They contain as special cases pseudo-BL-algebras, pseudo-MV-algebras and, consequently, BL-algebras and MV-algebras. Two types of morphisms \(\sigma : M \rightarrow M\) are considered, so-called state operators and strong state operators, and connections between them. Moreover, states \(\sigma : M \rightarrow [0, 1]\) are studied and a bijection between \(\sigma\)-compatible states on \(M\) and states on \(\sigma (M )\) is discovered.