WMV-Algebra and Its Wajsberg´s form

BL-algebras are basic logic algebras from which logic algebras based on continuous t-norms can be derived, but BL-algebras do not contain the well-known NM-algebras that have been proposed by professor F.Esteva and L.Godo. In the present paper a new kind of logic algebra, WMV-algebra, is introduced that contains both the BL-algebras and NM-algebras. Firstly, WBL-algebra is proposed by adding to MTL-algebra weak Divisibility. Then WMV-algebra is proposed by adding to WBL-algebra Regularness. Secondly, The connections among the members of family of MTL-algebras that we concern with are investigated. Thirdly, weak Wajsberg´s algebra is proposed, and it is proved that weak Wajsberg´s algebra is an equivalent form of WMV-algebra.