semiring valued fuzzy sets, semiring valued fuzzy relations, rough semiring valued fuzzy relations

Many of the new fuzzy structures with value sets in complete $MV$-algebras, such as hesitant, intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into one common type of fuzzy sets with values in special semirings. This transformation of fuzzy structures is then used to unify the various specific methods used in these new fuzzy structures, such as special fuzzy relations, fuzzy approximation, or fuzzy rough sets. The unification of these methods uses the existence of monads defined by special semirings.