基于落影理论的MV-代数的刻画
Characterizations of MV-algebras based on the theory of falling shadows.
作者信息
Yang Yongwei, Xin Xiaolong, He Pengfei
机构信息
School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China ; School of Mathematics, Northwest University, Xi'an 710127, China.
School of Mathematics, Northwest University, Xi'an 710127, China.
出版信息
ScientificWorldJournal. 2014;2014:951796. doi: 10.1155/2014/951796. Epub 2014 Aug 28.
Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T ∧-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T ∧-fuzzy (implicative) ideal are provided. Some characterizations of falling fuzzy (implicative) ideals are presented by studying proprieties of them. The product ⊛ and the up product ⊚ operations on falling shadows and the upset of a falling shadow are established, by which T-fuzzy ideals are investigated based on probability spaces.
基于落影理论，在MV - 代数中提出了落影模糊（蕴涵）理想的概念，作为T∧ - 模糊（蕴涵）理想概念的推广。讨论了落影模糊（蕴涵）理想与T - 模糊（蕴涵）理想之间的关系，并给出了落影模糊（蕴涵）理想成为T∧ - 模糊（蕴涵）理想的条件。通过研究落影模糊（蕴涵）理想的性质，给出了它们的一些刻画。建立了落影上的乘积⊛和上积⊚运算以及落影的上集，据此在概率空间上研究了T - 模糊理想。
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