Pseudo-BL algebras and pseudo-effect algebras

详细信息    查看全文

• 作者：Xiao-Hong Zhang ; Xue-Shuang Fan
• 关键词：Non-commutative fuzzy logic ; Pseudo-BL algebra ; Pseudo-MV algebra ; Pseudo-effect algebra ; Pseudo-weak MV-effect algebra ; Quantum structures
• 刊名：Fuzzy Sets and Systems
• 出版年：2008
• 出版时间：1 January 2008
• 年：2008
• 卷：159
• 期：1
• 页码：95-106
• 全文大小：210 K

文摘

Pseudo-BL algebras and pseudo-effect algebras arose in two rather different fields: fuzzy logics and quantum logics. In this paper, by introducing the notion of pseudo-weak MV-effect algebra which is non-commutative generalization of weak MV-effect algebra, we investigate the mutual relationship between pseudo-BL algebras and pseudo-effect algebras. We prove that dual pseudo-BL algebra under certain condition can be restricted to a pseudo-weak MV-effect algebra, and a pseudo-weak MV-effect algebra can be extended to dual pseudo-BL algebra under certain condition. Moreover, we give some examples of pseudo-BL algebra which is corresponding to some pseudo-weak MV-effect algebra. Finally, we establish the relationship between pseudo-MV algebras and pseudo-MV effect algebras.