BZMV\(^{\text{dM}}\) algebras and Stonian MV-algebras (applications to fuzzy sets and rough approximations) (Q1965297)

This paper proposes, as the logic of fuzzy sets, de Morgan BZMV-algebras, which are both MV-algebras and distributive de Morgan BZ-lattices. The set of all closed elements with respect to the Brouwerian orthocomplementation in such a logic is shown to be a Boolean algebra. Two modal operators representing sharp approximations from the top and the bottom can be introduced by means of Kleene and Brouwerian orthocomplementations. The equivalence of de Morgan BZMV-algebras and Stonian MV-algebras is established.