QUANTALE-VALUED SUP-ALGEBRAS

Based on the notion of Q-sup-lattices (a fuzzy counterpart of com- plete join-semilattices valuated in a commutative quantale), we present the concept of Q-sup-algebras { Q-sup-lattices endowed with a collection of ni- tary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in [30], we characterize their subalgebras and quotients, and fol- lowing [20], we show that the category of Q-sup-algebras is isomorphic to a certain subcategory of a category of Q-modules.